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Fantasy Pieces






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Oxford University Press

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Copyright © 1999 Oxford University Press

Published by Oxford University Press, Inc.198 Madison Avenue, New York, New York 10016

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All rights reserved. No part of this publication may be reproduced,stored in a retrieval system, or transmitted, in any fo rm or by any means,

electronic, mechanical, photocopying, recording, or otherwise,without the prior permission of Oxford University Press.

Library of Congress Cataloging-in-Publication DataKrebs, Harald, 1955-

Fantcisy pieces : metrical dissonance in the music of Robert Schumann / Harald Krebs.p. cm.

Includes bibliographical references and index.ISBN 0-19-511623-2

1. Schumann, Robert, 181 0-1856 —Criticism and interpretation.2. Musical meter and rhythm. I. Title.

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Tor Sharon

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In this book I investigate the pathology of musical meter — the manifold disrup-tive and distortive conditions that affect what we generally call "the meter" of amusical work. I have drawn most of my musical case studies from the works ofRobert Schumann, which are particularly rich in "pathological" metrical states.I could just as well have based the book on the music of Beethoven, Brahms, orother composers (and I have included several analyses that demonstrate the oc-currence of metrical conflict in -works by composers other than Schumann). Itseemed to me, however, that Schumann's music in general and his metrical struc-tures in particular had been neglected in the music theory literature. Further-more, I have always been fascinated by Schumann's music and personality, and•was eager to spend some years in his company. I have not regretted my decisionto do so; I have grown even more fond of his music, and even more intrigued byhis personality.

I had begun to write this book as a "normal" academic study -when my col-league, pianist Bruce Vogt, suggested that it would be appropriate to includesome Schumannesque dialogues. His specific idea was that I should invent a newDavid&bund consisting of prominent twentieth-century rhythmic theorists, whowould scintillatingly discuss issues relating to metrical conflict. Appealing thoughthis idea was, I found myself reluctant to take the liberty of putting words intothe mouths of living individuals. I decided instead to write a summary of nine-teenth-century theories of metrical conflict in the form of a dialogue betweenFlorestan, Eusebius, and various others, which became the first part of chapter 1.I then found myself unable to keep Florestan and Eusebius out of the later chap-ters, and the volume became a theoretical manuscript counterpointed by theircommentary.

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viii Pre'fimhule

Some or the Florestan and Eusebius material is based on their writings, andsome of it on the events of their last two years. The first six chapters "take place"in mid-January of 1854 — a time when all of the interlocutors were still or alreadyalive, and when Florestan and Eusebius were still able to walk about freely. Theseventh chapter is set in April 1854, after their admission to the asylum in En-

denich. The Epilogue, finally, is set shortly before their death in 1856. Many ofthe words and events are invented; hence the designation of the book as a set of

"Fantasiestiicke." I have not only put many words into Florestan's and Eusebius'smouths, but have frequently ascribed particular compositional intentions tothem. I have, of course, no proof of these intentions, but my study of their music

and their manuscripts leads me to believe that the intentions I mention could have

been their actual ones.

I have organized the book as an alternation of theoretical chapters (to whichFlorestan, Eusebius, and occasionally Meister Raro and Clara contribute com-ments and musical illustrations), and "intermezzi" (in which the same interlocu-tors address issues peripheral to the theory of metrical conflict but central to an

understanding of Schumann's use of such conflict). In the first chapter, I outlinethe thoughts of nineteenth- and twentieth-century authors on metrical conflict(with emphasis on writings that invoke a metaphor that pervades the book — the

consonance-dissonance metaphor). I conclude that chapter with a summary ofprevious writings on Schumann's metrical anomalies. In the second chapter I de-scribe various categories of "metrical dissonance" and set out a terminology andlabeling system for the analysis of metrically dissonant passages. In the thirdchapter (the first intermezzo), Florestan discusses the music that influenced hismetrical style. In the fourth chapter I investigate the operation of metrical disso-nance within large contexts, particularly successions of metrical states and thetypes of processes in which they can be involved. In the fifth chapter (the secondintermezzo), Florestan and Eusebius reminisce about the "metrical revisions"

that played such a large role in their compositional process. The sixth chapterbroadens the discussion of metrical dissonance by addressing its interactionswith pitch structure, form and text, and considers the possible meanings of met-rical dissonance in Schumann's instrumental works. The seventh chapter (thethird intermezzo), couched in the form of a letter from Clara Schumann to a for-mer piano student, addresses some issues relating to the performance of metri-

cally conflicted passages. The eighth chapter is a collection of analyses of several•works and movements by Schumann, alternating with shorter discussions ofworks by other composers. The volume concludes with an epilogue, which is ananalysis of one of Schumann's very late works, as well as an attempt to suggest,with "dissonant" layers of prose and poetry, Schumann's mental state in the asy-

lum at Endemch.The "fantastic" portions of the book are disrupted by footnotes and musical

example numbers. I apologize for these intrusive, but necessary elements. (Asthey form a "dissonant" layer within the imaginary discourse of Schumann's per-

sonae, they are, in a way, appropriate!)I have included as many musical examples as possible, but readers who wish

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Preambule ix

to follow each of my analyses in detail will need to consult scores at times. I have,

for the most part, used the Clara Schumann-Brahms editions of Schumann's

music, but have compared them to the Henle edition and to extant autographswhere possible.

The book does not assume a great deal of prior theoretical knowledge. Somefamiliarity with recent writings about rhythm would be helpful but is not essen-tial, as the relevant ideas are summarized in chapter 1. I assume some knowledge

of Schenker's theory during a few of the analyses in chapter 6; most of the vol-ume, however, can be understood without that knowledge.

Florestan and Eusebius have added much pleasure to the writing of this book.

It is my hope that their presence will equally enhance the pleasure of readers.

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I thank the Social Sciences and Humanities Research Council of Canada for agenerous grant that enabled me to travel to Europe to study Schumann auto-graphs and secondary sources not readily available in North America. I am grate-ful to the librarians and archivists at the following institutions, who graciously andgenerously assisted me: the Manuscripts Division of the Universitats- und Lan-desbibliothek Bonn; the Schumann-Forschungsstelle at Dusseldorf; the MusicDivision of the Bibliotheque Nationale in Paris; the Manuscripts Division of theBritish Library in London; the Schumann-Haus in Zwickau; the Music Divisionsof both houses of the Deutsche Staatsbibliothek zu Berlin — PreuBischer Kul-turbesitz, Musikabteilung mit Mendelssohn-Archiv; the archive of the Gesellschaftder Musikfreunde in Wien, and the Music Division of the Osterreichische Nation-albibliothek inVienna; the Music Division of the Bayerische Staatsbibliothek inMunich; and the Pierpont Morgan Library in New York. I must thank in particu-lar Brigitte Berenbruch, former director of the Music Division of the Stadtbiblio-thek in Bonn, Dr. Gerd Nauhaus of the Schumann-Haus in Zwickau, and Dr.Matthias Wendt and Dr. Bernhard Appel of the Schumann-Forschungsstelle atDusseldorf, all of whom gave me much valuable assistance and advice.

I thank Mekala Padmanabhan, Stephany and Gordon Wolfe, DonaldMcDougall, and Todd Harrop, graduate students at the University of Victoria,all of whom assisted me at some point during the preparation of this book. I amespecially grateful to Donald and Todd for the many hours they spent in prepar-ing musical examples.

I thank Amadeus Verlag, Belmont Music Publishers, European American Mu-sic, Heinrichshofen's Verlag, Peermusic Classical, and Theodore Presser Co. forpermission to reproduce excerpts from musical works to which they hold the rights.

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Some or the material in chapter 5 previously appeared in Music Theory Spec-

trum, vol. 19, no. 1 (Spring 1997): pp. 35-54 (© 1997 by the Society for Music

Theory). I thank the University of California Press for permission to reuse thismaterial. 1 also thank Walter Kreyszig, editor of Aiulria, 996—1996: Music in a

Changing Society, Proceeding,./ o/ the International Millennium Conference, Ottawa,

Canada, 2-7 January 1996, for permission to include material that appears (albeit

in a very different form) in volume 2 of that publication (Issues in Music of the Late

Eighteenth, Nineteenth and Early Twentieth Centuries).

I thank Richard Cohn, Peter Kaminsky, William Kinderman, Justin Lon-don, and John Roeder for their comments on material that I shared with them.John Daverio, William Rothstein, and a third, anonymous reader provided many

extremely helpful comments on my manuscript, for which I am very grateful.I thank Mark Franklin and Ajana, of Media Magic Inc., for conjuring up

Florestan's and Eusebius's coffee beans, and Jill Michalski, Linda Sheldon, andRobert Malatest lor their help with various technical matters.

I thank my parents and sister for their unfailing moral support. Special

thanks, finally, to my wife, Sharon Krebs, for her assistance in innumerable

ways — for her help during computer crises; for preventing me, with her infalliblesense of direction, from getting lost (and thus wasting precious research time!)in European cities; and for exploring with me the wonderful Lieder of Robert


xii Reconnaujcuu'c

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ONE Nineteenth- and Twentieth-Century Theories of MetricalConflict 3

Promenade through the Town of Euphoma 3Waldscene: Ideas of Metrical Conflict in the Twentieth

Century 13

TWO Metrical Consonance and Dissonance — Definitions andTaxonomy 22

Layers of Motion 22Interaction of Layers 29Resultant Rhythms 39Relationships between Dissonances 41Distinctions between Dissonances 45

THREE Intermezzo I: Influences on Schumann's Metrical Style 63

FOUR Metrical Progressions and Processes 82Metrical Progressions 82Metrical Maps 85Metrical Processes 86

Intermezzo II: Metrical Revisions 115 FIVE

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xiv Contents

Six Interactions of Metrical Dissonance with Pitch Structure,Form, and Extramusical Elements 142

Interactions of Metrical Dissonance with Form and PitchStructure 143

Metrical Dissonance and Text 156Meanings of Metrical Dissonance in Instrumental Music


SEVEN Intermezzo I I I : Performing Metrical Dissonances 175

EIGHT Carnaval des analyses 187"Valse francaise" (Hector Berlioz, "Un bal," from

Symphonic, f a n t a s t i q u e ) 187"Metres Dansants" (Robert Schumann, Intermezzi

op. 4) 191"Chopin" (Frederic Chopin, various works) 199"Repliques" (Robert Schumann, Scherzo in

F Minor) 203"Chiarina" (Clara Schumann, Piano Trio op. 17, second

movement) 209"Valses contre les Philistins" (Robert Schumann,

Faschingsschwank aus Wien op. 26, first movement)213

"Kreisler jun." (Johannes Brahms, Piano Sonata op. 5,first movement) 219

"Eusebius" (Robert Schumann, String Quartetop. 41 no. 2, second movement) 224

"Blumenstiick" (Charles Ives, "Two Little Flowers")232

"Florestan" (Robert Schumann, Symphony no. 3 op. 97,first movement) 236

"Pierrot" (Arnold Schoenberg, "Valse de Chopin" fromPierrot lunaire) 244

Epilogue: Morning Song 249

Glossary 253

Notes 256

Bibliography 275

List of Cited Works by Robert Schumann 282

Index 285

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Nineteenth and Twentieth-Century Theories

of Metrical Conflict


Having already shown his guests Florestan and Eusebius many of the wonders ofEuphonia, Hector led them, with an air of having something particularly amazingup his sleeve, toward an area of that town which, he informed them, was calledthe Rhythmic Quarter.' As they neared this area, their attention was caught bya throbbing and apparently chaotic din, which, however, they soon perceived tobe composed of numerous noncongruent series of regular drumbeats. Theywalked slowly down one of the streets, briefly inclining their heads in a listeningattitude before each house. From one of these there issued the simultaneous per-cussions of groups of three and four pulses, from another groups of four pulsesagainst five, from another five pulses against six, from yet others even more ex-otic superpositions, such as five against eleven and eight against thirteen. Hectorled them after awhile into a second street, from whose houses emanated combi-nations of equivalent but nonaligned groups of pulses. After sampling the soundsof a number of houses in this street, Florestan walked back to the point of inter-section of the two streets and stood there for some time, listening to the intricaterhythms that resulted from the mingling of sounds from the two streets. WhenFlorestan returned to his friends, shaking his head in wonderment, Hector said,"I must show you some of the performers." Together they entered one of thebuildings—that from which there issued the sound of a superposition of fivepulses upon seven. Inside, Florestan and Eusebius were overwhelmed, not onlyby the now deafening uproar of the drumbeats, but also by the recognition thatthe performers of these intricate rhythmic superpositions were very young chil-dren, -who pounded away at their drums with intense concentration as well as ob-


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4 Fantasy Pieces

EXAMPLE 1.1. Excerpt from Michael Bergson' s Vier Mazurken, op. 1, reproduced in Robert

Schumann's review of the work

vious enjoyment. They watched and listened for a time, then stepped back onto

the street, where Hector explained, "Most systems of musical education neglectrhythm, or address only the most common and simple rhythmic devices; in Eu-phonia, however, the children are exposed to highly complex rhythms from anearly age. Within a few years, the children reach the point where the dividing of any heat in

the bar, the syncopated forms, the blending of irreconcilable rhythms, and so on, hold no 'dif-

ficulties for them. They learn to approach rhythmic complexities with excitementand joy rather than trepidation."2

Florestan said, "The Euphoman children are indeed capable of amazing-rhythmic feats. Of course, rhythmic complexities and metrical conflicts are not

of value in themselves. Look at the folio-wing excerpt from Michael Bergson'sVier Mazurken op. 1." On a sketchbook that he drew from his pocket, he quickly

reproduced the measures shown in Example 1.1.3 "The passage," he remarked,

"is conflicted enough with its nonaligned duple groups of quarter notes withina triple meter. But the composer seems to have been carried away by a passionfor complexity to notate the passage in a manner that makes it appear much

more abstruse than it is. I hope that your young drummers are not similarly in-toxicated by rhythmic complexity for its own sake." Hector replied, "It is our

concern that every activity in this town be subservient to expression; those who

take pleasure in works that are false as to expression are inexorably banished, unless they

consent to descend to some inferior employment, such as the making of catgut or the. prepa-

ration of skins for kettledrums. And this would, of course, apply to any who wouldworship rhythmic complexity for its own sake."4 He added with a grim smile,"Michael Bergson, by the way, operates a little rosin factory on the outskirts of

Euphoma."Eusebius remarked, "Serves him right! The inexpressive use of rhythmical

and metrical conflicts must result in tiresome compositions, overgrown withneedless intricacies, or, as the worthy Moritz Hauptmami has written, in 'merelawlessness, [in] a diseased rhythm in a healthy metre.'5 Some critics, no doubt,feel that your music, dear Florestan, with its frequent usage of syncopation andother metrical conflicts, exemplifies these problems. Those, however, who inspectyour music with due care must realize that all of your metrical complexities aresubservient to the laws of expression. What comical effects, what breathless ex-citement you have communicated, for example, by the pages of syncopation inCarnaval and the DavidsbiindL'rtanze\ And at times your metrical incongruities

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Nineteenth- and Twentieth-Century Theories of Metrical Conflict 5

EXAMPLE 1.2A. Excerpt from Beethoven's Symphony no. 7, third mvmt. (mm. 199-200), repro-

duced in Robert Schumann's essay "Das Komische in der Musik "

EXAMPLE 1.2B. Excerpt from Beethoven's Quintet op. 29, finale, (mm. 124—28), discussed in "LAS

Komiscbe in der Musik"

seem to me to reflect the irreconcilable conflicts within your soul." His lips trem-bled with pain.

Hector, tactfully pretending not to notice Eusebius's emotion, took him and

Florestan by the arms and guided them into as yet unexplored streets of theRhythmic Quarter. As they walked, Florestan said, "It is quite true that I haveoften attempted to create comical effects and to express emotional conflicts withvarious rhythmical and metrical devices. And I am by no means the only com-poser to have done so." Again he took recourse to his sketchbook and notatedtwo excerpts by Beethoven (Examples 1.2a and b), remarking, "The comical,

bizarre effect of the first passage stems primarily from the semitone oscillations inthe horns, which result in the intrusion of duple meter into the triple context. Inthe excerpt from the last movement of Beethoven's Quintet op. 29, the comedy

stems from the struggle between two-four and six-eight meters.6 Here is anothermore dramatic example by Beethoven of the effective employment of rhythmicand metrical conflict (Example 1.3); observe the weighty pressinq on weak beats,


which produces a sense of duple meter that yields to the notated triple meter asthe seventh chord is resolved. What perfect coordination between harmony andmeter!"

Florestan and Eusebius had been noticing for some time that the din of the

EXAMPLE 1.3. Excerpt from Beethoven's Symphony no. 3, first mvmt. (mm. 128-29), cited in Schu-

mann 's review of Christian Gottlieb Muller'j Third Symphony

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6 Fantasy Pieces

EXAMPLE 1.4. Fetid's fiirst mutation type

children's drums was receding into the distance. Hector told them, "We havenow entered that part of the Quarter where the residents, including the children,

are encouraged to speculate about rhythm and meter rather than just to performcomplex patterns. 1 must introduce you to one of the masters who oversees theirresearches and pursues his own in his spare time — a man with whom you as well

as 1 have had our disagreements, but who is nevertheless a fine musician.8 1 hopethat we shall find him at home." He knocked at one of the doors, which was, aftersome delay, opened by a thoughtful-looking side-whiskered gentleman. "M.Fetis, I am sorry to interrupt your work," said Hector, "but I thought you would

like to meet my two friends, Florestan and Eusebius, who are visiting this townfor the first time." M. Fetis bowed and said, "Gentlemen, I am enchanted to seeyou. Please come in." He led them into his study and, by moving stacks of booksand musical scores, made room for them on three chairs. Hector said, "We werejust discussing rhythmic and metrical conflict — a subject which I know you haveresearched for some time." M. Fetis responded, "Indeed, I have. Just two yearsago, I published a series of articles in the Revue el Gazette musicale de Paris in whichI pondered how future generations of composers might make use of such con-

flicts."9 Eusebius begged, "Pray unveil for us, Monsieur, what the future holds!"M. Fetis smiled and said, "There is much in the domain of rhythm that has notyet been exhausted, nor even broached, by the composers of today. Think, for

example, about the possibility of 'mutation' or transformation of a meter that hasbeen established within a piece of music. One type of mutation might take theform of the actual repositioning of the strong beat within the measure." He drew

a rhythm on a blackboard that: was mounted on his wall, then showed how therhythm could be 'mutated' by shifting it in relation to the measure (Example 1 A).

"This technique," he said, "could be applied within compositions as a form ofvariation, possibly during restatements of a theme."10 M. Fetis continued, "In myarticles, I also proposed another type of mutation, in which accentuation is mod-ified do ad to create the effect of dome new meter, even if the meter does not actually change"

Again he drew two examples on the blackboard (Example 1.5). "Such mutation,"he continued, "could prepare the actual motion from one rhythm and metrical system to

another'.'11 In my example, I take a passage in binary meter am) superimpose ternary

meter over it ("frappe. de trois en troll sur un rhythme binaire"), then actually change toa ternary meter.12 The state of ambiguity that lies between the two meters pre-pares the actual establishment of the new meter. The listener, still under the influence

of the compositions overall meter, will preserve its impression in spile of the new superimposed

meter; il id thud that the composer will he able to deceive hid ear am) actually pass into the

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Nineteenth- and Twentieth-Century Theories of Metrical Conflict 7

EXAMPLE 1.5. Fetis's second mutation type

[new] rhythm and meter. The nusic will have changed character, and the Listener will not no-

tice the moment of transition. "13 Hector nodded in agreement and said, "I, too, have,in a feuilleton in the Journal des Debats encouraged composers to explore as yetuntried rhythmic and metrical effects, such as accentuation of the weak beat in-stead of the strong, the alternation of duple and triple groupings, the superim-posing of phrases whose subdivisions bear to each other no compatible relation and have no

points of contact other than the first beat, the episodic introduction of a melody based on a

ternary rhythm into one based on four (or vice versa), and even the intermittent use of

sounds quite independent of both the main melody and the prevailing rhythm in the accom-

paniment, sounds which are separated from one another by intervals that lengthen or dimin-

Lth in proportions determinable in advance.14 There indeed remains much for futuregenerations of composers to explore. But we must keep you no longer from yourwork." They all thanked M. Fetis and took their leave.

Outside, Florestan said to Hector, "I did not wish to embarrass you and ourkind host while we were inside, but now I cannot resist pointing out that the veryinteresting techniques that M. Fetis and you have mentioned are already beingused by composers today. In fact, I have frequently employed them myself." Eu-sebius smilingly interjected, "I remember one occasion on which you applied M.Fetis's first mutation type! Please pass me that sketchbook for a moment." WhenFlorestan handed it to him, he jotted down the theme in Example 1.6a. "This wasmy idea for a passage near the beginning of the third movement of our PianoSonata op. 11," he said. "I wrote it down and left it on the table while I went tothe coffeehouse. When I returned, Florestan had 'mutated' the idea as follows"(and he wrote Example 1.6b). "Yes," said Florestan, "and since you approved,Eusebius, we used the mutated version in our sonata. Another passage that illus-trates this mutation type is found at mm. 26-27 of the 'Preambule' from Carnaval,

where we shift a motive forward by one beat.15 The second mutation type," Flo-restan continued, "plays a very large role in our works. Near the end of my veryearly Piano Quartet in C Minor, I transform triple meter into duple by firstgrouping eighth notes into twos, then actually altering the meter (Example 1.7a).There is also an example of such mutation near the end of the 'Preambule' fromCarnaval (Example 1.7b)." Eusebius, meanwhile, had jotted down the passagesthat Florestan had mentioned and passed them to Hector. As Hector was study-


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8 Fantasy Pieces

EXAMPLE 1 .6A. Sketch for the first Trio from Schumann's Piano Sonata op, 11, third mvmt.,

mm. 51-54, Deutsche Staatsbibliotbek zu Berlin — Preufiiscber Kulturbesitz, Musikabteilung mit

Mendelssohn-Archiv, Mus, ms, autogr. R. Schumann 35

EXAMPLE 1.6B. Later sketch for the same passage, Universitats-und) Landesbibliothek Bonn (ULB

Bonn), Manuscripts Division, R. Schumann 14 (Sketchbook II), p. 5, brace 2

ing them, Eusebius remarked, "Our young friend Johannes Brahms also seemsto be very interested in exploring these mutation techniques. You remember the

first movement of his Piano Sonata in F Minor, Florestan? It is in three-fourtime, but from the outset there are many duple groups of quarter notes. Just be-fore the end of the exposition, there is another such duple passage, the duple

grouping being achieved by a sequential pattern of falling fifths in quarter notes.

All of these instances of the imposition of duple upon triple meter prepare thecommon time at the beginning of the development section" (see Examples 8.26

and 8.27).Hector, having perused Eusebius's two examples, said, "You are right; these

are examples of the procedures that M. Fetis mentions in his articles. The excerptfrom Camaval is a particularly effective mutation from what sounds like duplemeter to triple meter, with a passage of powerful confrontation of the two metersbeginning at the fortissimo marking. I find it interesting that while the first two

bars sound as if they were in duple meter, you there maintain the notated three-four meter, whereas in the third bar you allow the duple meter to show itselfundisguised." Florestan responded, "Much metrical conflict can be notated withinthe established metrical framework, but at times that framework must be over-ridden, or rather overwritten."

At this point, Hector said, "1 must introduce you to one of the young resi-dents of Euphoma who has been pondering the appropriate notation of metricalconflicts." He led them into a house within that same quiet portion of the Rhyth-mic Quarter in which a group of young people was engaged in a lively discussionabout the opening theme of Beethoven's Piano Sonata op. 27 no. 1. Some of themargued that the theme should be rewritten so that the quarter notes became up-beats and the half notes downbeats, while others objected vociferously to any al-teration of Beethoven's barring. A very young member of the group, apparently

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Nineteenth- and Twentieth-Century Theories of Metrical Conflict 9

EXAMPLE 1.7 A. Robert Scbumann, Piano Quartet in C Minor (1828), ed. Wolf gang Boetticher,

fourth mvmt., mm. 283-98. © 1979 by Heinricbshofen's Verlag, Wilbeinu haven, Germany. Ed.

no. 1494. used by permission of publisher.

no more than five years of age, piped up and said, "Even the greatest composerssometimes fall short of absolute precision of notation, and we should have noqualms about revising their notation in order to clarify the score for the per-former. In the opening theme of Beethoven's Sonata op. 27 no. 1, the half-notechords are the most strongly accented events; they are the longest durationswithin the context, and some of them, moreover, act as appoggiatura six-fourchords resolving to the dominant harmony. For these reasons, I support the reno-tation of these chords as downbeats."16 Hector interrupted in order to introducethe boy, whose name was Hugo Riemann, to Florestan and Eusebius. He then

EXAMPLE 1.7B. Robert Schumann, Carnaval, "Preambule," mm. 99-109

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10 Fantasy Pieces

EXAMPLE 1,8A. Chopin, Ballade no. 3, op. 47, mm. 69-73

EXAMPLE 1.8B. Riemann's renotation of the passage

asked the young scholar to elaborate on his views on rebarring, particularly withreference to passages of metrical conflict.

Master Riemann complied with alacrity, saying, "I advocate renotation whenit clarifies metrical conflicts that otherwise are likely to remain undiscovered byperformers, In the Beethoven example, a subtle metrical conflict arises from har-monic ambiguity, that is, from the possibility of hearing the six-four chords eitheras unaccented continuations of existing tonic chords or as accented initiations of

dominant harmony. Beethoven's notation conceals the conflict; performers play-ing from his notation will simply opt for the first of the two harmonic interpreta-tions, tapering oft each measure and deemphasizing the half-note chords. The re-barring brings the potentially accented nature of these chords into focus andforces performers to address the subtle conflict within the passage."

Florestan and Eusebius frowned during these comments, but Riemann con-

tinued without noticing their displeasure, "I have become aware of a type of met-rical conflict that involves the intrusion of triple groups into duple contexts, the

'large triplet.'17 Such triplets, easily overlooked by performers, can be renderedvisually clearer by rebarring. There is a good example in the third Ballade of

Chopin."18 He shuffled through a sheaf of pages that lay before him — "notes for abook that he plans to write," Hector whispered to his friends — and drew out Ex-ample 1.8. "You will notice," Riemann continued, "that the large triplet in myrenotation (Example 1.8b) is motivated by harmony; the triplet encompasses the

duration of the cadential dominant."It would be wrong, however," he admitted, "to modify the composer's barring

in all cases of metrical conflict. Imagine, for instance, a syncopated passage like thisone." (He showed them Example 1.9a.) "If we were to turn the long durations intometrical downbeats, we would arrive at the following." (He showed them Example1.9b.)19 He continued, "This renotation implies that syncopation is nothing but an

abrupt displacement (ruckweise Verschiebunq) at 'NB. 1' followed by a realignment(Wiedereinrenkunq) at 'NB. 2.' Syncopation is, however, actually a conflict between abasic meter (Grundrhythmus) and a simultaneously presented nonaligned meter thatendures throughout the syncopated passage, as Herr Moritz Hauptmann has al-ready stated.20 The traditional notation, with its ties across the bar lines, makes thatcontinuing conflict much clearer than the renotation.

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Nineteenth- and Twentieth-Century Theories of Metrical Conflict 11

EXAMPLE 1.9A. Reconstruction of a syncopated passage discussed by Riemann

EXAMPLE 1.9B. Riemann's (deliberately) incorrect notation of a syncopated passage

"Some metrical conflict," Riemann observed, "arises from the noncongru-ence of motivic lengths and metrical groups. Frequently, motives within a triplemeter are two beats long; here is an example, Herr Florestan, from one of yourown works (Example 1.10). The reverse, three-beat motives within a duple

meter, is much less common.21 When such conflicts appear in the music, we

should by no means renotate the music in accordance with the conflicting ele-ments. The notated meter remains in effect as a significant contender within the

conflict, in fact, as the background without which the conflicting quality of otherelements would be imperceptible.22 Just as a harmonic sequence at times sus-pends the logic of harmonic progression on the surface while ultimately remain-

ing subservient to it, so does this type of metrical conflict create a series of pseudo-measuresthat for a time contradict the notated meter but that find their justification and

motivation only through their continued subordination, to the actual meter. "23

When young Riemann paused, Eusebius said, "I find many of your argu-ments very convincing, Master Riemann. One of your ideas particularly in-trigues me; aside from metrical conflict that occurs on the musical surface, you

have also mentioned the possibility of larger-scale conflict—the 'large triplet,'

which is actually a disturbance of phrase rhythm. The concept of large-scale met-rical conflict is certainly worth exploring further." Florestan interjected, "Suchlarge-scale conflicts, like those of smaller scale, must be used with care. I have re-viewed a number of works in which there is at various points something missingor something superfluous in the phrase rhythm —that is, a conflict between theestablished phrase rhythm and shorter or longer units. In Amadeus Mereaux's

Grande Fantaisie, for example, in the first part of the third variation, there is, against all

EXAMPLE 1.10. Robert Schumann, Novellette op. 21 no. 4, mm. 108-14 (with grouping analysis

by Riemann)


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12 Fantasy Pieced

norms of phrase rhythm, one measure too many.24 Similarly, in Johann Friedrich

Kittl's Seeks ldyllen, there is frequently a problem at section endings, for example in

no. 2, two measures before the end, the same in no. 3 ant) in no. 4, etc. The composer simply

cannot finish at the. right time.25 The same flaw can be found in this composer's Drei

Scherzi op. 6, and in Ferdinand Miller's Etudes op. 15."26 Eusebius answered, "It

seems to me that when such large-scale irregularities occur in the works of goodcomposers, they are resolved at the appropriate time so that the listener is not leftat the end of the work or movement with an unpleasant sense of incomplete-ness."27 Florestan said, "In other works, the irregularity is so widespread that it

becomes the norm and thus, again, has no unpleasant effect upon listeners oncethey become accustomed to it. I am thinking, Hector, of your works, especially ofthe Symphonic fantastique.. The flexibility of large-scale meter seems to me to be the

most distinctive feature of your musical ideas. Your phrase rhythms appear to strive for the

reestablishment of a primeval state, in which the law of metrical accent (Gesetz der

Tactesschwere) did not yet weigh upon music, and for the. unfettered discourse (ungebun-dene Rede,) and higher poetic, punctuation (hoheren poetischen Interpunktion) of

Greek choruses, the Bible, and Jean Paul's prose. The novelist [Johann] Ernst Wagner's

statement that the composer who completely veils and renders imperceptible the tyranny of

meter Will (at least apparently) liberate the art of music seems to me to apply to yourmusic."28

As Florestan concluded his remarks, the great organ that announces the hour

to the Euphomans blared forth, and Florestan and Eusebius realized that it wasalmost time for them to begin their homeward journey. They bade farewell to

young Riemann, and Hector led his friends back into the street. As they walkedtoward the coach-house, he thanked Florestan for his tribute, then said, "MasterRiemann is an interesting youngster, is he not?" Florestan responded, "Yes, very

interesting, though somewhat verbose. And I strongly disagree with his analysisof the opening theme from Beethoven's Sonata op. 27 no. 1. I find his hearing ofthe half-note six-four chords as accented appoggiaturas unconvincing. In m. 1, Ihear an implied El) below the right-hand chord, and in m. 3, El actually sounds inthe bass; as a result, the right-hand chords do not suggest dominant, but tonicfunction to me, and I hear much less metrical conflict than does Master Riemann.

I agree that the durational accents and harmonic changes in the passage are notcoordinated, but that is not sufficient reason for a sweeping revision of Bee-

thoven's notation!"Eusebius, who had hardly been listening to Florestan's remarks, said, "The

Rhythmic Quarter of Euphonia is a most fascinating place, and I have very muchenjoyed our visits and conversations. I must share with you two ideas that haveoccurred to me here. First, it seems to me that metrical conflict can be reduced totwo types of phenomena: to the association of unequal or noncongruent layers ofmotion on the one hand, and to the association of congruent but shifted layers onthe other." Florestan interposed, "You are right. These two categories are implicitin Hector's description of rhythmic education in Euphonia; he mentions the blend-

inq of irreconcilable rhythms but also the syncopated forms (which, as Master Riemannstated, result from the conflict of simultaneously presented congruent but non-

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Nineteenth- and Twentieth-Century Theories of Metrical Conflict 13

aligned layers). The two categories are also implicit in Hector's feuilleton. He

writes of the alternation of duple and triple groupings, of the superimposing of

phrases whose subdivisions bear to each other no compatible relation and have no points of

contact other than the first beat, and of the episodic introduction of a melody based on a

ternary rhythm into one based on four (or vice versa), all of which techniques fit into the

first category. He also mentions, however, accentuation of the weak beat insteadof the strong, which would result in a conflict of the second type. M. Fetis's mu-tations also imply these two categories; those that involve the shifting of rhythmsin relation to the bar line result in a conflict between two equivalent but non-aligned layers, whereas those in which a new grouping is superimposed onto theexisting one result in a conflict between noncongruent layers." Eusebius said,"And young Hugo Riemann discussed conflicts engendered by the noncongru-

ence of motive and meter and by the large-scale superimposing of duple and tripleunits, but also mentioned conflicts arising from syncopation or displacement.

"Second," Eusebius continued, "I have noticed suggestions of analogies be-tween pitch and rhythm running like a thread through today's discourses on met-rical conflict. Master Riemann's sequence analogy, which links the notions of

surface and subliminal levels in the areas of pitch and rhythm, is an obvious ex-ample. Some of M. Fetis's mutations also imply such an analogy; his reference tomotion from one meter to another, using passages of metrical conflict as a sort ofpivot, recalls one of the most common techniques of modulation in the domain of

pitch. My allusion to 'resolution' of large-scale conflicts hints at an analogy be-tween metrical conflict and dissonance: the metrical conflicts are 'dissonances'that lead the listener to expect subsequent resolution."

Hector interjected, "I must tell you that I explicitly drew an analogy betweenrhythmic and metrical conflict and pitch dissonance in the feuilleton that I men-tioned earlier, where I wrote: '[Combinations of this sort] constitute in the domain of

rhythm clusters and progressions analogous to the clusters and progressions that make up

chords, melodies and modulation. There are such things as rhythmic dissonance; there are

rhythmic consonances; there are rhythmic modulations.' "29 "A fascinating analogy," cried

Florestan. "Here lies much food for thought for us and for later generations ofmusicians." They had now reached the coach-house, where Florestan's and Eu-sebius's conveyance was waiting. Having thanked Hector for acting as their

guide and for introducing them to so many interesting people and ideas, theymounted their seats and waved to Hector as the coach moved off into the gath-ering dusk. Eusebius, fatigued from the promenade through Euphonia, almostimmediately fell asleep. Florestan, who remained awake awhile longer, smilinglyobserved that the horses' hooves and Eusebius's soft, regular snores togetherproduced a metrical dissonance of three pulses against four.


At dawn, they both awoke to sounds of scrabbling and thumping on the roof ofthe coach. The coachman apparently had noticed nothing out of the ordinary, for

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14 Fantasy Pieces

the vehicle continued to rumble through the snowy forest of the Harz. Florestanwrenched the window open and was about to stick out his head in an attempt tocatch a glimpse of the roof when, with much flapping of wings and flying offeathers, a bird fluttered in and settled on Eusebius's shoulder. It was a bird of

extraordinarily colorful plumage, but the men's attention was attracted primar-ily by a sheaf of paper which it carried in its beak and which, with an air of relief,it dropped into Eusebius's lap. They were even more astounded when, having re-

leased its burden, it began to speak. "Well met, my friends," it chirruped, "andthank you kindly for opening the window so promptly. It was cold out there, andlanding on a moving coach is no simple matter, especially when one is burdenedwith a heavy theoretical manuscript." Florestan somewhat quaveringly asked thebird, "What manner of bird are you?" Their avian visitor chuckled and answered,"You two, of all people, should know me! 1 am a Prophet Bird." Eusebius, con-

torting his neck to catch a glimpse of the bird on his shoulder, exclaimed, "Ofcourse! You look just as I imagined you many years ago." Meanwhile, Florestanhad snatched the pages from Eusebius and had begun to leaf through them."How uncanny!" he burst out. "This manuscript is concerned precisely with theissues that we were discussing in Euphonia." The Prophet Bird said, "Yes, I

thought that it would interest you. Not only does the manuscript explore M.Berlioz's analogy between pitch and rhythm, but it makes mention of a largenumber of your compositions." When Eusebius inquired as to the author, theProphet Bird said, "It is nobody you know — a music theorist from the late twen-

tieth century." As Florestan and Eusebius gasped in amazement, the bird contin-ued, "I see that you are eager to peruse the manuscript, so I shall leave it with

you. I shall return someday to retrieve it. Farewell." The Prophet Bird flutteredout and soon disappeared in the depths of the forest.

The men might well have shrugged the episode off as a dream had the man-

uscript not remained in Florestan's hand. They stared at it in a daze for someminutes. Then Florestan shook himself and said, "Well, Eusebius, there is nowsufficient light to read. Shall we?" Eusebius shut the window and moved to the

seat beside his friend. They turned over the first leaf, and read:

Nineteenth-century references to metrical conflict are by no means nu-

merous, and most of them are mere allusions to the topic rather than detaileddiscussions. In the twentieth century, the subject has been much more fre-quently addressed; most of the important large-scale studies of rhythm of thesecond half of the century discuss metrical conflict at least briefly. GrosvenorCooper and Leonard Meyer, the authors of one of the earliest books of this cen-tury devoted entirely to rhythm, present brief analyses of conflicted passages byBrahms, Mozart, Dufay, and Beethoven, referring to the conflicts by a varietyof terms, notably "metric crossing" and "rhythmic dissonance" (by which theymean superposition of nonequivalcnt layers), and "noncongruence" (by whichthey mean nonaligned statement of equivalent layers).30 Conflict is much morecentral to Wallace Berry's discussion of meter. In his view, meter is "not to be


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Nineteenth- and Twentieth-Century Theories of Metrical Conflict 15

equated with regularity" but is, "by definition, subject to fluctuation." Several of

his analyses show how various determinants of meter move in and out of "ac-cord" with the notation, and thus highlight the fluctuating, processive aspect ofmeter.31 The term "in accord" implies the consonance/dissonance metaphor, andthat metaphor is at some points explicitly invoked in Berry's discussion.32

Several studies of musical rhythm from the 1980s include interesting,though brief, investigations of metrical conflict. In A Generative Theory of Tonal

Music, Lerdahl and Jackendoff, while hypothesizing a set of preference rulesthat listeners invoke when metrically interpreting tonal music, present some in-stances of passages where the musical evidence results in conflicting prefer-ences and hence in metrical conflict.33 In their presentation of preference rulesfor grouping structure (which they regard as separate from, but affectingmeter), they also consider conflict; their designations of particular interpreta-

tions of grouping as "preferred" do not negate the possibility that some aspectsof the music may conflict with those interpretations.34 Joel Lester refers in The

Rhythms of Tonal Music to a state of "nesting" of metrical levels, but also to thepossibility of metrical levels that do not nest, and gives examples from Mozart,Schumann, and Brahms.35

Carl Schachter's articles on rhythm contain a considerable amount of dis-

cussion of metrical conflict.36 Schachter analyzes excerpts containing "incom-mensurable levels," for example, a seven-against-two conflict by Mozart, a two-against-three conflict in a work of Beethoven, and similar conflicts fromSchumann's Davidsbundlertanz op. 6 no. 1 (which he terms "rhythmic disso-nances.")37 He also gives examples of the nonaligned association of congruentlayers; in his analysis of Schumann's op. 6 no. 1, for example, he shows that the

music encourages two ways of parsing the passage into six-quarter-note andtwelve-quarter-note groups. Schachter's discussion of Mendelssohn's "Songwithout Words" op. 102 no. 4 draws attention to a similar conflict; he demon-strates that the work is permeated by a struggle for supremacy between twometrical schemes, one (beginning on the notated downbeats) being strongly ar-ticulated by the accompaniment, the other (beginning on third beats) articu-

lated by the melody. Schachter's durational reduction traces this conflictthrough the entire piece, showing the two layers of motion moving out of and

back into phase.38 Schachter's and Berry's demonstrations of the large-scaleprocesses involving metrical conflict significantly influence the approach adoptedin this volume.

Florestan sighed, "So far, this manuscript is quite boring." Eusebius agreed,but said, "Of course it is boring for us; we are not familiar with the writings thatthe author cites. But let us read on; perhaps it will become more interesting."

A number of the authors mentioned thus far allude to or actually employthe terms "consonance" and "dissonance" in connection with metrical conflict.These, and other twentieth-century applications of these terms to rhythmic and


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metrical structure to be mentioned below, do not seem to descend from thoseof the nineteenth century; to my knowledge, none of the numerous twentieth-century writers who have employed this metaphor has mentioned its origin inBerlioz's writings.

Not all twentieth-century writers have applied the metaphor in the samemanner; three quite different usages can be discerned. One of the earliest, thatof Henry Cowell, appears to be unique. Cowell's discussion of rhythm is based

on his perception of its close relationship to pitch; he regards pitch as greatlyaccelerated rhythm.39 Taking his departure from this basic assumption, Cowelldevelops numerous analogies between pitch and rhythm. He refers to combina-

tions of "times" (essentially, meters) as rhythmic "intervals," and applies theterm "in harmony" to rhythmic combinations based on ratios that produce pitchconsonances, such as 2/1, 3/2, and 5/4. The wording "in harmony" hints at theconsonance-dissonance metaphor. It is noteworthy that Cowell, rigidly follo-w-ing a pitch-rhythm analogy, regards as consonant rhythmic relationships thatmost other writers would deem "dissonant" (3/2 and 5/4!).40

Concurrently with Cowell, Charles Seeger also pursued analogies betweenpitch and rhythm, and specifically the consonance-dissonance metaphor.41 Ar-guing that "rhythmic harmony" should be recognized "as a category on a parwith tonal harmony" (p. 26), he proceeds to investigate the nature of "the rhyth-mic interval and chord" and to "classify the rhythmic consonances and disso-nances." Although his terminology is similar to Cowell's, his application of the

consonance-dissonance metaphor is quite different. Seeger defines rhythmic re-lationships such as "two against three" and "three against four" as "rhythmicdissonances," basing the definition of consonance and dissonance not on criteriaderived from pitch theory but on the nature of the rhythmic phenomena them-selves, namely on the degree of alignment of rhythmic layers. He complains thatmodern music still favors simple dissonances such as "two against three" and

"three against four," and encourages composers to employ more complex "rhyth-

mic intervals" such as 5/6, 5/7, or 6/7. He hints at a categorization of these in-tervals in terms of intensity of dissonance: "The classification of the rhythmicintervals in their chordal (vertical) sounding may be accorded the terms mild,medium and strong, starting with 2/3 and graduating toward such as 4/7 . . ."

(p. 27).The conception of rhythmic dissonance as an association of nonahgned lay-

ers underlies numerous later applications of the consonance-dissonance meta-phor. Whereas Joseph Schillinger's theory of rhythm, as set down in his System

of Musical Composition, does not include the terms "consonance" and "disso-nance," the theory is based to a large extent on the notion of interferences of pe-riodicities, which suggests conflict produced by the association of noncongruent

layers.42 Schillinger indicates how the interference of two or more noncongru-ent periodicities creates resultant rhythms and demonstrates, in a variety of me-ters, the resultants of three-against-two and four-against-three dissonance inthe form of "vamps" (pp. 30-31). Schillinger's Encyclopedia of Rhythms expandsupon these pages of the System; this book is a catalog of resultant rhythms of

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Nineteenth- am) Twentieth-Century Theories of Metrical Conflict 17

dissonances.43 In the introduction to the latter volume, Charles Colin, one ofSchillinger's students, explicitly designates superpositions of noncongruent lay-

ers as "dissonances." His use of the dissonance metaphor, then, is similar toSeeger's. Interestingly, Colin drifts into the Cowellian application of the meta-phor at one point; his distinction between greater or lesser rhythmic dissonance

depends on the degree of dissonance of the pitch intervals suggested by the ra-

tios involved, recalling Cowell's rigid analogy between pitch and rhythmic in-tervals. Colin does not, however, follow through on this analogy: he classifies3/2, for example, as a dissonance in the rhythmic domain.44

Other authors mentioned earlier, namely Cooper and Meyer, Berry, andSchachter, for the most part use the consonance-dissonance metaphor in thesame manner as does Seeger. Maury Yeston's Stratification of Musical Rhythm is

a larger-scale development of the Seegerian application of the consonance-dissonance metaphor.45 Yeston describes a number of ways in which strata ofmotion can be produced in musical works; whereas he stresses stratification

through pitch structure, devoting an entire chapter to it (chapter 3), he alsoconsiders attack point, timbre, dynamics, density, and pattern recurrence as de-lineators of layers of motion.46 Yeston then defines rhythmic consonance anddissonance as products of the interaction of numerically congruent and incon-gruent layers, respectively.47 The primary focus of his discussion of rhythmicdissonance is not on the dissonant states themselves, nor on the manner in

which these states are deployed within musical works (Yeston analyzes no com-plete works or movements), but on the rhythms arising from the interaction ofnoncongruent layers, i.e., on resultant rhythms. Much of his discussion of met-

rical dissonance centers on the compositional exploitation of the resultant oftwo-against-three dissonance.48 His final chapter explores other dissonant com-binations in a more abstract manner.

Yeston and others who adhere to Seeger's application of the consonance-dissonance metaphor regard only associations of incommensurate layers of mo-tion as dissonant. In other words, dissonance is defined by these authors in an

arithmetical manner; if the constituents of a rhythmic relationship are based onincommensurate integers (integers that are not multiples or factors of each other),the relationship is deemed dissonant. Wallace Berry, however, begins to shift the

definition of dissonance into the geometric rather than arithmetic domain whenhe refers to "metric asymmetries as horizontal and vertical noncongruities . . . inprecise parallel to the geometric sense having to do with the potential for exact

alignment (or nonalignment) of figures in superposition."49 My article "Some Ex-tensions of the Concepts of Metrical Consonance and Dissonance" expands uponthe geometric model; nonalignment of layers is taken to produce dissonance, nomatter what the arithmetic relationship between those layers might be.50

The shift from an arithmetic to a geometric approach brings a second type ofmetrical dissonance into play; dissonance may arise not only from the associationof arithmetically incommensurate layers, but also from the nonaligned associationof equivalent (congruent) layers. These are precisely the two types of metricalconflict at which nineteenth-century writers already hinted. Numerous twentieth-

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century writers show an awareness of the two types, applying to them a variety of

terms. We have seen that Cooper and Meyer refer to "metric crossing" as well as"non-congruence," and that Schachter analyzes examples of both types. In two

succinct articles, Karl Hlawicka discusses two rhythmic/metrical phenomena that

correspond precisely to our two types of conflict: his "Verwechslung" (inter-

change or substitution—apparently used in the sense of substitution of noncon-

grucnt layers tor potential and expected congruent ones) involves the super-

imposing of noncongruent layers, and his "Verschiebung" (displacement) thenonaligned presentation of congruent layers. He gives examples of "Verwech-

slung" in various ratios (3/2, 4/3, 5/2, 5/3, 675, 7/6, and 8/7) and categorizes them

by the manner in which the antimetrical layers are produced (dynamic accents,melodic contour, harmony, etc.). His discussion of "Verschiebung" is similarly or-

ganized, involving a quantitative categorization of examples (by amount of dis-

placement in relation to the notated meter) and a qualitative one (by origin of thedisplaced layers, such as register, ornamentation, melodic grouping, and stress).51

Hlawicka comes close to a conceptualization of the two types of metrical

conflict as subcategones of a single broad phenomenon, a conceptualization

that I brought to the surface in "Some Extensions." My manner of applying the

consonance-dissonance metaphor has been taken up by a number of writers, in-

cluding Peter Kaminsky and Richard Cohn. Cohn has formalized the defini-

tions of rhythmic consonance and dissonance and has presented superb analy-

ses showing how dissonance, particularly on large-scale levels, shapes entire

movements by Mozart and Beethoven.52 Kaminsky's work on the music of

Robert Schumann will be discussed in detail below.

Florestan said, "Ah, the next section seems to include more names with

which we are familiar!" They read on with renewed interest.

Aside from theoretical writings on rhythm, some books and articles deal-

ing with composers in whose music metrical conflict plays a significant role

have provided valuable insights into the nature of such conflict. Studies of Bee-thoven's music, including Andrew Imbrie's "'Extra' Measures and Metrical Am-

biguity in Beethoven," David Epstein's study of the first movement of the Eroica

Symphony, William investigation of numerous sonata movements,and my own analysis of the first movement of the Ghwt Trio, among many oth-

ers, have drawn attention to that composer's interesting usages of metrical con-

flict.53 Writings about the music of Brahms, not surprisingly, furnish further ex-amples."4 Analyses of a number of other composers could be cited here.66 Let us

turn, however, to the Schumann literature, which is rich in relevant material,ranging from brief comments on Schumann's rhythmic inventiveness, throughlists or detailed analyses of conflicted passages, to large-scale studies of Schu-

mann's rhythmic style.Virtually every author who has written about Schumann makes some men-

tion of the fact thai his music is particularly interesting Irom the standpoint of


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Nineteenth-and Twentieth-Century Theories of Metrical Conflict 19

rhythm and meter. August Reissman already recognized in 1865 that the "mostpleasing treatment of syncopation" was "a primary characteristic of Schumann'smusic." Early in the twentieth century, Walter Dahms similarly remarked that"it was in Schumann's [music] that syncopation assumed its reign." WolfgangGertler's study of Schumann's early piano works includes numerous insightfuldiscussions of syncopation and other types of rhythmic conflict. Daniel Mason,writing about the early piano works, refers to the "whimsicality" expressed inthe "boldness of their rhythms, especially their use of strong dislocations of ac-cent and long-continued syncopations."56

One early-twentieth-century writer, Christian Knayer, ventures beyondmere recognition of Schumann's rhythmic ingenuity by identifying and catego-rizing a large number of relevant musical passages from Schumann's pianomusic. His first category, accentuation of upbeats and syncopation in one orboth hands, corresponds roughly to our second type of conflict (association ofequivalent layers in a nonaligned fashion). Knayer's second category includesactual changing of the meter through repeated insertion of asymmetrical mo-tives in both hands (but with preservation of the meter on paper), as well ascombination of two different meters; this category corresponds to our first type(association of noncongruent layers). Knayer proceeds to list many examples ofeach type (unfortunately by title only, not by measure number). Although hiscomments on the examples are rather superficial, it is obvious that he studiedSchumann's metrical conflicts quite carefully — the first writer, to my knowl-edge, to do so. Aside from listing examples, Knayer makes some valuable,though brief, comments on the meaning of metrical conflict in Schumann, men-tioning that it can suggest vagueness, dreaming, indecisiveness, and hovering,or that it can create humorous, witty effects.57

Later German writings on Schumann have continued to deal, in varying de-grees of detail, with Schumann's metrical structures. Whereas meter is not thefocus of Hans Kohlhase's investigation of Schumann's chamber music, he doesmake numerous remarks about metrical conflict. He refers to examples of thepassing over of the downbeat by syncopation, the placement of the most signifi-cant harmonies on the weaker beats, and the consistent accentuation of weakbeats, and draws attention to the fact that metrical conflict is the primary sourceof beauty and charm in many of Schumann's themes.58 In a dissertation focusingon Schumann's Humoredke op. 20, Bernhard Appel refers to "metrical polyphony"and displacement, and comments on the relation of these phenomena to musicalhumor.59 Arnfried Edler draws attention to metrical conflict in many of his ana-lytical comments on Schumann's works.60 Gerhard Dietel argues that Schumannapproached the dissolution of "the tyranny of meter" by his rhythmic displace-ments ("rhythmischen Gegeneinanderverschiebungen").61

"It is gratifying to learn that our music will generate so much interest!" saidEusebius. "But not surprising!" countered Florestan. "Our rhythmic structuresare unique, if I say so myself!" "True, true," Eusebius agreed smugly.

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As they read the following sentence, their gratification gave way to horror:

The title of Dieter Schnebel's important essay "Ruckungen—Ver-ruckungen"puns on the double meaning of "verruckt" ("displaced" as well as "insane"), and

the article draws a connection between Schumann's mental deterioration and

his use of pervasive displacement. Schnebel analyzes conflicts of both cate-

gories in numerous works throughout Schumann's life and notes particularly

sharp conflicts of the second type in works from periods during which Schu-

mann suffered from severe mental disturbances and psychic strains. The ideathat Schumann's metrical dissonances might be a symbol of mental illness willbe further addressed in later chapters of this book.62

Discussion of Schumann's metrical conflicts is not restricted to the Germanliterature. A sensitive recent account of displacement in Schumann's music is

found in Charles Rosen's book The Romantic Generation. Rosen, as a fine per-

former, is able to perceive and to illuminate some of the visceral aspects of

Schumann's rhythm: its "shock value," the sense of "competing system[s] of

rhythm," and the effect of "dislocation." He writes eloquently on some of Schu-

mann's reasons for pursuing "out-ot-phaseness" — his desire to represent "anxi-ety" and his "idiosyncratic pleasure in hidden contradictions."63

There exist several studies of Schumann's metrical conflicts that fall more

into the category of theory and analysis than those mentioned so far. MelittaHonsa's dissertation on syncopation, hemiola and meter change in Schumann's

instrumental works and Mary Evans Johnson's dissertation on metrical anom-

aly both present categorizations of metrical conflicts and provide illustrations ofthe various categories from Schumann's works.64 Honsa categorizes syncopa-

tion as follows: simple syncopation (a momentary breaking away from the met-

rical accentuation pattern); continuous syncopation (chains of syncopations);supported ("gestutzt") syncopation (only one or some of the voices participate

in syncopation); and unsupported syncopation (all voices take part in the syn-

copation). She categorizes hemiolas into those arising from syncopation andthose arising from melodic grouping, then discusses actual meter change (in

which area she feels Schumann was a pioneer). Johnson's categories of metrical

anomalies are quite different from Honsa's. They include empty downbeats; lilt(where the role of the third beat in triple time as upbeat or afterbeat is ambigu-

ous); consistent metrical displacement (our second category of conflict); obliqueharmonic rhythm; metrical repositioning (which is equivalent to our first cate-gory of conflict); hemiola (which also falls within the first category); metrical

flexing (brief insertions of noncompatible meters); and polymeter (by which shemeans superposition of lines with different time signatures). Johnson considers

in some detail the performance problems created by these anomalies. Her dis-sertation is even richer than Honsa's in examples from Schumann's oeuvre.Both authors, however, present the examples out of context without investigat-

ing their role wi th in the respective compositions.Peter Kaminsky, using the conceptual framework from my article "Some


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Nineteenth- and Twentieth-Century Theories of Metrical Conflict 21

Extensions" with many useful additions of his own, does turn his attention to-ward the function of metrical dissonance within large contexts.65 He provides adetailed analysis, for example, of the succession of metrical consonance and dis-sonance in the "Preambule" and the "Marche des Davidsbundler" from Car-

naval, and broadens the context even further by pointing out that the "Marche"picks up and resolves some of the dissonances of the "Preambule." Through thisand other analyses, Kaminsky is able to demonstrate that rhythm and meterparticipate both in the forging of coherent single movements and of unified cy-cles. Kaminsky's work is by far the most thoroughgoing investigation of metri-cal dissonance in Schumann's music thus far.

The above summary reveals that there has been a significant number ofdiscussions, some brief, some detailed, of metrical conflict in the music of Schu-mann. In the present volume I attempt to go beyond these discussions in a num-ber of ways. First, I take into consideration a larger body of Schumann's oeuvrethan do earlier studies, in the hope that a clearer picture of Schumann's metricalingenuity will thereby emerge. I discuss a large number of instrumental works,but also take vocal music into account. Second, I investigate Schumann's com-positional process as it relates to metrical matters, an issue that has hardly beenconsidered in print. Third, I attempt to put Schumann's rhythmic techniquesinto perspective by discussing similar (though usually less striking) techniquesin the works of composers whose music he knew. Fourth, and most important,I investigate not only brief passages but entire works and movements in orderto track, in greater detail than earlier authors, the roles of metrical conflictswithin their actual contexts, and the relationships between metrical structureand other musical elements.

My basic theoretical tools in these endeavors are those hinted at in nine-teenth-century sources and developed to some extent in earlier twentieth-cen-tury sources: pitch-rhythm analogies, in particular the consonance/dissonancemetaphor and other concepts that grow out of it; and the notion of two classesof metrical conflict or dissonance. These elements of my approach are unfoldedin a systematic manner in the following chapter.

They were about to read on when, glancing out of the window, Florestannoticed that they were entering the gates of Dusseldorf. Hastily, they stowed themanuscript in Florestan's bag and gathered their other effects together. At thecoach-house, they dismounted and strode off toward the BilkerstraBe.

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Metrical Consonance and Dissonance:

Definitions and Taxonomy

Florestan and Eusebius had intended to go home immediately to share their re-cent experiences with Chiarina, but as they approached their favorite coffee-house, the enticing aroma of fresh coffee wafted over them, and they determinedthat a few cups were just what they needed after their night in the coach. Theyentered and sat down at their usual table. Having ordered, received, and sampledtheir beverages, they propped the Prophet Bird's manuscript against the coffeeurn and continued to read where they had left off.


Several nineteenth-century theorists imply a conceptualization of musical meteras a set of interacting layers of motion, each layer consisting of a series of ap-proximately equally spaced pulses.1 Fetis's wording "frappe de trois en trois sur an

rhythme binaire" for example, implies a set of three layers: an underlying pulselayer, a layer that groups those pulses into twos (resulting in the rhythme bi-

naire), and a third layer that groups the pulses into threes. Hauptmann's (andafter him Riemann's) definition of syncopation as the interaction of two series('Reihen") of durations, and Riemann's discussion of the imposition on a meterof motives noncongruent "with that meter, similarly suggest a model of superim-posed layers of pulses.2 This model, which has been explicitly embraced by anumber of twentieth-century theorists, particularly by Maury Yeston, FredLerdahl and Raymond Jackendoff, Richard Cohn, and John Roeder, also un-derlies this study.3 In the following paragraphs, I elaborate upon the model andthe numerous concepts that grow out of it.


luisa balaguer

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Metrical Consonance am) Dissonance: Definition and Taxonomy 23

Florestan mused, "The conception of meter as a set of interacting layers ofmotion appeals to me because it suggests a link between music and our lives.Our heartbeat is an uninterrupted pulse that spans our entire life. That pulse isoverlaid with other more or less regular layers, some of them less continuousthan our pulse, many of them much slower—for example, our breaths, our foot-falls, our recurrent daily activities, and so on."

1, define the meter of a work as the union of all layers of motion (i.e., seriesof regularly recurring pulses) active within it. The layers that contribute to the

meter of a work can be divided into three classes: the pulse layer, micropulses,and interpretive layers. The pulse layer is the most quickly moving pervasive se-

ries of pulses, generally arising from a more or less constant series of attacks on

the musical surface. (The omission of a few pulses here and there does not seri-ously disrupt the pulse layer once it is clearly established.) More quickly mov-

ing layers, or "micropulses," may intermittently be woven into the metrical tap-

estry of a work as coloristic embellishments. Of greater significance are series

of regularly recurring pulses that move more slowly than the pulse layer. These

allow the listener to "interpret" the raw data of the pulse layer by organizing its

pulses into larger units. The pulses of each "interpretive layer" subsume a con-stant number of pulse-layer attacks; an interpretive layer can therefore be char-

acterized by an integer denoting this constant quantity. I refer to this integer n

as the "cardinality" of the layer, and to an interpretive layer of cardinality n as

an "n-layer."

I conceive of interpretive layers not as components of an abstract, "given"

metrical grid, but as perceptible phenomena arising from the regular recurrenceof musical events of various kinds. Interpretive layers often arise from a regu-

larly spaced succession of what Lerdahl and Jackendoff call phenomenal ac-

cents— "event [s] at the musical surface that give emphasis or stress to a moment

in the musical flow."4 Dynamic accent, shown in scores by markings like o f , f z , rf,

and by various hairpins and carets, is a particularly obvious type of phenomenal

accent. Such accentuation is, however, also produced by the placement of long

durations among short ones (agogic or durational accents), thickly texturedevents among more thinly textured ones (density accents), by dissonant events

among consonant ones, by registral high and low points (registral accents), by

the affixing of an ornament to a note, by changes in harmony and melody (new-

event accents) -—in short, by any perceptible deviation from an established pat-

tern.5 A succession of accents occurring at regular intervals—that is, the high-lighting of every nth member of the pulse layer — results in the establishment ofan interpretive layer of cardinality n.

The following musical excerpts, drawn from the music of Robert Schu-

mann, demonstrate the generation of interpretive layers by accentuation. In theleft hand of Example 2.1, regularly recurring dynamic accents carve a 6-layer

out of the sixteenth-note pulse (shown by the uppermost series of 6s). Registral

(or contour) accents, created by the low points within the left-hand line, rein-

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24 Fantasy Pieces

EXAMPLE 2.1. Intermezzo op. 4 no. 4, mm. 8-9

force this 6-layer. Another 6-iayer, coinciding with the dotted-quarter-note

beats in Example 2.1 (shown by the lower series of 6s), is created by durationalaccents (the longest note values in the right hand) and by new-event accents in

the harmonic domain (i.e., by the harmonic rhythm). In Example 2.2, one 6-layer (1= 8th) arises from a series of dynamic and durational accents; the dy-namically accented attacks within the first violin part tire also the longest dura-

tions. Durational and registral (low point) accents in the cello part, as well asnew-event harmonic accents (harmonic changes), create another 6-layer whoseattacks coincide with the downbeats of the notated meter.

Florestan said, "I am suddenly seized by an irresistible urge to order a sliceol Torte" He beckoned to a waiter, and ordered a three-layer Schwarzwalder-

kirschtorte. Carelully keeping the manuscript away from the icing, they continued

their perusal.

Left-hand durational accents contribute to the creation of a clear 6-layerin Example 2.3 (1= 8th). Regularly recurring density accents and new-event

harmonic accents reinforce this layer. In the uppermost voice of the first twomeasures of the excerpt, melodic new-event accents establish a 3-layer, whilethe left-hand half- and quarter-note attacks suggest a 2-layer.6 In Example2.4, registral accents (low points) create one 6-layer (l = 8th), and durational

accents (the quarter notes immediately following the sixteenth notes) create


EXAMPLE 2.2. String Quartet op. 41 no. 3, second mvmt., mm. 193-96


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Metrical Consonance and Dissonance: Definitions and Taxonomy V 25

EXAMPLE 2.3. Davidsbundler op. 6no. 2, mm. 1-4

Eusebius interjected, "The latter 6-layer is enhanced by one's perception of the

first quarter note in each measure as an appoggiatura." Florestan added, "True,

but my crescendo markings detract from the appoggiatura effect since they pre-

vent the pianist from tapering off in the usual fashion during the resolution. In

fact, if the crescendo markings are followed, the second quarter note in each

measure receives a dynamic accent, which results in yet another 6-layer." Euse-

bius said, "So many 6-layers! I think the pianist would have to choose to articu-

late just two of them; otherwise, every quarter-note pulse would be accented, and

from these undifferentiated pulses no 6-layers would clearly emerge!" They con-tinued to read:

The above excerpts raise a number of significant points about interpretive

layers. Example 2.1 bears out the earlier statement that omission of some at-

tacks of an interpretive layer does not significantly disrupt that layer; the 6-layer created by dynamic accents is perfectly perceptible although two expected

accents are missing.7 The examples also show that various accent types gener-

ally work together rather than in isolation to form interpretive layers. (I do notregard coinciding series of accents as distinct interpretive layers; rather, I re-

gard them as collaborating in the creation of a single layer.)

Finally, the above examples show the importance of pitch structure, specif-ically of change in the harmonic or melodic domain, in the formation of layers;

EXAMPLE 2.4. Davidsbundler op. 6no. 1, mm. 1-4

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26 Fantasy Pieces

EXAMPLE 2.5. Symphony no, 3, firdt mvmt., mm. 1—9

new-event accents in these domains are among the most frequent producers oflayers of motion. Not only surface-level melodic or harmonic change, but also

change below the surface forms layers of motion.8 A good example is found at

the opening of Schumann's Third Symphony (Example 2.5), where subsurface

melodic progression occurs at a regular rate; a rising arpeggiation of the tonic

triad is succeeded by a descending stepwise line, each pitch of both the rising

and the falling gesture occupying twelve eighth-note pulses.The above examples also reveal that accentuation is not the only factor that

can gather pulses together to form interpretive layers; a variety of musical

grouping techniques independent of accentuation may be active as well.9 Nota-

tional devices such as slurs and beams of consistent length, for instance, may

suggest interpretive layers. In Example 2.1, slurring reinforces the 6-layer pro-

duced in the left hand by dynamic and registral accentuation. In Example 2.3,the left-hand slurs contribute to the 6-layer created by durational, density and

harmonic new-event accents.

Eusebius observed, "As the author states, slurring can reinforce layers produced

by other means; it rarely, however, creates perceptible layers on its own. In Ex-

ample 2.2, for instance, I would not regard the recurring slurs in the first violinpart as forming a layer; there are so many other features that create prominent

layers that the effect of these little slurs is negligible."

Repetition of various types frequently creates interpretive layers. In Example2.1, a 2-layer (1 = 16th) arises from the regular recurrence in the left hand of par-ticular pitches — of C, then A in the first measure, and of E, then Ctt/Dt in thesecond. The repetition of patterns rather than individual pitches, be they me-

lodic, rhythmic, harmonic, or any combination of the three, contributes evenmore commonly to the creation of interpretive layers. Most of the passages cited

above illustrate such pattern repetition. In Example 2.1, the rhythmic pattern"quarter-eighth" in the first two beats of the right hand reinforces the 6-layercreated by harmonic change, as does the left hand's simultaneously presented

pitch and contour pattern (a complete neighbor figure followed by a downward

leap, an upward leap, then C-B). In Example 2.2, the repetition of rhythmic

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Metrical Consonance and Dissonance: Definitions and Taxonomy

EXAMPLE 2.6. 2-layers in the Presto in G Minor


patterns in all instruments reinforces the 6-layers. The second violin and viola

also establish 2-layers by repeated third- or fourth-oscillations in eighth notes.

In the first two measures of Example 2.3, exact repetition of pitches and rhythm

reinforces the 6-layer. In the next two measures, a repeated rhythmic pattern inthe right hand (a quarter followed by four eighths) has the same effect. In Ex-

ample 2.4, repetitions of rhythmic patterns reinforce the 6-layers, and in the

first six measures of Example 2.5, repetition of a two-measure-long rhythmicpattern corroborates the 12-layer. 10

Florestan, swallowing his last mouthful of Torte, commented, "In our works,

we have fully explored the many ways of producing layers of motion that the au-thor has mentioned. Do you recall our inventiveness with 2-layers (l = 16th) inthe original finale of our Sonata in G minor, op. 22? The generation of the 2-layerby dynamic accentuation is suggested in mm. 1, 2, 5, 6, 9, and 10, in all of whichwe stress the third sixteenth notes (Example 2.6a). In mm. 11-12 (Example2.6b), we articulate the 2-layer more clearly by a series of dynamic accents, and

reinforce that layer with slurs. In mm. 3-4 (Example 2.6a), 7-8, and 13-1-4, the

attacks of an eighth-note melody create a 2-layer. The same is true in mm. 99-106

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28 Fantasy Pieces

(Example 2.6c), and in the similar passages in mm. 129-36 and 337—44, where

the triplet eighths have exactly the same duration as the regular eighth notes inmm. 3—4 and 7—8.

"In m. 14, the 2-layer arises not only from melodic attacks but also from den-sity accents within the right-hand figure. Such accents also play a role in mm.

43—52, where every second sixteenth-note attack is thicker in texture (Example

2.6d). In these measures, pitch repetition in the uppermost voice is a second fac-

tor that contributes to the production of a 2-layer; the first two upper-voice duple

attacks in each measure are the same in pitch. Note repetition articulates the

2-layer even more clearly in mm. 107—18; in the sixteenth-note inner voice, suchrepetition marks off duple durations (F's in m. 107, Et's in m. 108, etc.). Many

other passages in the movement are based on 2-layers — remarkably many for a

movement ostensibly in 6/16 time — but the variety of methods of layer produc-tion m the movement is, I believe, exhausted by those that 1 have mentioned."

Eusebius, who had been pursuing his own train of thought, now queried, "Given

the many different means by which interpretive layers can be produced, wouldnot any piece of music be absolutely riddled with them?" Florestan said, "You are

right. I see that the author addresses this issue."

Layers of motion are ubiquitous m pieces of music. As listeners, how-

ever, we inevitably focus on those interpretive layers that are most perceptibleand filter out those that are relatively hard to hear. In many cases, the most

perceptible layers are those that are articulated by the greatest number of mu-

sical features. A layer expressed, for instance, only by pattern repetition willbe less perceptible than one delineated by pattern repetition in conjunction

with accentuation. Thus, in Example 2.4, consideration of pattern repetition

alone would uncover four patterns, each six eighth-note pulses in length, and

hence each potentially suggesting a 6-layer; one pattern begins with the low-

est bass notes, a second with the sixteenth notes, a third with the quarter

notes on the notated downbeats, and a fourth on the notated second beats. Ifwe take accentuation into account, however, as any listener would, two of

these layers move into the perceptual forefront: the layer formed by the re-

curring pattern beginning on the upbeats and by registral accentuation, and

the layer formed by the recurring pattern beginning on the downbeats in con-

junction with durational accentuation (and the annotated dynamic accentua-tion that most performers intuitively add to appoggiaturas and suspensions).Similarly, in Example 2.2, two potential 2-layers arise from repeated patterns

in the inner voices. One, the pulses of which coincide with metrically weak

eighth notes, is formed by repetition of the vertical interval pairs Fit/A andA/Ct, then E/Gt and Gt/Ctt, etc. The other, whose pulses coincide with quarter-

note beats, is formed by the repetition of the pairs A/Ctt and Ft/A, then Gl/Cttand Gi/E, etc. The latter of these layers is much more perceptible, for it is atleast partially reinforced by accents (duralional accents in the cello and dy-

namic accents in the first violin).

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Metrical Consonance and Dissonance: Definitions and Taxonomy 29

Eusebius observed, "The perceptibility of layers, of course, depends to a large ex-tent on the performer, who must decide which layers to bring out. Frequently,the composer's notation will make clear which layers are intended to be promi-nent. In Example 2.2, our placement of one of the 2-layers on the metrical beatsindicates that that layer is to be brought out. Had we wished the performer toemphasize the metrically weak 2-layer, we would have affixed dynamic accentsto its pulses." They read on:

Not always is mere quantity of articulative musical features an indicatorof perceptibility, for some features are more potent delineators of layers thanothers, and can form very clearly perceptible layers of motion independently ofother factors.11 One such feature is accentuation arising from harmonic change("new-event" accentuation in the harmonic domain). In most pre-twentieth-century music, such change takes place in a regular fashion, sometimes on thesurface level, sometimes below the surface. Layers of motion formed in thismanner, often termed "harmonic rhythms," are very easy for us as Western lis-teners to hear, perhaps because we are conditioned to attend primarily to pitch.Also of great perceptual significance are dynamic accents. These are perhapsthe most obvious of accents; many musicians immediately think of them whenthey hear the word "accent." Dynamic accents, like accents of harmonic change,often act in isolation to create prominent interpretive layers.12

Eusebius looked at his watch and said to Florestan, "Now that we have reachedthe end of a section, we should go home; Chiarina will be worried about us." Flo-restan responded, "We shall go very soon, but first I must wash down my Torte

with one more cup of coffee." He placed his order, and while they waited for thecoffee, they began the next section:


In the above examples, as in most tonal music, more than one clearly percepti-

ble interpretive layer is active at once. These layers interact in one of two ways:

they align (or "nest," to use Joel Lester's term) or they do not. A set of layersaligns when each pulse of each interpretive layer coincides with a pulse of every

faster-moving layer. This state of alignment always exists when only one inter-

pretive layer is imposed on a pulse layer. Two or more interpretive layers, how-ever, may or may not align with each other. I refer to the metrical state resultingfrom the alignment of interpretive layers as "metrical consonance." The appro-

priateness of this metaphorical use of a term traditionally applied to pitch restson the literal meaning of the word "consonance"; metrical consonance existswhen pulses sound together. The metrical state arising when interpretive layers do

not sound together can, applying the same metaphor, be termed "metrical dis-sonance.

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30 Fantasy Pieces

Before we investigate these two states more closely, let us briefly considerthe adjective "metrical." Its aptness is obvious when states of alignment or non-alignment result from the interaction of layers whose pulses are metrical beats,or beats above the level of the bar line (hypermetrical beats, or hyperbeats). But

what of sets of layers whose pulses are submetrical, in some cases not even no-tationally present (for instance, the micropulse arising from superpositions ofeighth notes and triplet eighth notes)? It might be argued that sets containingsuch layers should not be termed "metrical" consonances or dissonances. Since,however, I am defining meter as the union of all layers of motion active within acomposition, I include even these submetrical interactions under the terms

"metrical consonance or dissonance." In a later section, I introduce a series ofmore specific terms by which interactions of submetrical layers are distin-guished from interactions of larger scale.


Metrical consonance, the normal state of pre-twentieth-century tonal music, in-volves the aligned or nested presentation of interpretive layers whose cardinal-ities are multiples/factors of each other.13 What is usually termed "the meter" of

a work is in fact a particular consonance that functions as the normative metri-cal state of that work. Three-four meter, for instance, is a consonance consistingof a nested 6-layer and a 2-layer (1= 8th) imposed on an eighth-note pulse, six-

eight meter a consonance consisting of a nested 6-layer and a 3-layer imposedon the same pulse, nine-eight meter a consonance composed of a nested 9-layerand a 3-layer, and so on. I refer to the nested layers that form the normativemetrical consonance of a work as "metrical layers."

In clearly metrical music, one of the metrical interpretive layers generallyassumes particular significance for the listener, its pulses becoming reference

points for all rhythmic activity in the given work. The layer formed by thesepulses frequently, though not always, occupies a privileged position in the score,being rendered visually apparent by notational features such as bar lines andbeams. I refer to this layer (as does Joel Lester) as the "primary metrical layer,"and to the consonance that it creates in interaction with the pulse layer as the"primary consonance" of the work.14

Consonances can conveniently be labeled by ratios composed of the cardi-nalities of the interpretive layers involved, the highest number being statedfirst. Where the consonance arises from only one interpretive layer imposed ona pulse layer, the cardinality of that one layer suffices to characterize the con-sonance. Thus, in Example 2.2 the interaction of the metrical 6- and 2-layersproduces the primary consonance 6/2 (l=8th). In Example 2.3, the 2-layer(1= 8th) suggested in the bass in mm. 1-2 and clarified in mm. 3—4 (where it iscreated by subsurface, then surface melodic change) interacts with the metri-cal 6-layer to form the same primary consonance (6/2). The metrical 6-layer,however, also interacts with the 3-layer formed by melodic new-event, accents

to create the consonance 6/3.

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Metrical Consonance and Dissonance: Definitions and Taxonomy 31

Grouping and Displacement Dissonance

Although it contains two metrical consonances, Example 2.3 is by no means en-tirely consonant; the 3- and 2-layers do not align and hence result in a state ofdissonance. In Examples 2.1, 2.2, and 2.4, a sense of dissonance arises from thesuperposition of nonaligned 6-layers. We turn now to a closer investigation ofsuch dissonant states, which are the primary focus of this volume.

As nineteenth-century theorists already hinted, there are two basic ways inwhich nonalignment or dissonance between regular layers of motion can occur.First, dissonance can be formed by the association of at least two interpretivelayers whose cardinalities are different and are not multiples/factors of eachother.15 In several earlier writings, I labeled this type of dissonance as "type A."Here I adopt Peter Kaminsky's term, "grouping dissonance"—an appropriatedesignation, for this dissonance type arises from the association of nonequiva-lent groups of pulses.16

Grouping dissonances may be labeled with a "G" followed by a ratio of thecardinalities of the layers involved, the larger cardinality being listed first. Thus,in the first two measures of Example 2.3, the dissonance formed by the 3- and2-layers would be labeled G3/2 (1= 8th). If more than two interpretive layersare present, all of them can be listed in descending order in a similar format.

Florestan asked a passing waiter to bring some coffee beans. When the puzzledwaiter had laid a handful of beans on the table, Florestan said to the equally puz-zled Eusebius, "I thought we might find it easier to understand the author's de-scriptions if we constructed some little models. Why don't you build a coffee-bean model of the dissonance G3/2 while I build G5/3?"17 They both laid out arow of closely spaced coffee beans, denoting the pulse layer, then placed addi-tional rows of more widely spaced beans below to suggest the respective inter-pretive layers (Figure 2.1). After studying each other's models, they read on:

Grouping dissonance in pre-twentieth-century tonal music generally in-volves one of the metrical layers and one conflicting interpretive layer, or "anti-metrical layer." Other situations are possible (and occasionally do occur in prac-tice), for instance, dissonances composed of a metrical layer and more than oneantimetrical layer (see the section on "compound dissonances" later in thischapter), or dissonances involving two or more antimetrical layers in the ab-sence of metrical layers (see the unit on "subliminal dissonance").

Grouping dissonance invariably involves some alignment of attacks, thealignment occurring after a number of pulses generally determined by the prod-uct of the cardinalities of the interpretive layers. If in a grouping dissonanceGx/y, x and y have a common factor z, alignment will occur more frequently,namely after a number of pulses determined by the equation (xy)/z. Thus in thedissonance G9/6, alignment occurs at every 18th pulse (9 times 6, divided by 3,the common factor of 9 and 6), and in the dissonance G12/8, at every 24th pulse

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32 Fantasy Pieces

FIGURE 2.1. Grouping dissonances (G3/2 and G5/3)

(12 times 8, divided by the common factor 4). Atter Maury Yeston and

Gretchen Horlacher, I refer to a segment demarcated by the points of alignmentwithin a grouping dissonance as a "cycle."18

"The cycles of our dissonances G3/2 and G5/3," said Florestan with a glance atthe coffee bean diagrams (Figure 2.1), "would thus encompass six and fifteenpulses, respectively." Eusebius quickly verified these results, then said, "I wonder

if the author's rule would work if there were three interpretive layers. If I add a2-layer, for instance, to the five-against-three model, the cycle should by this rulecomprise 30 pulses (5 times 3 times 2)." When he added a 2-layer to his diagram,he found that the length of the cycle indeed corresponded to the product of thethree cardinalities. They read on:

I n spite of their characteristic periodic alignment, however, grouping dis-sonances are dominated by nonalignment. In a grouping dissonance Gx/y, there

is for every point of alignment a number of nonaligning pulses determined bythe formula (x+y)—2. In the dissonance G3/2, there are thus three nonaligningpulses for each point of alignment, in G4/3, five nonaligning pulses, and so


They verified the author's statement about G3/2 by looking once more at Euse-

bius's coffee-bean model (Figure Florestan pointed out that in G5/3 (Figure2.1b), there \vere (5+3)—2, or six nonaligning pulses between points of alignment.

Then Florestan remarked, "Grouping dissonance, which the author has dis-cussed in such dry arithmetical terms, appears in interesting and exciting ways in

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Metrical Consonance and Dissonance: Definitions and Taxonomy 33

EXAMPLE 2.7. G3/2 in the "PreambuLe"from Carnaval, mm. 28-32

our music, especially in the specific form G3/2. The author has mentioned yourpoignant application of this dissonance at the opening of the Davidbundlertanz

op. 6 no. 2 (Example 2.3). In the tenth piece of op. 6, I employ the same disso-nance, but in a much more impassioned vein. The passage beginning at m. 99 ofthe original finale of our Piano Sonata op. 22 (Example 2.6c) is another beautifulexample of G3/2." Eusebius added, "You used this dissonance with humorous ef-fect in the 'Preambule' from Carnaval. In that piece, the left hand's accompanimentpattern, suggesting a warped waltz, frequently establishes a 2-layer (1= quarter),while repeated right-hand motives maintain a 3-layer. This occurs in mm. 28 — 34(Example 2.7), more briefly in mm. 48—49, then at greater length in mm. 54—66.In most of the latter passage, you create the 2-layer not only with left-hand patternrepetition, but also with dynamic accents and harmonic changes. The dissonanceG3/2 returns once more, with exhilarating effect, in the rising sequential passagethat we discussed in Euphonia (Example 1.7b); at mm. 102 — 5, pattern repetitionand durational accents in the right hand as well as recurring sforzandos delineatethe metrical 3-layer, while left-hand pattern repetition and dynamic accents forma 2-layer." Florestan interposed, "We could both mention many more examples,but I am eager to read the author's description of the second type of dissonance."

1 he second basic type of dissonance involves the association of layers ofequivalent cardinality in a nonaligned manner; that is, dissonance of this typedoes not depend on the association of noncongruent layers, but merely on thedifferent positioning of congruent layers. For this type, I again adopt Kamin-sky's term "displacement dissonance" rather than the term "type B" employed inmy earlier studies.19 Much displacement dissonance takes the form of "synco-pation," which term, in its most common usage, designates a conflict between ametrical layer and an antimetrical layer formed by durational accents. The term"displacement dissonance," however, encompasses conflicts involving displace-ment produced in any manner.

Eusebius suggested, "Let us construct some models of displacement disso-nances. I shall build a dissonance in which 2-layers are misaligned, and you couldbuild one in which 3-layers are presented in nonaligned fashion." Thejf left the

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FIGURE 2.2. Displacement dissonances

pulse layers of their earlier models intact, but rearranged the coffee beans denot-ing interpretive layers as in Figure 2.2.They read on:

W'hereas grouping dissonance involves periodic intersection of layers, dis-

placement dissonance involves no intersection at all. .No matter how long two

identical but nonaligned interpretive layers are associated, they can never meet;

each pulse of the metrical layer is contradicted by a pulse of the antimetrical layer.

It is because of this very strong effect of nonalignment and contradiction that I

consider such associations of layers dissonant (unlike Yeston, who considers themconsonant on the basis of the numerical congruence of the constituent layers).

Most displacement dissonance in tonal music involves a metrical layer and

one antimetrical layer (although the possibility of larger numbers of constituentlayers exists whenever the shared cardinality is greater than 2; see the section

on compound dissonance later in this chapter). When a metrical layer is present

within a displacement dissonance, we generally perceive the antimetrical layeror layers as a shifting out of the "normal position" designated by the metricallayer; the pulses of the metrical layer, in other words, function as a series of ref-

erence points in relation to which the pulses of the antimetrical layer are per-

ceived as being displaced.20

Given the referential function of metrical layers, it is appropriate to mea-

sure the amount of displacement within a particular dissonance in relation tothose layers. I refer to the constant number of pulse-layer attacks that separates

the metrical and antimetrical layers throughout a particular displacement disso-

nance as the "displacement index." The displacement index is an integer be-tween 1 and x-1 (inclusive), where x is the value of: the shared cardinality. (Theamount of displacement must, of course, be smaller than the cardinality.)

34 Fantasy Pieces34

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Metrical Consonance and Dissonance: Definitional and Taxonomy 35

EXAMPLE 2.8. Papillon op. 2 no. 10, mm. 24-28

Does displacement proceed in a forward or a backward direction from the

pulses of a referential metrical layer? Measuring in the direction of musical flow

from these pulses intuitively seems more reasonable; I believe that it is possible

to hear virtually all displacements in a "forward" manner. There are, however,

displacement dissonances that can also be perceived in a backward direction —

dissonances whose antimetrical pulses can be heard as "early onset" in relation

to the following metrical pulses.21 This effect is most likely to arise when dis-

placed pulses occur closer to the end than to the beginning of measures. It

would be too hasty to conclude, however, that displaced pulses close to the end

of a measure are always perceived in relation to the following downbeats. In the

above passage from Schumann's tenth Papillon (Example 2.8), the accented

third beats do not give the impression of "early onset" in relation to the follow-

ing downbeats. There are two reasons why this displacement is more easily per-

ceived in relation to the preceding downbeats. First, m. 25, separated from the

preceding music by a rest, is clearly a beginning, and hence an obvious refer-

ence point for the displacement. Second, and more important, this displacement

is more likely to be heard in relation to the preceding downbeats because the

harmony during the displaced pulses is a continuation of that of the preceding

downbeats. Harmony appears to be the main factor that can counteract our in-

tuitive tendency to hear displacement in a "forward" direction.

My labeling system for displacement dissonances, though based on my as-

sumption that "forward hearing" is more natural for the listener, does take into

account the possibility of "backward hearing." I routinely assign to displace-

ment dissonances labels of the form "Dx+a," where "D" stands for displacement,

"x" is the shared cardinality of the interpretive layers, the plus sign denotes a

shift in a forward direction, and "a" is the displacement index —the amount of

displacement measured in pulse-layer attacks. When a backward interpretationis reasonable, I append a label of the form "Dx-a." Thus, in Example 2.1, I apply

to the displacement dissonance created by two nonaligned 6-layers the label"D6+3" (l = 16th); the points of initiation of the two 6-layers are consistentlyseparated by three sixteenth-note pulses. In Example 2.2, two 6-layers lie twoeighth-note pulses apart, measuring forward from the attacks of the referential

metrical layer; I therefore label the dissonance as D6+2. There is no reason to

hear either of these displacements in a backward direction. In Example 2.4,however, the label D6+4 (1 = eighth), suggesting forward displacement from the

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36 Fantasy Pieces

EXAMPLE, 2.9. "Paganini"from Carnaval, mm. 1-2

downbeats, should be supplemented by D6-2. Unlike in the earlier examples,the registrally accented third beats harmonically anticipate the following down-beats, resulting in an effect of backward displacement.22

Eusebius surveyed the coffee beans on their table (Figure 2.2) and noted,"The labels for the displacement dissonances that we have constructed would be

D2 + 1 and D3+2, respectively, or, if the musical context justified a backwardhearing, D2-1 and D3-1." Florestan said with some asperity, "I am growing tiredof all of these numbers. Must every metrical state be labeled with numbers? Ismetrical conflict only a matter of measurement and counting?" Eusebius calmlyreplied, "Whereas I, too, am not overly fond of numerical labels, I must admitthat the author's labels nicely encapsulate some of the properties of the various

metrical states. And perhaps the usefulness of the numerical labeling system willbecome clear later on in the manuscript." Florestan grunted and said, "Let us

hope so."At this point, Meister Raro walked in. They greeted him warmly, and urged

him to join them. When he had done so and had ordered his coffee, Florestanbriefly told him about their visit to the Rhythmic Quarter of Euphonia, abouttheir mysterious acquisition of the manuscript, and about what they had readthus far. So absorbed did they become in their conversation that they completely

forgot that Chiarina was awaiting them at home.When Florestan had explained displacement dissonance and the author's la-

beling system, Raro said, "Innumerable dissonances of this type exist in yourmusic. In 'Paganini' from Carnaval, the metrical 2-layer (1 = 16th) is articulated bythe octave leaps in the right hand (Example 2.9), and in mm. 9—15, repetition ofhigh notes adds further support to that layer. The dynamic accents and harmonicchanges in the left hand, however, establish a strong antimetrical layer, and hencethe dissonance D2 + 1 (which can here also be heard as D2-1). In the piece fromCarnaval that you named after Chiarina (Example 2.10), you express the metrical3-layer by harmonic change and by left-hand dynamic accents. A conflicting

3-layer arises from right-hand dynamic accents and new-event melodic accentson the upbeats, resulting in D3+2. In addition, you frequently associate the

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Metrical Consonance and Dissonance: Definitions and Taxonomy 57

EXAMPLE 2.10. "Cbiarina"from Carnaval, mm. 1—4

pulses forming the displaced layer with strong pitch dissonance against the pre-vailing harmonies, a factor that further accentuates the displaced layer." Eusebiusquietly interjected, "The melody notes on the upbeats belong to the harmoniesinitiated on the following downbeats. Do you not find that the displacement cantherefore be heard in a backward direction, and that a label of the minus form —D3-1 —would be appropriate?" Meister Raro agreed, then proceeded to mentionanother example: "In mm. 151—57 of the sixth Novellette (Example 2.11), the har-mony changes on each downbeat, so that the metrical 2-layer (1 = quarter) isclearly articulated. Dynamic accentuation, however, takes place on each upbeat,resulting in the dissonance D2+1."

Florestan said, "You have so far mentioned instances of displacement disso-nance from our early piano works. But there are many in our more recent com-positions as well. I included some exciting displacements in our Piano Quintetop. 44. Near the end of the first movement, there is an example of D4+3(l = quarter). Each of mm. 320—23 (Example 2.12a) is based on a different triad,resulting in a clearly expressed metrical 4-layer (1 = quarter). I set against it anantimetrical layer created by stabbing dynamic stresses of the final beats. In theagitato episode of the second movement of the same work (mm. 92 — 98), the har-monies again change at the beginning of each bar. All instruments, however, dy-namically stress the second quarter note, resulting in D4+1 (Example 2.12b). Inthe second Trio of the third movement (mm. 122—29), the dynamic accents

EXAMPLE 2.11. Novellette op. 21 no. 6, mm. 151-54

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within the -whirling sixteenth-note figure in the cello and violin articulate themetrical 4-layer (1 = 8th). The harmonies announced by the piano, however, con-sistently begin on the upbeats, establishing a strong antimetrical layer and hence

the dissonance D4+2. In a passage in the fourth movement (mm. 21—29), I sim-ilarly pitted the strings and the piano against each other to form D4+2 (^quar-ter). The dynamic stresses on the first of four repeated eighth-note chords in the

strings articulate the metrical layer, while the piano establishes an antimetrical

4-layer by harmonic change, dynamic stresses, and a repeated melodic patternof four rising steps."

Raro remarked, "Your symphonies, too, are rich in displacement dissonance.

In the second movement of the First Symphony, mm. 55 — 66, harmonic change isprecisely coordinated with the notated measure and thus articulates the metrical

3-layer (l = 8th). In mm. 55—59 in the high strings and woodwinds, dynamic

stresses and registral and durational accents on the second beats create an anti-metrical 3-layer, which is continued in the following measures primarily by regis-tral and durational accents; the result is D3+1. Similar passages are found in thefirst movement of the Second Symphony (mm. 50 — 57 and 174—202) and in thethird and fourth movements of the Fourth Symphony (mm. 9-14 and mm.39 — 57, respectively). At the opening of the second movement of your ThirdSymphony (Example 2.13), durational accents in the bass as well as a repeatedrhythmic pattern express the metrical layer. The durational accents on secondbeats within the cello and viola melody, however, create the illusion that thosebeats are downbeats, resulting in subtle D3+1 (1 = quarter)."

Eusebius, after pointing out that this passage illustrates the relative inconse-quence of layers formed by slurs, suggested that they should have their bever-ages replenished and then continue their reading. As it was d i f f i cu l t for all threeof them to see the manuscript at once, Florestan volunteered to read it aloud.

38 Fantasy Pieces

EXAMPLE 2.12. Displacement dissonance in the Piano Quintet op. 44

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Metrical Consonance and Dissonance: Definitions ant) Taxonomy 39

EXAMPLE 2.13. Symphony no. 3, second mvmt., mm. 1—4

"But please put a rein on your impetuosity and read slowly," begged Eusebius.

Florestan promised to read "in tempo comodo," and began:


Any combination of interpretive layers generates a rhythmic pattern consisting ofthe summation of the attacks of the layers — a "resultant rhythm," or resultant forshort.23 The resultant, which can be expressed as a series of integers (where each

integer represents a number of pulses) is a useful means of characterizing a givenmetrical state, for it encompasses the overall rhythmic information conveyed by

that state. In consonant associations of layers, the resultant is always equivalent tothe regularly spaced attacks of the fastest interpretive layer in the collection. Themore complex and interesting resultants of dissonant combinations also exhibit

regularity (the summation of regular pulses being, of necessity, regular as well).Resultant rhythms of grouping dissonances are recurrent palindromes, eachpalindrome occupying one cycle; the palindrome is the inevitable result of the su-perposition of layers of pulses equally spaced between points of coincidence,

Eusebius arranged the coffee beans so as to recreate the original grouping disso-nances G3/2 and G5/3, and they all verified that in both cases the resultantswithin each cycle were palindromic (Figure 2.3). Florestan continued:

Resultant rhythms of displacement dissonances are merely recursive ratherthan palindromic. In a typical displacement dissonance, including the metricallayer and one antimetrical layer, each segment of the recursive series containsonly two elements x and y, where x is the value of the displacement index andy is the difference between the displacement index and the shared cardinality.Thus, the resultant rhythm of D4+3 is "3—1-3—1 . . . ," and that of D5+2 is"2-3-2-3

Eusebius nimbly reorganized the beans again to show these dissonances, andthey together counted out the resultants (Figure 2.4). Florestan then said, some-

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FIGURE 2.3. The patuidromic nature of' resultant tt of grouping duuonancej (G3/2 and G5/3)

FIGURE 2.4. Rejiittantj aft)Lipliiceincnli)i,i,ii)nancej (D4+ 5ant) D5+2)

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Metrical Consonance and Dissonance: Definitions and Taxonomy 41

FIGURE 2.5. The relationship between G3I2 and its augmentation, G6/4

what hoarsely, "I need to wet my whistle. Eusebius, would you please takeover?" Eusebius took the manuscript and read:


Dissonances may be related in various ways. All dissonances related in a par-ticular way may be regarded as belonging to the same "family." Relationshipsbetween dissonances are frequently evident from a scrutiny of their labels. Thedegree of relatedness of two dissonances is best determined, however, by a com-

parison of their resultant rhythms; resultants, as encapsulations of the rhythmicactivity of dissonances, are appropriate bases of comparison.

The labels of the dissonances G3/2 and G6/4, for instance, are composed ofequivalent ratios, and thus suggest a close relationship between these dissonances.The relationship is clarified by comparison of the resultant rhythms, which re-veals that the rhythms are the same, although that of G6/4 is augmented.

Florestan and Raro verified the author's claim by juxtaposing diagrams of G3/2and G6/4 (Figure 2.5).

The same type of relationship exists between the displacement dissonances

D3+2 and D6+4 — and again the obvious numerical relationship between the la-bels enables us to predict the rhythmic relationship,

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42 Fantasy Pieces

FIGURE 2.6. The relationship between 1)5+2 and its augmentation, D6+4

Again, Florestan and Raro constructed appropriate models (Figure 2.6).

in general terms, the grouping dissonances Gx/y, G2x/2y, G3x/3y . . . belong to

the same family. The same is true of the displacement dissonances Dx+a,

D2x+2a, D3x+3a. ... I designate individual families of this type by the labels of

their simplest members (that is, the members whose labels are composed of the

smallest integers), placed within quotation marks to distinguish them from the

specific dissonance otherwise indicated by that label.24

Certain relationships are relevant only to displacement dissonances. For

example, Dx+a and Dnx+a, where n is a positive integer, are closely related, the

resultant of the latter dissonance being a simplification of that of the former.

By removing alternate coffee beans from the interpretive layers of the model of

D3+2, Raro created the dissonance D6+2 (Figure 2.7). He remarked, "The fact

that it is so easy to transform D3+2 into D6+2 certainly suggests that these dis-

sonances are closely related." Eusebius read on:

lust as closely related as Dx+a and Dnx+a are Dnx + (a+x), Dnx + (a+2x),. . . Dnx + (a+[n—l]x). All of the latter dissonances are simplified, gapped ver-

sions of Dx+a; each of them can be created by eliminating equally spaced pulses

from the antimetrical layer of a displacement dissonance Dx+a.

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Metrical Consonance and Definitions: Definitions and Taxonomy 45

FIGURE 2.7. The relationship between displacement dissonances D3+2 and D6+2

Florestan, who had grown increasingly restive during these algebraic para-graphs, smashed his fist on the table, scattering coffee beans in all directions, andshouted, "Is this a manuscript about music or about mathematics? I am sick to

death of these numbers and x's andy's!" Eusebius, furtively glancing at the otherpatrons who were staring in their direction, soothingly said, "Perhaps we canbetter understand this last passage, too, with the help of some coffee-bean mod-

els." Raro beckoned to the waiter to bring more coffee, then began to restore thecoffee-bean model of D3+2 (Figure 2.8a). When he had done so, he again re-moved alternate beans from the metrical layer, then also removed from the anti-metrical 3-layer those alternate beans that had remained in place during his con-struction of D6+2 (Figure 2.8b). They pondered the result, and Raro observed

that the appropriate label for the newly created relative of D3+2 was D6+5. Eu-sebius smiled at Florestan and said, "Permit me to point out that we have justverified one of the author's formulas. The author stated that Dx+a and Dnx +(a+x) are closely related. We have before us the case where x is equal to 3, and nand a are both equal to 2; D3+2 is related to D(2x3) + (2+3), or D6+5." Florestanonly frowned and motioned to Eusebius to continue his reading.

I he members of such families of displacement dissonances differ in thenumber of antimetrical pulses sounding within any arbitrarily selected time-span, and hence also in the number of metrical pulses that are explicitly contra-

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44 Fantasy PiecesLECES

FIGURE 2.8. The relationship between displacement dissonance D3+2 and D6+5

dieted. I refer to displacement dissonances in 'which relatively many metrical

pulses are contradicted as "tight" dissonances, and those in which relatively fewmetrical pulses are contradicted as "loose." I regard Dx+a as a "tight" relative of

the other dissonances listed above, and those dissonances, conversely, as "loose"

relatives of Dx+a.

Given two displacement dissonances, relationships between them based on

tightness and looseness may often be recognized from their labels by the exis-tence of a constant difference between cardinality and displacement index.

Thus, D12+7 and D6+1 may immediately be identified as relatives, because the

differences between both their respective cardinalities and their respective dis-

placement indices is 6.

Eusebius observed, "The latter remark applies to the related dissonances D3+2and D6+5 (Figure 2.8), the difference between both the cardinalities and the dis-

placement indices being 3." Raro added, "And D6+5 is a tight relative of D3+2,D3+2 a loose relative of D6+5." Florestan, who, having begun to realize that theauthor's numerical labeling system had its advantages, was gradually regaining

his composure, now guffawed, "No doubt old Wieck frequently applied the des-ignation 'loose relative' to Eusebius and me!" Raro and Eusebius joined in his

laughter, -whereupon the latter continued to read:

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Metrical Consonance and Dutsonance: Definitions and Taxonomy >? A 5

/I final type of family of displacement dissonance is the entire group of pos-sible displacements for a particular cardinality, from Dx+1 through Dx+n (wheren is equal to x—1). Dissonances belonging to a family "Dx" are not related byvirtue of similar resultant rhythms, but simply by their shared cardinality.


It is important in musical analysis to be able to recognize relationships be-tween dissonances; but it is equally important to be able to recognize differ-ences between them. With the distinctions between grouping and displacementdissonance, and between tight and loose displacement dissonances, I have in-troduced two significant types of differentiation. In the following paragraphs, Idraw attention to additional distinctions that are useful in the analysis of metri-cal dissonances.

Direct and Indirect DLuonance

So far, I have considered only dissonances formed by the superposition of lay-ers of motion. It is also possible, however, for effects of dissonance to beachieved by the mere juxtaposition of layers. I refer to dissonance resultingfrom superposition as "direct dissonance," and that resulting from juxtapositionas "indirect."26 Indirect dissonance exists because of our tendency as listeners tomaintain an established pulse for a short time after it is discontinued in actual-ity.26 When two noncongruent interpretive layers x and y, or two nonalignedcongruent layers are juxtaposed, the listener inwardly continues the first layeras the second begins, so that there arises a brief but clearly perceptible conflictbetween the mentally retained first layer and the actually sounding secondlayer. The actual duration of indirect dissonance varies from passage to passageand from listener to listener. If the second layer persists, it will likely erase thememory of the first and hence dissolve the indirect dissonance after a fewpulses. This adjustment is particularly easily made in the case of indirect dis-placement dissonance. The horizontal confrontation of a given layer of motionwith a differently aligned but equivalent layer results in a brief effect of stam-mering or interruption, but the new layer, a mere repositioning of the earlierone, quickly effaces the memory of the original placement.

Indirect dissonance is inherent in all direct dissonances. At the inception ofa direct dissonance, the antimetncal layer clashes not only with the portion ofthe metrical layer on which it is superimposed, but also with the pulses of themetrical layer that immediately precede it. Similarly, when a direct dissonanceends, the listener's mental maintaining of the antimetrical layer continues thedissonance indirectly for a few pulses. 4*

Eusebius looked up and said, "Direct dissonances, then, do not have sharpedges, so to speak; they do not end abruptly, but yield to consonance through

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46 Fantasy Pieces

an intermediate stage of indirect dissonance." Raro remarked, "The opening ofyour second Davidsbndlertanz illustrates this point (Example 2.3); the 3-layer isnot articulated in m. 3, but the listener would likely maintain it at least throughthat measure, so that the direct dissonance G3/2 of mm. 1—2 would continue in-directly." Florestan said, "Indirect dissonances apart from those embedded indirect dissonances are common in our music. The agitato passage from the sec-ond movement of the Piano Quintet that 1 mentioned earlier (Example 2.12b)is a good example; the indirect dissonance created by juxtaposition of dupleand triplet eighth notes adds even greater complexity to this displaced passage.Another relevant example is found in Eusebius's piece entitled 'FreundlicheLandschaft,' the fif th of the Waldscenen op. 82. In mm. 14-15, you abruptly jux-tapose the hitherto prevalent triplet-eighth-note pulse with duple eighth notes."Eusebms added, "And I render this indirect dissonance direct on the secondbeat of m. 16. But. now let me read the next section, which appears to deal witha related topic."

Surface-Level and Subliminal Dissonance

Closely related to the idea of indirect dissonance is that of subliminal disso-nance— a class of dissonance that is particularly common in Schumann's music.Subliminal dissonance arises when all musical features — accents, groupings,etc. — establish only one interpretive layer, while the context and the metricalnotation imply at least one conflicting layer. The implied interpretive layerwithin such dissonances is usually the primary metrical layer, and the stronglyarticulated layer an antimetrical one. For instance, when in a work in three-fourtime there appears a passage in which accents and grouping organize the quarter-note pulse only into an antimetrical 2-layer, then the interaction between the no-tationally expressed 3-layer and the strongly articulated 2-layer results in thesubliminal grouping dissonance G3/2. Similarly, if m a work in three-four timethere appears a passage in which no musical features support the primary met-rical layer, but many features express a nonaligned 3-layer, then there exists astate of subliminal displacement dissonance.

Subliminal and indirect dissonances are similar in that they involve no ac-tual superimposing of conflicting interpretive layers. Furthermore, the cate-gories overlap in that each subliminal dissonance must begin with an indirectdissonance arising from the intersection of a metrical and an antimetrical layer.Whereas indirect dissonance, however, is a short-lived surface-level phenome-non occurring at intersections of conflicting layers of motion, subliminal disso-nance is a deeper-level conflict that may (although it need not) endure for longperiods. Furthermore, whereas indirect dissonance arises from the listener'sbrief maintaining of an abandoned interpretive layer, subliminal dissonancecannot, except in brief instances, be assumed to result from such mental main-taining. As was mentioned above, it is a listener's tendency to maintain an aban-doned layer for only a Few pulses, and then to be captured by whatever new in-terpretive layer the composer has offered. It is unlikely that a listener would

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Metrical Consonance and Dissonance: Definitions and Taxonomy 47

EXAMPLE 2.14. Faschingsschwank aus Wien op, 26, first mvmt., mm. 87-90

indefinitely maintain a layer — even the primary metrical layer—if it remainedunarticulated for an extended period of time.

Because they involve only one obvious interpretive layer, subliminally dis-sonant passages can easily take on the semblance of consonances. It is the per-former's duty to ensure that this does not occur. In many cases, the performercan subtly stress a heavily contradicted and otherwise unarticulated primarymetrical layer; strongly stated antimetrical layers will certainly remain audible,and the performer's gentle reminders of the suppressed metrical layer will cre-ate a perceptibly dissonant effect. Obviously, the perception of subliminal dis-sonance depends to a much greater extent on signals sent by the performer thandoes the perception of indirect dissonance. The longer the subliminal disso-nance lasts, the harder the performer must work to convey to the listener asense of conflict and tension.

Some writers have suggested that there is in fact nothing that the per-former can do to actualize subliminal metrical conflicts—that they are merelynotational curiosities, symbolic rather than real.27 Composers who so tortuouslynotated such conflicts, however, surely did not mean them to be a secret be-tween themselves and the performer, but rather wished performers to commu-nicate them. The performer must encourage listeners to join him or her in sens-ing a subliminal metrical dissonance instead of simply giving themselves over tothe new and different state of consonance that the musical surface suggests,

Florestan said, "The author is right. We took great pains to notate subliminaldissonances. For instance, in the first movement of the Faschingschwank MU Wien,

I could so easily have notated mm. 87—126 in recurrent metrically consonant al-ternations of half notes and quarter notes (see Example 2.14). And in the finaleof the Piano Concerto op. 54, I could have notated mm. 188-228 —surely mymost celebrated example of subliminal dissonance —in three-two meter. But in-stead, I employed in both cases a much more cumbersome notation involving nu-merous ties and bar lines that conflict with the apparent meters. I would certainlynot have wasted so much time and ink if I had desired the performer to play, andthe listener to hear, metrically aligned chords."

Eusebius said, "The examples of subliminal dissonance that you have justmentioned are among the most extensive in our oeuvre. There are, however, as the

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EXAMPLE 2.15. Subliminal dissonance in the Piano Sonata op. II, fourth mvmt.

author points out, a great many other instances of such dissonance in our works.

At the beginning of the coda of the finale of our Piano Sonata op. 11 (mm.

407-28), I take care to establish the primary consonance 6/2 (l = 8th) very clearly

by reiterating a dotted figure occupying two eighth-note pulses, thus setting up

Florestan's subsequent indulgence in some striking metrical dissonance." Raro in-terjected, "The obsessive repetitions of rhythmic patterns that are so common in

your music surely occur for just such reasons: to establish the metrical layers

strongly enough that subsequent conflicts against them will be more easily per-

ceptible." Eusebius continued, "In this case, the conflict takes two forms: first, asubliminal displacement dissonance (D2+1), then a subliminal grouping disso-

nance (G3/2), where 1 is equal to an eighth note. In mm. 429—37 (Example 2.15a),

Florestan ceases to articulate the metrical 2-layer, while establishing a displaced

2-layer by harmonic changes and sustained melodic attacks in both hands. In mm.

438—49, he alternates segments of metrically uninterpreted eighth-note scales

with two-measure arpeggiating segments, within which dynamic accentuation andmelodic patterns organize the eighth-note pulse into a 3-layer. In mm. 450-57, he

vehemently and continuously announces the 3-layer; these measures, governed onthe surface by the consonance G6/3, are subliminally dissonant (Example 2.15b).The cadential V-I harmonies that Florestan places on the downbeats of mm.

458—61, though they strongly assert the metrical 6-layer, are noncommittal with

respect to its subdivision into a 2- or 3-layer, and only the pair of eighth notes onthe upbeat to the final chord reestablishes the metrical 2-layer — too late fully to

wipe out the subliminal dissonance!""Ha, Euscbius, that was a bold ending!" shouted Florestan. He continued,

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Metrical Consonance and Dissonance: Definitions and Taxonomy 49

EXAMPLE 2.16. "Grillen"from Phantasiestucke, mm. 61-72

"One of my favorite instances of subliminal and also indirect three-against-twodissonance occurs in 'Grillen' from the Phantasiestucke (Example 2.16). Before m.61 the metrical 3-layer is quite clearly perceptible. In the new section beginningat that measure, however, I no longer articulate the metrical layer. The new-event

harmonic accents suggest a 2- rather than a 3-layer (1 = quarter), resulting in sub-liminal G3/2. Beginning with the last beat of m. 66, I hint at a resurrection of the3-layer; pattern repetition (pitch and rhythm) suggests two pulses of a 3-layer(which is not, to be sure, aligned with the notated measure). But I do not allowthis layer to come to full fruition; I dynamically stress the last quarter note of thesecond group of three (m. 68), thus curtailing it to a duple group. The result isadditional subliminal G3/2.28 I continue the 2-layer begun with the dynamic ac-cent, and the subliminal dissonance, until the last two bars of the phrase, wherethe final cadence of the section firmly reestablishes the metrical 3-layer." Euse-bius interjected, "You paradoxically change the time signature to two-four nearthe first attempt at reassertion of the metrical 3-layer (m. 68), and revert to three-four notation while the 2-layer is, for the moment, being confirmed (mm. 69-70) —a typically Florestaman 'Grille'!29

"Do you remember the third of the Nachtstucke, op. 23?" Eusebius continued."It is metrically a straightforward piece, except for a brief interlude moving insteady quarter notes (mm. 165—204), which contains much subliminal disso-nance. A rising scalar passage leading to fanfare-like cadences (Example 2.17a)continues the metrical 3-layer that was so clearly in effect in the preceding sec-tion. We answer this section by another, based on falling scales, during whicha 2-layer is established by harmonic changes and reinforced by slurring; the

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EXAMPLE 2.17. Subliminal dissonance in Nachtstucke op. 23, no. 3

3-layer disappears from the musical surface (Example 2.17b). This passage thusillustrates the subliminal dissonance G3/2. After we restate the rising scalar pas-sage (and reassert the metrical 3-layer), we continue with a segment that fuses el-ements of the preceding two, combining rising scales with a 2-layer (Example2.17c); the rising scales are imitated at two-beat intervals, and groups of twoquarter notes are slurred together. Nothing within this segment articulates themetrical 3-layer, resulting in a continuation of subliminal G3/2. A final statementof the original rising passage concludes the interlude." Raro pointed out, "Thefact that the clearly triple rising passage recurs throughout the section remindslisteners of the metrical 3-layer and thus facilitates the perception of the sublim-inal dissonance during the duple passages."

Raro continued, "Eusebius mentioned Florestan's usage of subliminal disso-nance very close to the end of a work — the Sonata op. 11. Even bolder are thesituations where you start a work with subliminal dissonance, that is, without es-tablishing what is to become the primary metrical layer. The opening of the finaleof the Piano Sonata op. 1 1 is an example; it could give the impression of being intwo-four time, because the main harmonic changes take place at two-quarter-note intervals (see Example 5.10). The notated 3-layer does not make a clear ap-

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EXAMPLE 2.18. Symphony no. 3, fifth mvmt,, mm. 46-54

pearance until the second section (m. 17). The subliminal dissonance at the endof the movement belongs to the same family as that with which it begins ('G3/2'),resulting in a pleasing unity." Florestan interjected, "You mentioned that theopening 'could give the impression of being in two-four time.' You are right; but agood performer should ensure that the primary metrical 3-layer, and hence theG3/2 dissonance, is audible. A very slight stress on the downbeats would allowthe listener to perceive a delicious hovering between two meters rather thanstodgy, square duple time."

Eusebius said, "Additional movements that begin with subliminal dissonanceare the second movement of the Piano Sonata op. 14, the Scherzo of the StringQuartet op. 41 no. 2 (see Example 5.9b), and the Scherzo of the Piano Quintet.In the latter movement, the scale figures sound like upbeats, and the chords, be-cause they carry new-event harmonic, density, and durational accents, sound likedownbeats. These apparent downbeats are not coordinated with the notatedones, which always fall in the midst of the 'upbeat' scales. The resulting sublimi-nal dissonance, using the author's labeling, is D12+9 (l = 8th). In the coda (m.258), we for the first time align one of the thick chords with the notated down-beat to create a sense of triumphant resolution —an effect which would not havebeen possible without the subliminal displacement dissonance earlier." Florestanremarked, "Do you recall how Chiarina used to place subtle stresses on the no-tated downbeats at the opening of this movement, and how the string players fol-lowed suit in their subsequent scale figures? I felt that these stresses were appro-priate as long as they remained subtle; I would have objected if they had been sopowerful as to suggest that they were notated dynamic accents!"

Eusebius resumed, "I must mention one of your more recent examples of sub-liminal dissonance. In mm. 45-46 of the finale of the Third Symphony (Example2.18), you establish a displaced 4-layer (l = quarter), and the dissonance D4+1, bydurationally accenting the second quarter-note pulse of each measure. At m. 47,you supply a dramatic cadence on a downbeat, but even as the cadence occurs,you initiate a new theme in the horns, whose durational and dynamic accents con-tinue the displaced 4-layer and the dissonance. You confirm the antimetrical layerin the full orchestra at mm. 48-51 and push the metrical layer mercilessly belowthe surface. At m. 52, you abruptly bring that layer into play again by placing du-rational and harmonic new-event accents on the notated downbeats."


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EXAMPLE 2.19. Faschingsschwank aus Wien op. 26, fifth mvmt., mm. 23-29

They listened inwardly, with smiles of admiration, to Florestan's thrillingpassage, whereupon Raro said, "I wish to return once more to the subject of sub-liminal grouping dissonance. As the examples that we have mentioned indicate,associations of 2- and 3-layers are especially common in your works, both on thesurface and subliminally. But you do occasionally indulge in associations of lay-ers of other cardinalities. I recall one subliminal example from the last movementof the Faschingsschwank op. 26 (Example 2.19). The movement begins with theprimary consonance 4/2 (l = 8th). You present the metrical 4- and 2-layers withparticular insistence at mm. 17-25; surface harmonies alternate in two-eighth-note pairs, and in mm. 21-25, the larger-scale harmonic changes occur at four-eighth-note intervals, on the notated downbeats. At m. 25, you whimsically in-crease the length of the surface pattern of harmonic change by one eighth note,and simultaneously eliminate the metrical layers, resulting in a 3-layer and in theindirect and subliminal dissonances G4/3 and G3/2." Eusebius said, "Anothersubliminal grouping dissonance involving layers of cardinalities other than 2 or 3occurs in the Study op. 3 no. 4 (Example 2.20), where a 5-layer created by dy-namic accents abruptly intrudes on a passage that has adhered to the metrical6-layer. The metrical 6-layer is abandoned during the section containing the5-layer, so that the dissonance (G6/5, l = 8th) is indirect and subliminal. Ofcourse, we cannot take credit for this passage: the conflict is already present inthe Paganini Caprice on which our study is based. But we should continue withour reading. Meister Raro, would you please take a turn?" And Raro read:

EXAMPLE 2.20. G6/5 in Study op. 3 no. 4, mm. 9-13

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Metrical Consonance and Dissonance: Definitions and Taxonomy 55

Low-level, Mid~level, and High-level Dissonance

We can distinguish different levels of metrical dissonance on the basis of the rel-ative durations of the pulses that are organized by the constituent layers. Low-level grouping dissonances are formed by the association of noncongruent sub-divisions of metrical beats. In many cases, the "micropulse" underlying such

dissonances is not articulated within any single voice but is merely the resultantof the pulses of different voices. Low-level displacement dissonances are thosewhose shared cardinality is smaller than the value of a metrical beat. Even suchlow-level displacement dissonances are more than minor rufflings of the metri-cal surface: each pulse of a metrical layer is contradicted (whereas in low-levelgrouping dissonances the conflicting layers merge at some of the metrical beats).

"Eusebius" from Carnaval, with its seven-against-two conflicts, is a goodexample of low-level grouping dissonance. The implied micropulse is one-four-teenth of a half note; the right hand frequently organizes this implied pulse into

groups of two (eighth-note septuplets), while the left hand presents groups ofseven (quarter notes). Some measures present a low-level indirect grouping dis-sonance based on an implied micropulse of one-fifteenth of a half note, i.e., jux-

tapositions of quintuplet sixteenth notes and triplet eighths. Further interestingexamples of low-level grouping dissonance are found in the last movement ofthe Fantasy op. 17 (mm. 72 — 79), where Schumann follows a metrically conso-

nant chordal passage with eight measures of delicately traced two-against-three,four-against-three, and five-against-six dissonances,

"Such effects are by no means restricted to our piano music," Florestan said."At the recapitulation of the slow movement of the First Symphony (m. 78), the

violins and violas engage in a three-against-two conflict at the thirty-second-notelevel. In the first episode in the second movement of the Piano Quintet (mm.29 — 61), the first-violin melody is accompanied by persistent eighth notes in thesecond violin and viola combined with triplet quarter notes in the piano, resulting

in low-level three-against-four dissonance. The piano part contains low-levelthree-against-two dissonance as well; harmonic change determines a 3-layer (es-pecially from m. 32 onward), and density accents, occurring on every secondtriplet, determine a 2-layer."

Raro drew their attention to a low-level displacement dissonance in the fi-nale of the Piano Quintet (see Example 4.12). "In mm. 224-28," he pointed out,

"there are two nonaligned layers moving in quarter notes (i.e., twice as fast as theprimary metrical 2-layer). The displacement index is a mere eighth note, and theresultant rhythm moves in eighth notes as well." Florestan reminded them thatmany of their song accompaniments consisted of slightly displaced quickly mov-ing layers. "'Schone Wiege,' op. 24 no. 5," he stated, "begins with such a pattern.The left hand expresses the metrical layer while the attacks of the right consis-tently occur an eighth note later. During a later section, at 'Wahnsinn wuhlt inmeinen Sinnen'. . . ." Florestan abruptly sank into brooding silence. Raro and Eu-sebius gazed at him sympathetically; then the former picked up where Florestan

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EXAMPLE 2.21. Piano Trio op. 80, first mvmt., mm. 404-14 (piano part)

had left off, saying, "During that later section (see Example 6.12), the displace-

ment moves to an even lower level; the two hands state the same line a sixteenthnote apart." Eusebius continued, "Florestan placed a particularly complex low-level dissonance near the end of the first movement of our Piano Trio op. 80 (Ex-

ample 2.21). The duplet eighth-note layer beginning in m. 402 results in low-levelindirect grouping dissonance against the established triple eighth-note pulse; thisdissonance can be labeled as G3/2 (1 = 16th). At m. 406, Florestan initiates low-

level displacement dissonance, the two hands of the piano part stating the samemelody in duplet eighth-note durations, a sixteenth note apart. Florestan mo-mentarily resolves this dissonance (D3 + 1.5) at m. 410, but reinstates it after one

measure."30 Raro said to the still silent Florestan, "At m. 410, you set into motiona somewhat higher-level dissonance — a dissonance involving different groupingsof the duplet eighth-note pulse; you juxtapose the established 6-layer (l = 16th)with a 9-layer, created by slurring three duplet eighth notes together, and by dy-namic stress and melodic pattern repetition. The resulting dissonance, G9/6, is anaugmentation of that at m. 402. Indirect G9/6 reappears when you reestablish the

6-layer at m. 418."Florestan remained unresponsive. Raro shrugged and began to read the next

section of the manuscript:

Dissonance at high levels could be termed "hypermetrical," as it involveslayers moving more slowly than the primary metrical layer.31 In Schumann's


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EXAMPLE 2.22. Waldscenen no. 1 ("Eintritt"), mm. 1-8

music, hypermetrical dissonance seems to be relatively rare; like much nineteenth-century music, his is dominated by undisturbed four-bar hypermeter. Some of

his works do, however, contain indirect and subliminal dissonance at high lev-els. The beginning of the first piece of the Waldscenen op. 82 (Example 2.22) il-lustrates subliminal hypermetrical displacement dissonance.32 The second four-

bar hypermeasure is expected to begin with m. 5. Instead, it begins two beatsearlier, in the middle of m. 4, the point of early onset being dynamically ac-cented. We could label this dissonance between expected and actual four-bar

hypermeasures as D16+14, or D16-2 (l = quarter), the minus sign designatingthe effect of premature initiation of the second hypermeasure. The dissonancecontinues through the first ending; the second hypermeasure, which "should"conclude at the end of m. 8, actually ends in the middle of that measure. The

second half of m. 8 appears to initiate a repetition of the first hypermeasure, twobeats too soon. The actual restatement of the first measure reestablishes, with asurprising stammer, the original hypermetrical 16-layer.

Florestan, who had emerged from his gloom, said, "If this excerpt is simplyan example of backward displacement by two quarter-note pulses, why is the ca-dential melody of m. 7 not displaced in relation to that of m. 3?" Eusebius brieflymulled over the music, then responded, "I believe it is because of the presence ofan 'extra' chord at the beginning of m. 7. The dotted portion of the cadential mo-tive could easily have begun during the F major harmony in the second half of m.6 (with the notes C and F in the melody); the C major harmony with the eighth-note turn figure above it could then have followed directly at the beginning of m.7, and the resolution to F major could have occurred on the third beat of thatmeasure, resulting in a displacement with respect to m. 3."

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Raro said, "Not all of your metrical and hypermetrical manipulations, then,can be explained by the author's theories." He continued, "Another high-leveldissonance is found in the passage from the finale of Faschingsschwank that we dis-cussed earlier (Example 2.19). In m. 25, the subliminal dissonances G4/3 and

G3/2 (l = 8th) coincide with a subliminal and indirect hypermetrical dissonance:four-bar hypermeasures yield to three-measure hypermeasures (mm. 25—28,28—31, 31—34, and 34-37), whereupon four-bar groups are reinstated. The re-

sult is a nice correspondence between the mid- and high-level four-against-threedissonances — or, to use the author's labeling, between two members of the family'G4/3'(G4/3andG16/12)."

Eusebius said, "I must mention one more indirect hypermetrical dissonance,from the finale of our Fourth Symphony. The exposition is dominated by two-and four-bar hypermeasures. Near its end, we present rocketing rising-scale se-quences in two-bar waves (mm. 67—68, 69-60, 71-72, and 73 — 74). The final,cadential hypermeasure of the exposition, however, is three measures long, the"extra" measure being our repetition of m. 75 an octave lower (Example 2.23).33

A measure of silence after m. 77 would have rendered the end of the expositionmuch more stable. The instability (or high-level grouping dissonance) resultingfrom the three-bar unit is appropriate tor it propels the music across the doublebar line, either back to the opening of the exposition or onward into the develop-ment section. I find the latter continuation especially effective. Whereas the re-turn of the opening at the first ending immediately restores unambiguous two-

and four-bar hypermeter (because the listener already knows how to parse thisfamiliar music), the first bar of the development section has an ambiguous status;

56 Fantasy Pieces

EXAMPLE 2.23. Symphony no. 4, fourth mvmt., mm. 75-85

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it is not certain whether it belongs with the previous three bars as the final bar of

a four-bar hypermeasure, or whether it is to be interpreted as the beginning of a

new hypermeasure. The possibility of the former interpretation welds the open-ing of the development section onto the end of the exposition."

Florestan interjected, "By m. 82, the ambiguity is resolved; in retrospect it isclear that the first four bars of the development section form a four-bar hyper-measure. The succeeding fugato passage, however, introduces additional hyper-

metrical conflict: the fugal entries take place at three-measure intervals. Thus wepick up on the three-bar layer of motion suggested at the end of the exposition.The juxtaposition of three- and four-bar hypermeasures results in clearly per-

ceptible indirect hypermetrical dissonance."34

They sipped some coffee as they let this striking passage move through their

minds. Then Raro continued his reading:

Most of Schumann's metrical dissonances lie at levels between the two ex-

tremes of micropulse and hypermeter; they are formed by the interaction ofmetrical and antimetrical layers, as defined above. It is on these mid-level dis-sonances that I focus in this study, although I also refer to higher- and lower-

level dissonances where they are significant within the overall metrical struc-ture of a given work.

Strong and Weak Dissonance

Whereas it is intuitively obvious that metrical dissonances are not all of equalintensity, it is by no means obvious precisely how the intensity of dissonances

should be ranked. I make no attempt to rank the intensity of dissonances of dif-ferent types (i.e., grouping and displacement dissonances); there is no reason to

assume that grouping dissonances are inherently more dissonant than displace-ment dissonances, or vice versa. Individual dissonances within each basic typecan, however, be said to be more or less inherently dissonant than others. One

factor that determines inherent intensity of grouping dissonances is length ofcycle; the more pulses elapse before attacks of the constituent layers coincide,the more intense the dissonance. Thus, G5/4, with a 20-pulse cycle, is inherentlymore dissonant than G3/2, with a 6-pulse cycle.35

A basic principle governing inherent intensity of displacement dissonancesappears to be proximity to consonance; the more closely a given dissonance ap-proaches a state of alignment, the more strongly dissonant it is.36 In numericalterms, dissonances whose displacement indices are 1 or x-1 (where x is theshared cardinality) are the most intense. Another factor that affects inherent in-tensity of displacement dissonance is relative tightness. Since tight dissonancescontradict the metrical layers more frequently, they are perceived as more in-tensely dissonant than loose dissonances.

The inherent intensity of a given dissonance is also determined in part bythe number of pairs of noncongruent layers that it contains; the more such pairs

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there are, the more intensely dissonant the given collection. This statement ap-

plies primarily to grouping dissonances37 but is, to some extent, also relevant to

displacement dissonances. Within a work in six-eight time, for instance, a com-

bination of displacements by two and by three eighth notes, resulting in the dis-

sonances D6+2 and D6+3, would be more intensely dissonant than either of

those dissonances alone. Paradoxically, however, a combination of all possibledisplacements of a given cardinality is not as intensely dissonant as any of the

less exhaustive combinations. The association of all possible displacements re-sults in accentuation of all members of the pulse layer, and hence in the virtual

elimination of an effect of nonalignment or dissonance.

Florestan remarked, "I am reminded of our earlier discussion of the first Davids-

bundlertanz (Example 2.4), where the abundance of 6-layers could produce the

result that the author mentions." Eusebius added, "Is the middle section of 'Es-

trella' from Carnaval perhaps another illustration of the latter statement? In youreffort, Florestan, to render the displacement dissonance particularly intense by

multiplying the displaced layers, did you nullify the dissonance entirely?" Flo-

restan answered, "I do not believe so. Although each beat is accented, my use ofdistinct registers should make possible the perception of three conflicting layers."

He motioned to Raro to read on:

Of more musical significance than inherent intensity is contextual intensity

— that is, intensity determined not by the inherent properties of a given disso-

nance but by its manner of presentation. The general principle determining con-

textual intensity is perceptibility or prominence of the dissonance, which in turn

depends mostly on the prominence of antimetrical layer(s).Various aspects of presentation influence the prominence of antimetrical lay-

ers, and hence contextual intensity of dissonance. To some extent, contextual in-

tensity is dependent on the number of accent types that contribute to the forma-tion of antimetrical layers. If, for instance, an antimetrical layer is produced only

by durational dissonances, the resulting metrical dissonance will be much weaker

than if dynamic and durational accentuation collaborate to form that layer. Mea-suring intensity exclusively by the number of active accent types, however, is

problematic because some accent types — dynamic and new-event harmonic ac-

cents—create more perceptible interpretive layers than others. When an antimet-rical layer is formed by either of the above accent types, I consider the resulting

dissonance intense, no matter whether other accent types are present or not.

Dissonances whose antimetrical layers are formed by accentuation aremore intense than those formed by grouping alone. Accentuation is based on

the prominence, on the marking for consciousness, of particular events, and

thus has a greater capability of rendering dissonance intense than does group-ing. If, however, accentuation and grouping collaborate in the formation of an-

timetrical layers, the resulting dissonance will be more intense than one whose

antimetrical layers are formed by either of those factors alone.

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The degree of sustention of pulses within constituent layers plays a role incontextual intensity. A displacement dissonance in which the antimetrical pulsesare released before the next metrical pulse is considerably less intense than onein which antimetrical pulses are sustained during the metrical pulses. As in a di-alogue, the sense of contradiction and conflict is much greater when the utter-ances of the interlocutors overlap.38

The prominence of the voices involved in antimetrical layers may be a fac-tor in the contextual intensity of a dissonance. If only one voice of a multivoicedtexture participates in the establishment of such a layer, the resulting disso-nance will be less intense than if a number of voices participate. If only an innervoice participates, the dissonance will again be less intense than if an outervoice does so.39

The number of antimetrical attacks within a dissonance affects its contex-tual intensity. One or two antimetrical attacks may suggest a particular disso-nance, but that presentation of the dissonance will necessarily be weaker thanone in which the antimetrical layer is announced at greater length. By the sametoken, when an antimetrical layer is sporadic (i.e., some pulses are not articu-lated), the resulting dissonance will be weaker than one in which all pulses arepresent.

A final feature that seems to be of importance in determining the degree ofintensity of a dissonance is the extent to which the antimetrical layer is formedby a consistent event type. As was mentioned above, layers of motion are notnecessarily generated by just one event type; the occurrence of some event atregular time intervals, no matter what type of event it is, generates a layer ofmotion. The more similar the type of recurring event, however, the more per-ceptible is the layer of motion; similarity of event type invites the listener toperceive the events as a connected series.

Eusebius observed, "The dissonance G3/2 in my second Davidsbundlertanz (Exam-ple 2.3) is, then, much less intense than your G3/2, Florestan, at the opening of thetenth piece of that set; you render your antimetrical 3-layer particularly prominentby using dynamic accents. Furthermore, your piece as a whole is much more in-tensely dissonant than mine, for your dissonance goes on for no less than 60 mea-sures, whereas mine occurs only in two- or four-measure bursts."

Raro now begged Florestan to continue to read out loud. Florestan con-sented, and read:

Simple and Compound Dissonance

I refer to metrical dissonances composed of the minimum number of layers — apulse layer plus two conflicting interpretive layers — as "simple" dissonances.When more than two noncongruent interpretive layers are combined, "com-pound" grouping dissonances may result. If a 3-layer, a 4-layer, and a 7-layerwere combined, for instance, the compound grouping dissonance G7/4/3, in-cluding the simple dissonances G4/3, G7/3, and G7/4, would be created.40

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60 Fantasy Pieces

Compound displacement dissonances are also possible. It could be arguedthat all displacement dissonances are, in a sense, compound dissonances; eachdisplacement dissonance Dx+n includes D2x+n, D4x+n, and so on (D2+1, forinstance, includes D4+1, D8+1, etc.). Such inclusions can often be disregardedas trivial. Sometimes, however, superpositions of the type Dx+n/ax+n are per-ceptible as compound dissonances. V

Florestan looked up and said, "I believe mm. 102 — 5 of the first movement of ourFirst Symphony demonstrate the difference between trivial and nontrivial com-bination of D4+1 and D2+1. Syncopation in the viola, cello, and wind parts keepsD2 + 1 active throughout the passage, and D4+1 is therefore present as well. Inmm. 102—3, however, dynamic accents on the second eighth note make possiblethe perception of D4+1 against the continuing background of D2 + 1, so that onecould refer to the passage as a genuine compound dissonance."

He continued to read:

The most striking compound dissonances are those that contain bothgrouping and displacement dissonance. Example 2.1 illustrates such com-pound dissonance; the passage contains not only the dissonance D6+3 men-tioned earlier, but also G3/2. The right hand suggests a 2-layer (l = 16th),while the contour of the left hand line implies a 3-layer, the complete neighborfigure forming one triple group, the dynamic accent and downward leap ini-tiating another.

Raro interjected, "The author could also have mentioned the compoundgrouping/displacement dissonance in mm. 29-31 of the Preambule of Carnaval

(Example 2.7). Your 'oom-pah' accompaniment pattern expresses a 2-layer,against which the motive in the right hand articulates two 3-layers. The metrical3-layer is created by sforzandos as well as durational accents (quarter notes aftereighth notes). The antimetrical 3-layer, displaced by one beat, arises from group-ing; since the motive's first announcement in m. 26, you have conditioned the lis-tener to hear the first eighth note as the beginning of a group, and a layer of mo-tion is therefore formed by recurrences of that initial note. At four-measureintervals, you reinforce this second triple layer with a dynamic stress, as in mm.27, 31, and 35. Two dissonances emerge from this melange, namely G3/2 andD3+1." Florestan pointed out that similar compound dissonances occur in thefirst Trio of the third movement of the Piano Sonata op. 11 (see Example 4.8c)and at the beginning of the Scherzo from the op. 32 piano pieces.

Eusebius had been punctuating the remarks of Florestan and Raro by heartyyawns, and now said, "I am having trouble staying awake; our journey has fa-tigued me. And what must Chiarina be thinking?" Florestan, who had regainedhis usual ebullience, slapped him on the back and responded, "No doubt you arealso fatigued by this manuscript; a little of it goes a long way! There is only one

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Metrical Consonance and Dissonance: Definitions and Taxonomy 61

more paragraph in this chapter; I shall read it, and then we shall break off fortoday and go home to put Chiarina's mind at ease." He read:

in this chapter, I have described a wide variety of metrical states, have setout a system of terminology and labeling for these states, and have applied theterminology in the analysis of short musical excerpts. In the following chaptersI demonstrate how various metrical states operate within larger contexts, andhow the terminology unfolded here is helpful in the analysis of such contexts.

Florestan closed the manuscript and called for their reckoning. As the waiterbrought it to the table, Clara entered the coffeehouse. She stared at the litter ofplates, cups, and coffee beans on the table, then said reproachfully, "Robert! Ihave been looking for you for hours." He stammered an apology and an elaborateexplanation involving the town of Euphonia, the Prophet Bird, and a theoreticalmanuscript. She could make neither head nor tail of his story. With tears in hereyes, she took his arm and led him toward the door. He resisted, saying, "First Imust pay my reckoning." He looked over the bill and expressed surprise at thelowness of the total, which came to exactly one-third of what he expected. ButClara assured him that everything was in order. They paid, and walked home-ward together.

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Intermezzo 1

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Influences on Schumann's

Metrical Style

At home, Clara excused herself, as she needed to practice. Florestan, Eusebius,and Meister Raro entered the drawing room and, after helping themselves tobrandy and cigars, settled into comfortable easy chairs. Eusebius had barely lithis cigar when he nodded off. The cigar fell from his grasp and would haveburned the carpet had not Florestan stooped to retrieve it. He and MeisterRaro sipped and smoked in silence for a time, smiling indulgently at the sleepingEusebius.

Then Raro inquired, "I assume that the interest in metrical dissonance, soclearly evident in your works, did not arise spontaneously, but was triggered bythe music of others. Do you recall which composers influenced you in this re-spect?" As Florestan gazed pensively into his glass, there arose before him a vi-sion of himself at the age of eight at a concert in Karlsbad, staring in awe at aman seated behind him, who had just been pointed out to him as the greatIgnaz Moscheles.1 Smiling at the memory, he turned to Raro and said, "Like allyoung pianists of our time, I first studied the works of pianist-composers likeMoscheles, Hummel, Cramer, and Kalkbrenner, and performed some of them asearly as 1821. I continued to play their works during the period when I had theambition of becoming a virtuoso pianist; in 1828 through 1830 I was engaged,under Wieck's guidance, in practicing the studies and a few other works of Hum-mel and Moscheles, and in 1831 I worked hard on the etudes of the latter com-poser.2

"It was in the works of these composers that I first encountered metrical dis-sonance. Their music was, for the most part, rhythmically uninteresting; all themore striking, therefore, were the few instances of metrical conflict, which al-most always took the form of displacement dissonance. I remember a few exam-


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EXAMPLE 3.1. Metrical dissonance in lgnaz Moscbeles's Twenty-Four Studies op. 70

pies that intrigued me. The fifth of Moscheles's Twenty-Four Studies op. 70 be-gins with left-hand syncopation, resulting in D2 + 1 (1 =quarter). At mm. 8—9, an-timetrical slurs and dynamic accents intensity this dissonance (Example,and at m. 21 harmonic changes and dynamic accents produce yet another flash of

intense dissonance; this one could be heard as D2—1 (Example 3.1b). Occasionaldynamic accents on the second beats of the common-time measures result in theclosely related, looser dissonance D4 + 1. This variant appears within the major-

mode middle section as well, providing a subtle link between sections. The eighthstudy of the same set features much D2 + 1 (l=8th). At first, the antimetrical layer

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is articulated merely by attacks on offbeats (m. 12 — Example 3.1c). At mm.18—20 (Example 3.Id) and 25—27, the notes that form the antimetrical layer are

sustained through the metrical beats, so that the antimetrical layer is reinforced,and in mm. 28 and 46—49, Moscheles writes some antimetrical dynamic accents.In mm. 36—38, the related looser dissonance, D4+1, is produced by dynamic ac-cents as well. The study is thus spanned by a gradual intensification of displace-

ment dissonance."In April 1829 I performed Hummel's Piano Concerto in A minor, op. 85, a

work in which I noted a few fairly prominent displacement dissonances.3 Within

the orchestral introduction of the first movement, three consecutive measurescontain second-beat dynamic accents, resulting in D8+2 (1 =8th). A few measures

later, antimetrical slurs and dynamic accents create the tighter dissonance D4+2.Near the end of the first movement, piano and orchestra dynamically accent thefourth beats of two measures, then both weak beats of the next measure. Finally,

the piano and orchestra part company, the latter dynamically accenting the met-rical beats, and the former, the weak eighth notes. The result is a progressionfrom D8+2 to the tighter dissonance D4+2, then to the diminution of the latter,

D2+1. This successive 'contraction' of displacement dissonances renders the ap-proach to the final cadence of the movement quite dramatic. Occasionally Hum-mel's pianistic figuration contains displacement dissonance. In mm. 95—98 of theRondo, for instance, Hummel places dynamic accents on weak eighth notes oftwo measures (Example 3.2a), then registral accents on the third sixteenth-notetriplets for two measures. At one and only one point in the work, there is aprominent grouping dissonance (low-level, to be sure): within a brilliant passagebased on dominant harmony, just before a big cadence, the left hand plays bro-

Influences on Schumann 's Metrical Style 67

EXAMPLE 3.2. Metrical dissonance in Johann Nepomuk Hummel's Piano Concerto op. 85

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EXAMPLE 5.5. Metrical(dissonance in Hummel's Pianoforte Method

ken octaves in triplet sixteenths, the octaves superimposing a duple layer upon

the established triplet pulse (Example 3.2b).

"Even the musically most arid etudes that 1 was forced to practice containeda few crumbs of metrical dissonance. In Hummel's Pianoforte Method, for in-stance— a. work that contains much that is useful, but just as much that is point-

less4— I encountered in the twenty-fourth exercise a triple/duple conflict, themetrical 2-layer being created by pitch repetition in the lower voice, the antimet-

ncal 3-layer by pitch repetition in the upper voice and by registral accentuation(Example 3.3a). A similar conflict occurs in exercise no. 263, "where registral anddensity accents superimpose an intermittent 2-layer on the triplet pulse (Exam-ple 3.3b). Another example of grouping dissonance is found in that perennial

companion of budding pianists, dementi's Gradus ad Parnassum. The fully no-tated version of: Study no. 68, with its eighth-note neighboring motions in alia

breve time, is metrically consonant, dementi's suggested variant, however, forcesthe neighboring motion into a twelve-eight context (Example 3.4). The dottedquarter-note beats are to be dynamically accented, so that the metrical 3~layer re-mains clearly perceptible; the oscillations of the neighboring motion, however,maintain the duple layer that was consonant within the fully notated version, butthat creates grouping dissonance within the variant.

"All of the passages that 1 have mentioned are flashes in the pan — isolated

events within compositions or sets of studies that are otherwise rhythmicallyrather monotonous. Nevertheless, my ears pricked up at such passages, and Ibelieve that I began to learn certain lessons from them beyond the pianistic onesthat they were intended to teach. The climactic usages of grouping dissonance inHummers Concerto, for instance, taught me that metrical dissonance is an ef-

EXAMPLE 3.4. Metrical dissonance Muzio Clementi's Gradus ad Parnassum

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Influences on Schumann's Metrical Style 69

EXAMPLE 3.5. Metrical dissonance in Niccola Paganini's Caprice for Solo Violin op. 1 no. 13

fective means of increasing tension within a work, and some of Moscheles'sstudies alerted me to the possibility of generating musical processes using met-rical dissonance."

As Florestan paused to sip some brandy, his eye fell upon the looking glassabove the mantel. To his consternation, the glass reproduced not his image, butshowed instead the figure of a slim, demonic violinist standing within a magiccircle, playing for a merry group of dancing skeletons.5 He forced himself toturn away from the horrifying vision toward Meister Raro. "Another virtuoso-composer," he continued somewhat tremulously, "influenced me more deeplythan those whom I have mentioned so far, namely Niccolo Paganini. I was fasci-nated with his playing (I heard him in Frankfurt in 1830), and I was equally im-pressed with his Caprices for Solo Violin op. 1 . Florestan glanced furtively atthe mirror, where, to his relief, he now saw only his own features. He went on, "Ibegan in 1832 to transcribe some of the Caprices for piano and, in the process,gained an ever greater appreciation of their rhythmical and metrical finesse. Met-rical dissonance takes many forms in these works. At the coffeehouse, we dis-cussed the opening section of Caprice no. 13, with its indirect G6/5—not at all acommon grouping dissonance in the music of our time (Example 2.20). At m. 17of this Caprice, a different dissonance follows (Example 3.5); registral accents ineach group of six sixteenth notes in mm. 17—18, 21—22, 25—27, etc.—low-pointaccents on each fourth note and high-point accents on each fifth note — renderthe grouping of the sixteenth notes ambiguous and result in G3/2 (l = 16th). The3-layer is enhanced by the alternation between contrasting articulations (slurredand detached triplets of sixteenth notes), and by the ringing of open-string G's onthe fourth sixteenth.

"The sixth Caprice is also riddled with metrical conflict. The opening mate-rial (Example 3.6a) and numerous later passages hover uneasily between tripleand duple grouping of eighth notes. The slurring generally suggests a 3-layer(l=8th), and accentuation at times clearly expresses this layer; there are registralaccents (high points) on the fourth eighth notes of mm. 1, 3, 39, and 41, and dy-namic accents at the corresponding points of mm. 32-34. A number of harmonicchanges, however, corroborate the 2-layer suggested by the notated meter. In m.3, for instance, that layer is reinforced by the appearance of a new harmony onthe third of the notated quarter-note beats. In m. 4, the resolution of a cadentialsix-four, and in m. 5 the motion to C minor harmony, coincide with duple pulses.In each of mm. 32-35, the main harmonic changes occur on the second duple

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EXAMPLE 3.6. Metrical dissonance in Niccolo Paganini's Caprice for Solo Violin op. 1 no. 6

pulse, so that the 2-layer, and its conflict against the 3-layer created by slurringand accentuation, become quite pronounced.

"Paganini resolves the metrical conflict at several significant points of the

work. At the strongest cadence in the first section, for instance (mm. 10 — 11),he brings the chord changes into alignment with the 2-layer and (in m. 10) re-

inforces that layer with the slurring and dynamics as well. Similarly, at the end

of the first section (m. 18), Paganini coordinates harmonic change and slurringwith the 2-layer. Alter the double bar, G3/2 returns. At the recapitulation (m. 39),

the dissonance is resolved in favor of the 3-layer, which predominates just as it

did at the opening. Soon thereafter, however, Paganini initiates a definitive res-

olution in favor of the 2-layer. Harmonic changes are particularly active in as-

serting that layer; from m. 42 onward (Example 3.6b), significant harmonic

changes appear almost consistently on quarter-note beats, so that the metrical2-layer is prominent. After m. 45, the slurring suggests the 2- rather than the 3-

layer. In mm. 48-49, a dynamic accent falls on one of the duple pulses, and, in

the final two measures, quarter-note repetitions of: the tonic note further clarifythe 2-layer. The Caprice, in short, is permeated by G3/2, which is resolved atthe end of the first section, reinstated, then resolved definitively at the end of

the work."I could mention many other instances of metrical conflict in Paganini's op. 1

— the displacement by one sixteenth note in Caprice no. 3, mm. 58 — 61 and67_70, and in no. 16, mm. 46-49; the displacement by an eighth note in no. 12,

mm. 24 and 32-33, in no. 16, mm. 13-20 and 50-51, in Variation 7 of no. 24,

and so on."Horestan sipped some brandy, then continued, "My discussion of the

Caprices reminds me of another significant influence on my rhythmic style: Pa-

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Influences on Schumann 's Metrical Style 71

EXAMPLE 3.7. Metrical dissonance in J. S. Bacb's French Suite no. 2, Courante, mm. 46-49

ganini could, of course, never have written these works had he not learned theart of writing for solo violin from Johann Sebastian Bach. I, too, learned a greatdeal from old Bach, including some aspects of the treatment of metrical conflict.I became very familiar with the master's keyboard works in the early 1830s, atwhich time I was not only playing but also assiduously analyzing them.7 These

works, particularly the various dance movements of the suites, are filled with ex-amples of both grouping and displacement dissonance. Some of the dissonancesarise from traditions associated with particular dances. Sarabandes, tor instance,

often involve durational accentuation of the second beats, and hence the weakdisplacement dissonance D3 + 1 (l=quarter). Many of Bach's dances in triplemeter are rich in hemiolas (or G3/2 dissonances); like other composers of his

time, he frequently uses these dissonances to highlight cadences. At times, how-ever, he employs G3/2 in a striking manner within phrases — that is, in locationswhere they are not traditionally found. In mm. 3—5 of the second Courante of thefirst English Suite, and in mm. 5—6 of the Courante of the second English Suite,

Bach superimposes on the metrical 2-layer (1 =quarter) a 3-layer formed by har-monic changes. In mm. 46—48 of the Courante of the second French Suite, har-

monic changes and new-event melodic accents in the bass result m a 4-layer(l=8th) -within three-four meter (Example 3.7)." Raro, who knew the works ofJ. S. Bach just as well as Florestan, interposed, "In the latter passage, there is alsogrouping dissonance at the eighth-note level; a contour pattern divides the right-hand figuration into groups of three eighth notes, which conflict with the metri-cal 2-layer (1 =8th)." Florestan nodded and continued, "At the end of the first sec-

tion of the Sarabande of the second EngLish Suite, grouping dissonance similarlyoccurs on two levels. In mm. 9-10, registral accents and harmonic change to-

gether organize the eighth-note pulse into threes, resulting in G3/2 in interaction-with the metrical 2-layer. In mm. 10-11, harmonic changes occur at four eighth-note intervals; the interaction of the resulting 4-layer with the metrical 6-layerproduces G6/4. The Gigue of the third English State includes a fine example ofhigher-level grouping dissonance. In mm. 13-15, harmonic changes result in a9-layer (l=8th), and hence in subliminal dissonance against the metrical 6- and12-layers." Raro interrupted once more, saying, "My favorite example of group-ing dissonance from the works of Bach is the 'Tempo di Minuetta' from the fifthPartita, in which the steady eighth notes are grouped into threes by a recurring

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72 Fantasy Pieces

contour pattern, and in which the 2-layer expected in three-four meter is appar-ent only at cadences." Florestan said, "A superb example! These and many other

metrical dissonances in Bach's keyboard music revealed to me how metrical con-flict can be generated within steadily moving passages, even without dynamic ac-centuation (for Bach does not use the latter)."

Florestan paused to puff on his cigar. As he gazed up into the cloud of smokethat hovered above him, he was visited by another vivid vision: he saw himselfbending down to pick up a pen near the graves of Beethoven and Schubert — apen which he was to treasure as if it were a gift from the two masters.8 He turnedto Raro and said, "Also of great significance for the development of my rhythmicstyle were the compositions of Schubert and Beethoven.9 Schubert's chamberworks, with which I was occupied intensely in late 1828, and which strongly in-fluenced my own first efforts at writing chamber music, contain some metricallydissonant passages that interested me.10 For example, at the end of the first section

of the slow movement of the Piano Trio in Bl Major, Schubert creates the dis-placement dissonance D6+2 (1 = 16th) by dynamically accenting syncopated oc-taves in the piano part. During the following section, he presents the related dis-

sonance D3 + 1, at first even employing syncopated octaves to forge a clearconnection between two sections that are otherwise strongly contrasted. In the fi-nale of the Kl major Trio, Schubert quite frequently superimposes a 2-layer on the

metrical 3-layer by placing density and dynamic accents at unexpected points."Among other works by Schubert that had an impact on my 'metrical edu-

cation,'" Florestan continued, "were his waltzes for piano. Their significance forme must be clear to anyone who plays my early sets of piano pieces (particularlythe Papillons), and to anyone who reads my writings; I reviewed the dances of

Schubert's op. 9 and op. 33 in the Neue Zeitschrift in 1836.11

"The Viennese waltz in general, with its duple steps within a triple metricalframework, is conducive to metrical conflict — this is one reason why I was al-ways drawn to this dance.12 Schubert's waltzes, however, contain more displace-ment than grouping dissonance. The first few waltzes in op. 9, for instance, areperfectly consonant, in fact, predictable and somewhat square. The second sec-tion of no. 7 begins with a hint at D3+1 (l=quarter); the second beat of m. 9 is

dynamically accented. In op. 9 no. 8, Schubert expands upon this dissonance, ac-centing the second beats of mm. 1, 2, 5, and 9. The dissonance is absent in nos. 9to 11, but reappears in nos. 12, 16, 17, 18, and 21, where half notes on secondbeats result in durational accents (which are at times reinforced by dynamic ac-cents). In no. 20, accents on the third beats of mm. 5—6 and 13—14 create the dis-sonance D3+2, which is also present in the first half of no. 21, throughout no. 22,

in the first half of no. 23, in no. 25, and in the first half of no. 26. Nos. 27-30 areconsonant. In no. 31, accentuation of alternate third beats m the first half and ac-centuation of alternate second beats in the second half results in loose relatives ofD3+1 and D3+2 (D6+1 and D6+2). No. 33, dominated by D3+2, also containsincursions of D3+ 1 (m. 3, 11), and no. 34 begins with D3+2 (mm. 3-14) but endswith D3 + 1 (Example 3.8). The final two dances ol the set restore consonance atthe quarter-note level." As Florestan paused for some brandy, Raro remarked,

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Influences on Schumann ',s Metrical Style 73

EXAMPLE 3.8. D3+1 and D3+2 at the end of Schubert's Waltz op, 9 no. 34

"From what you have said, it appears that the succession of metrical dissonancesin op. 9 is planned; Schubert introduces D3+1 and D3+2 gradually and sepa-rately, then juxtaposes them within individual dances (first in no. 21, then inthree dances near the end of the set)." Florestan agreed, and added, "This andother sets of waltzes by Schubert thus taught me how metrical dissonance couldaid in the construction of a unified work out of a collection of short piano pieceswritten at different times — a problem with which I was often confronted in thoseyears.

"Beethoven's music," he continued, "influenced my rhythmic style even moreprofoundly than did Schubert's. I heard some of Beethoven's symphonies in thelate 1820s, notably the Eroica and the Seventh, and during my pianistic studiesand my later critical endeavors became increasingly familiar with his pianosonatas. I mention but a few passages from Beethoven's piano sonatas whosemetrically conflicted quality fascinated me: the opening theme of the slow move-ment of op. 7, in which durational accents and new harmonies fall on secondbeats until m. 4, creating a shifted 3-layer that strongly collides with the metricallayer in m. 5; the accents on third beats in mm. 9—15, and on second beats in mm.55 — 65 in the second movement of op. 10 no. 2; the accents on the last quartersof mm. 75—77, 79-81, and 83—85 in the first movement of op. 10 no. 3; the dis-placements by a sixteenth note that permeate the first movement of op. 31 no. 1;the contraction, in mm. 67—71 of the first movement of op. 31 no. 3, of a three-beat cadential gesture (in three-four time) to a two-beat gesture, resulting in in-direct grouping dissonance; the sforzandos on the final eighth notes of two-fourmeasures in the scherzo of the same sonata; the strong displacement dissonancein the poignant passage at mm. 142-58 of the finale of op. 57, created by dynamicaccentuation of the second eighth notes of two-four measures; mm. 47—50 of thefirst movement of op. 90, where right-hand durational accents and new har-monies fall on second beats (in mm. 55-58 and 61-64, durational accents on sec-ond beats continue the dissonance); the first movement of op. 101, where the dis-placement dissonance D3+2 (l=8th), created both by durational and dynamicaccentuation, is used frequently, particularly dramatically at climactic passages(mm. 48-49 and 85-87); mm. 10-13 of the Molta Allegro movement of op. 110,where sforzandos and melodic repetition result in a shifted 2-layer. In the lattermovement, the dissonance D2 + 1 (l=quarter) is augmented to D4+2 in the coda,where dynamically accented triads consistently fall on the weak bars within four-measure groups."13

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KXAMPLE 3.9. Metrical dissonance in Beethoven It Eroica Symphony, first mvint.

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As Raro gaped in astonishment at Florestan's deep familiarity with thepiano sonatas of Beethoven, the latter puffed smugly on his cigar, then contin-ued, "Beethoven's use of metrical dissonance is not, of course, restricted to hispiano sonatas. Let me remind you of just one relevant movement that I havementioned in my writings:14 the first movement of the Eroica Symphony, inwhich Beethoven exploits the dissonances G3/2, D3+1, and D3+2 (l=quarter).Within the first twenty-five measures, the only dissonance is the striking synco-pation at the eighth-note level in mm. 7—8. Thereafter, Beethoven emphaticallyintroduces G3/2 and D3+2. In mm. 25—32, sforzandos in all instruments andregistral accents in the first violins mark off a 2-layer, resulting in G3/2 (Exam-ple 3.9a). In mm. 32—34, G3/2 is replaced by indirect and subliminal D3+2;sforzandos and registral accents now articulate a displaced 3-layer rather thana 2-layer. In the final measures of the first theme area (mm. 35—36), Beethovenrestores the metrical 3-layer and metrical consonance. During the transition,D3+1 makes its first appearance (mm. 45—54, Example 3.9b); the motivic frag-ments tossed from instrument to instrument, each beginning with a durationalor dynamic accent, establish a 3-layer shifted by one pulse, while the metrical 3-layer is intermittently expressed by the cellos' and double basses' reiterations ofthe note F on notated downbeats. In mm. 55-57, as the second theme begins,consonance is reestablished.

"Later in the second theme area, however, Beethoven brings back D3+I.The second beats are emphasized by instrumental entrances (density accents) inmm. 83—87, 91—93, and 95—98, and by initiations of new harmonies in mm. 99-101, so that a clear antimetrical layer shifted by one quarter-note pulse is estab-lished. The metrical 3-layer is intermittently expressed by durational accents(mm. 86 and 96) and changes of harmony (mm. 91 and 97). Beethoven also hintsat D3+2 in this passage by placing sforzandos on third beats in mm. 85 and 89.

"D3+1 becomes unpreccdentedly intense at the beginning of the closinggroup in mm. 109-16 (Example 3.9c). In mm. 109-12, dynamic and density ac-cents on the second beats and, in mm. 113—16, initiation on the same beats of a

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EXAMPLE 3.9. (continued)

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76 Fantasy Pieces

repeated rhythmic figure beginning with a durational accent (reminiscent of mm.45 — 54) result in a clear antimetrical 3-layer. The metrical 3-layer is to some ex-tent maintained by harmonic changes in this passage. Two measures of conso-nance (mm. 117-18) lead in mm. 119-27 to a reappearance of G3/2, absent sincemm. 32, the antimetrical layer resulting from sforzandos on alternate beats. Beet-hoven reiterates the progression D3+1 to G3/2 with different music in mm.124—31. The motivic displacement dissonances each make one more brief ap-pearance within the exposition; dynamic accents in the violas and second violinsform D3+1 in mm. 145—46, and in mm. 135—39, ties initiated on beat three resultin durational accents and hence in weak D3+2. Otherwise, the final measures ofthe exposition are primarily consonant.

'In the development section, Beethoven continues to play the three motivicdissonances off against each other. D3+2 in mm. 160 — 65 (durational accents onbeat three versus bass attacks on beat one) yields to D3+1 in mm. 166—77 (whichrecall mm. 45-54). Measures 198-202 contain D6+2, a loose relative of D3+2;sforzandos fall on alternate third beats rather than on each third beat. SubtleG3/2 appears in mm. 208—9 and 212-13, where pattern repetition in the first vi-olins creates a duple layer. D3+1 is featured in the passage leading up to the mainclimax of the development section (mm. 220—49), the antimetrical layer beingformed by displaced motivic groups (as in mm. 45 — 54) and, after m. 236, bysforzandos on beat two (resulting in an effect of intensification). In mm. 248—53(Example 3.9d), D3+1 is answered by G3/2, and regular alternation between thetwo dissonances—two bars of D3+1 followed by four of G3/2 — continues untilm. 271. In mm. 271—79, the climactic measures, one gams the impression thatD3 + 1 and G3/2 are forced into even closer association — compressed or crushedtogether, so to speak. (How appropriate is this gesture for these particularly in-tense measures!) In mm. 270 — 75, for instance, the duple layer is expressed with-out interruption by the accented attacks of the winds and high strings. Harmonicchange at m. 272 and 274, however, results in clear articulation of notated down-beats, and thus in hints at D3 + 1 (although G3/2 continues as well). In mm.276-78 (Example 3.9e), D3+1 is emphatically articulated as the strings andwinds shriek at each other, but in mm. 278-80, where the 2-layer predominates,D3 + 1 merges into G3/2. Measures 280-84 gradually resolve the metrical disso-nance (just as they resolve the intense pitch dissonance). Some listeners mighthear the first chord in m. 280 as the downbeat, and the resolution of the ninth inm. 282 might similarly be heard as a metrical accent. These prominent secondbeats imply a shifted 3-layer and hence, continuing D3+1. Full metrical resolu-tion takes place at m. 284, beautifully coordinated with harmonic resolution.Most of the remainder of the development section is metrically consonant. Hintsat D3+2 appear at mm. 305, 307, 309, and 317 (where sforzandos appear on thirdbeats), and the climactic G3/2 is weakly echoed at mm. 338-64 (where the risingnotes of string arpeggiations establish a duple layer while durational accents inthe winds maintain the metrical 3-layer).

"The coda (beginning at m. 551) brings some interesting new developments.Beethoven begins it with consonance, then states G3/2 in the same fashion as at

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Influences on Schumann's Metrical Style 77

the end of the development section (cf. mm. 603-14 and 338-64). In mm.615-20, Beethoven superimposes D3+1 and G3/2. The metrical layer, expressed

by the durational accents in the horns, is set against a duple layer formed by pat-tern repetition in the low strings, and against a 3-layer displaced by one beat,which is created by durational accents in the winds. Beethoven resolves this com-pound dissonance in two steps: the shifted 3-layer and hence D3+1 disappears

after m. 620, and G3/2 resolves as the duple layer is abandoned in m. 631.Whereas the motivic dissonances are absent in most of the final, triumphant,tonic-prolonging passage, Beethoven does grant them one more appearance each

(Example 3.9f): the V7 within the final cadential progression (mm. 681-88) is as-sociated first with D3+1 (the shifted 3-layer being expressed by syncopation anddynamic accents), then G3/2 (the duple layer being articulated by the attacks of

a rising arpeggiation within the first violin melody). This final gesture not onlyreviews the two motivic dissonances, but also recalls the close associations be-

tween them earlier in the movement."Beethoven's metrical dissonances opened my eyes and ears to the immense

dramatic possibilities of metrical conflicts deployed across large musical expanses.In Beethoven's music, 1 also discovered the effectiveness of simultaneous pitchand metrical dissonances (as at the climax of the development section of theEroica and at the beginning of the coda of the first movement of op. 101).

"Of course," Florestan remarked as he refilled his glass, "I did not immedi-ately absorb all of the techniques that I have mentioned into my earliest works, inwhich metrical dissonance is uncommon. Individual movements and passages,however, demonstrate that I was even at this early stage beginning to employmetrical dissonance in interesting ways. In one unfinished b work—the Piano Con-certo in F from 1830-31 — the use of metrical dissonance is much the same as that

in the music of Moscheles and Hummel; amid virtuosic arpeggiations and scales,there appear occasional brief passages of displacement dissonance and, evenmore rarely, some striking grouping dissonance.15 In one passage, in alla breve

time, I form three-quarter-note groups by repeating a melodic pattern of that du-ration. A dynamic stress on a fourth beat is at first heard as the inception of afinal group of three, although later events do not bear out that hearing (Example3.10). Another unfinished project that grew out of my early preoccupation withvirtuosity was a collection of finger exercises, intended for a treatise on pianotechnique; I incorporated a number of these into my Foreword for the op. 3 stud-ies after Paganini.16 Many of these exercises contain displacement dissonance,particularly the set of nine that appears at the end of the Foreword. Here I forcethe pianist to accentuate points other than the metrical beats, in order to'strengthen the individual fingers and to make them independent.'

"In some of my unpublished exercises, grouping dissonance arises from therepetition of scale segments within a metrical context with which they are incon-gruent. In one exercise, for example, I reiterate a pair of five-note scale segmentsin sixteenth notes within common time, with the result that the segments travelthrough several metrical positions before cycling back to their original one (Ex-ample 3.11).

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78 Fantasy Pieces

"My Piano Quartet in C Minor (1828-29) occupies a particularly impor-tant position in my development as a composer.17 Whereas I ultimately felt thatthe work was not worth publishing, I valued portions of it very highly, and itcontains my first serious compositional engagements with metrical dissonance.The first movement contains not only a great deal of low-level dissonance butalso an interesting treatment of the displacement dissonance D2+1 (1= quar-ter). During the first portion of the movement, I render this dissonance pro-gressively more perceptible. At the very opening, I suggest 132 + 1 by placingdensity accents on the offbeats (Example 3.12a). At m. 48, 1 imply the samedissonance by antimetrical slurring of quarter notes, and at mm. 58 — 59 inten-sify it greatly by writing dynamic accents on the offbeats. Echoes of the disso-nance in the form of the rhythm 'quarter-half-quarter' pervade the remainderof the movement.

"In the third movement, there is little striking dissonance, but at m. 104 in-direct grouping and displacement dissonance abruptly appear simultaneously(Example 3.12b). The durational accents in the melody result in a 2-layer(l=quarter) that forms G3/2 in conjunction with the previously established 3-

layer, and imitation of the melody a quarter note later results in D2 + 1 as well.This sudden piling up of metrical dissonance effectively heightens the sense ofclimax. At mm. 106-7 the dissonance resolves, and the remainder of the move-ment remains consonant.

"In the fourth movement, repetitions of the progression 1-V at mm. 40-42and 48 — 51 result in an antimetrical duple layer and in indirect and subliminalG3/2 (Example 3.12c). In mm. 283—98 (a passage that Eusebius and I discussed

EXAMPLE 3.11. Metrical dissonance in one of Schumann's unpublished piano exercises, ULB Bonn,

Manuscripts Division, Schumann 15 (Sketchbook III), p.23

Manuscripts Division, Schumann 13 (Sketchbook I), p.25

EXAMPLE 3.10. Excerpt from sketches for Schumann's Piano Concepts in E ULB Bonn,

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with M. Berlioz in Kuphoma — Example 1.7a), the same dissonance is even moreprominently stated; all notes in this passage have the duration of two eighth

notes—a significant departure from, and a subliminal conflict against, the no-tated meter. The passage is characterized not only by dissonance in the metricaldomain but also by pitch dissonance. Resolution in both domains occurs as the

next section begins. Here, then, I began to explore the coordination of pitch andmetrical dissonance, and of metrical dissonance and form.

"The second movement of the Piano Quartet is the most interesting from thestandpoint of metrical dissonance. Already in the first three measures of the Min-uet (Example 3.13), a 2-layer (l=quarter) formed by syncopation in the cello

conflicts with the barely established triple layer to result in indirect and sublimi-

nal G3/2. Durational accents in mm. 1—3 suggest an additional 2-layer, displacedin relation to that arising from the cello syncopation, so that D2+1 emerges. In m.

5, yet a third dissonance is introduced: the figure "8th-8th-8th-8th-quarter" is im-itated at the distance of a quarter note, resulting in D3+1. Measures 6-8 reiterateG3/2; the harmonic rhythm forms a 3-layer while two nonaligned 2-layers resultfrom the slurring and the durational accents, respectively. As in mm. 1 -3, the 2-layers produce D2+1. This metrically intricate opening section ends with a refer-ence to D3+1, again produced by imitation.

After the double bar, I elaborate on or intensify individual dissonances. Thelengthy passages encompassed by mm. 9—19, 34-39, and 46 — 57, for instance,are occupied by D3+1, produced either by dynamic and durational accents on

Influences on Schumann's Metrical Style 79

EXAMPLE 3.12. Metrical dissonance in Schumann's Piano Quartet in C Minor (1828), ed. Wolfgang

Boetticber; fiirst, third and fourth mvmts. © 1979 by Heinricbsbofen's Verlag, Wilhelmshaven,

Germany. Ed. no. 1494. used by permission of publisher.

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80 Fantasy Pieces

EXAMPLE 3.13. Metrical dissjonance in Schumann's Piano Quartet in C Minor (1828), ed.

Wolfgang Boettichei; second Mvmt. © 1979byHeinrich,thofen'd Verlag, Wilbelirubaven, Germany.

Ed. no. 1494. Used by permission of publisher:

the second beat or by imitation of a three-beat motivic pattern at one-quarter-note intervals. In mm. 72 — 74, the G3/2 dissonance weakly articulated at the be-

ginning of the movement and at the reprise (m. 42) is presented much more pow-erfully, the dissonance resulting here not from mere juxtaposition of a barelyestablished triple meter and duple groups, but rather from the superposition ofstrong expressions of the metrical 3-layer and an equally prominent 2-layer.These dissonances are interspersed with brief resolving passages, which, how-ever, are very much in the minority in this primarily dissonant Minuet. Part of

the reason for the prevalence of dissonance in the Minuet was my desire for con-trast against Eusebius's Trio, which is entirely consonant. The two complemen-tary sections combine to form a movement in which metrical consonance and dis-sonance are used, I believe, quite boldly and effectively."

When he finished, Florestan thirstily drained his glass. As he did so, hisgaze happened once more to fall upon the mirror across the room. He gasped interror when again he saw the gaunt violinist, providing demonic music for acrowd of dancing skeletons and wraiths. But now the wraiths had the faces ofHummel, Moscheles, Bach, Beethoven, and Schubert; and now he heard thesounds of the violin — the ferocious displacements from the ending of Pa-ganini's sixteenth Caprice.18 Before Raro was able to stop him, he hurled hisglass at the mirror. As slivers of snifter and mirror rained to the floor, Eusebiusstarted wildly out of his chair and, perceiving Florestan's frenzied state, rushed

to his side.

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Influences on Schumann's Metrical Style 81

Clara, to whom the noise had penetrated even through her practicing, burstinto the room. She stared, aghast, at the broken mirror and at Robert's wild-eyed

and terrified face. It took her some time to calm him and to convince him that itwas time to go to bed. With great effort — for in reaction to his outburst, he soonwent limp as a ragdoll — she succeeded in transporting him to his room andputting him to bed.

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Metrical Progressions

and Processes

When Eusebius, unable to sleep after the recent upheaval, suggested to Florestanthat they should begin another chapter of the manuscript, Florestan listlessly ac-quiesced. They rose, settled on their sofa, and began to read, and after a fewparagraphs Florestan became as absorbed as Eusebius in the author's argument.Clara, meanwhile, was attempting to calm herself by playing Beethoven's Emperor

Concerto, the noble tones of which provided a background for Florestan and Eu-sebius's reading.'


As was mentioned earlier, within each musical work a particular metrical con-sonance— the primary consonance — assumes the role of the normative statefor that work. This normative state, however, is generally not a steady state.Most works do not continuously articulate the primary consonance; the degreeof perceptibility of the primary metrical layer fluctuates, and antimetrical lay-ers fade in and out. Most musical works are, in fact, spanned by a succession ofmetrical consonances and dissonances — a "metrical progression."

Inspection of the metrical progression of a work can tell us a great dealabout that work's rhythmic structure. Among the questions that might be an-swered by the analysis of a metrical progression are the following:

1. Do particular dissonances recur? If particular themes of a work containmetrical dissonances, unaltered restatements of those themes will, of course, re-sult in the recurrence of those metrical dissonances. Recurrence is more inter-esting, however, where it occurs independently of the restatement of a theme.


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When a given dissonance recurs frequently within a work, that dissonance be-comes motivic in function.

2. Are particular families of dissonances active in the work? We have de-termined that dissonances fall into various types of families, generally on thebasis of similarities in their resultant rhythms. Musical works can be based onthe members of a particular family of dissonances, with the result that the met-rical structure of those works is highly cohesive.

3. Are particular metrical dissonances repeatedly juxtaposed or superim-posed? Again, recurrence of such associations is most interesting when it doesnot occur in connection with the restatement of entire passages. Recurring jux-tapositions or superpositions can act as motives, as can recurring individualdissonances.

4. What proportion of the work is consonant, and what proportion is dis-sonant on the surface level? There is a significant difference between a workthat is mostly consonant, with only a few incursions of dissonance, and one thatis mostly dissonant with a few islands of consonance.

5. How much subliminal dissonance does the work contain? The answer tothis question, combined with that to the preceding one, reveals the extent towhich the notated meter is contradicted within the work.

6. How frequently does the metrical state change? Does it change regu-larly? Does the frequency of change vary during the work? Frequency ofchange is an important way to characterize the rhythmic volatility of a work orsection.

7. To what underlying progression can the surface progression be reduced?The term "metrical dissonance" suggests that, by analogy with pitch theory, dis-sonance is ornamental and could be subjected to a reductive process to exposeunderlying consonances.

"I suppose," Eusebius mused, "that the 'reductive process' to which the au-thor refers is something like that which Johann Philipp Kirnberger applies toopera arias in his Kunst des reinen Satzes."


j, he most basic metrical consonance, that to which any metrical progres-sion would ultimately reduce (by analogy with the background tonic triad in thepitch domain), is the primary metrical consonance. In most works, dissonances,being temporary deviations from the primary consonance, are perceived as em-bellishments of that consonance.3 In fact, certain embellishment types that arecommon in the pitch domain have metrical analogues. A metrical progression ofthe type "C-D-C" (where C is the primary metrical consonance and D somemetrical dissonance) is often analogous to a neighboring motion in the pitch do-main and, like a neighboring motion, reduces to the framing event C. Manymetrical dissonances fall into this category.

Metrical Progressions and Processes 83

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84 Fantasy Pieces

Eusebius looked up, lifted his finger to command Florestan's attention to thepassage from the first movement of Beethoven's Fifth Piano Concerto that rangthrough the house, and said, "Chiarina is just playing an example of such a'neighboring motion'; a sixteenth-note passage clearly expressing the primary

consonance leads into a segment in which triplet eighths are grouped into twos,and in which, in addition, there is some low-level two-against-three dissonance.There follows another consonant passage in eighth notes (mm. 149 — 59)."

Some metrical progressions are more reminiscent of another pitch disso-

nance type, namely the passing tone: these begin with a consonance C1 andmove through some dissonance D to a different consonance C2. The analogy topassing motion is particularly clear when D is a grouping dissonance composed

of one layer contained in C1 and one contained in C2, so that the effect of pass-ing gradually from C1 to C2 is quite audible. Such dissonances reduce first tothe progression "C1—C2." The next level of reduction would eliminate whichever

of the two consonances is not the primary one (and which is therefore sublmn-nally dissonant against that consonance).

Although these pitch/rhythm analogies are intriguing, an attempt at rigor-

ous reduction of the metrical progression of an entire work does not lead to in-teresting results.4 There are two problems with such reductions. In the pitch do-main (in pre-twentieth-century tonal music), everything reduces to the tonic

triad on the highest level; below that level, however, numerous passages reduceto other consonances, with the result that middleground levels are quite inter-esting and varied. In the metrical domain, on the other hand, the contents of thelevel analogous to the middleground are predictable; there is usually only one

consonance (the primary consonance), and at most, two (the primary conso-nance and one other), to which all events reduce.

A second problem that arises when we attempt to reduce metrical progres-sions in a rigorous way is the role of duration. In pitch reduction of tonal music,duration is not a factor in the determination of structural significance; even verybrief events (such as a cadential dominant supporting the scale degree 2 of afundamental line) might be extremely significant. In the reduction of progres-sions that are composed of units of time, on the other hand, duration couldhardly be ignored. It does not seem feasible, however, to establish a set of rules

for the use of duration as a criterion for structural significance. Given a pro-gression of the type "C-D-C" in which "D" is considerably longer in durationthan "C," is the reduction to "C," by analogy to neighboring motion in the pitchdomain, still valid? Just how much longer than "C" must "D" be before such re-duction becomes unconvincing? Presumably, different listeners would answer

these questions differently.Given these problems, I abandon the attempt to reduce metrical progres-

sions in a systematic manner in favor of intuitive, informal reductions to an un-derlying basic progression that spans the given work. Possible progressions orthis type are large neighboring motions of the form "C-D-C" (where the work

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Metrical Progressions and Processes 85

begins in a primarily consonant fashion, becomes more dissonant, and ends

with restoration of the original mainly consonant state); curtailments of such

motions, namely C-D (where the work begins consonantly but becomes disso-

nant and ends dissonantly) and D-C (where the work begins dissonantly but ul-

timately resolves the dissonance); and innumerable shadings of the basic states

of consonance and dissonance (for example, a state "D," composed of a variety

of individual dissonances or of a variety of degrees of intensity of a single disso-

nance). Such informal "bird's-eye views" of a metrical progression take us to the

rhythmic heart of a given work—to its most basic metrical "narrative."


A "map" of the surface metrical progression of a work gives a convenient

overview of its metrical structure. Furthermore, the comparison of metrical

maps of different works quickly brings their metrical differences and similari-

ties into focus. There are various possible formats for such maps. For example,

one might list in the left margin the cardinalities of all metrical layers operative

within the work, and might draw horizontal lines, with reference to a measure

grid, to indicate where within the work the various layers are active. Pairs of

parallel lines would show the consonances and dissonances resulting from the

interactions of the layers. A map of this type, however, becomes difficult to read

when a work contains many different layers of motion. It is generally more con-

venient to list the labels of all metrical dissonances and all consonances other

than the primary one in the left margin. Horizontal lines, laid over a measure-

grid, indicate the locations of each dissonance. The distinction between weak

and intense versions of dissonances may be made by drawing different types of

lines; I use normal lines for intense dissonances and dotted lines for weak dis-

sonances. Those portions of the map not spanned by lines indicate passages

governed by the primary consonance.

Florestan, now having regained his customary energy, suggested, "Let us at-

tempt to construct a metrical map of a short piece—perhaps the 'Valse allemande'

from Carnaval" Eusebius said, "We should each construct a map and then com-

pare them. You go ahead with the 'Valse'; I shall work on 'Estrella,' a piece of sim-

ilar length." He fetched pencils and two sheets of paper, and for a time they scrib-

bled busily.

When they were both finished, they surveyed each other's diagrams (Figures

4. la and 4. Ib). Florestan remarked, "These metrical maps show that the metrical

progressions of the two pieces are similar in some respects: both are occupied al-

most entirely by dissonance, and both begin dissonantly and end consonantly.

We might say that they both play out the basic metrical narrative 'D-C.'" "On the

other hand," Eusebius countered, "the diagrams show significant differences be-

tween the pieces. For example, in 'Estrella,' one dissonance, D3+1 (l=quarter),

remains active throughout, and is joined in the central area of the piece by others.

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86 Fantasy Pieces

F I C U R I C 4.1. Metrical maps of "Valse allcmande "and "Estre/la "from Carnaval

The 'Valse' on the other hand is spanned by no single dissonance; D12 + 1 (1 =16th)

is active in the outer sections, but disappears in the middle section, where a dif-ferent dissonance, D12+4, takes over. Furthermore, the metrical states changemore frequently in 'Estrella'; in the 'Valse' there are three changes in metricalstate (at mm. 9, 16, and 21), whereas in 'Estrella' there are five, namely at mm.9, 11, 13, 28, and 35. If one were to count changes in intensity, there would be tenchanges of state." Florestan added, "Your map suggests that a particular processunderlies 'Estrella': the piece begins with weak dissonance, the dissonance is in-tensified, then gradually weakened and ultimately resolved." Eusebius noted, "Isee that the author addresses precisely such processes in the following section."They continued their reading:


Another question that we might ask about a given metrical progression is,"Does the progression involve some sort of logic and order?" The statementthat metrical progressions reduce to underlying narratives already implies thatthese progressions may be more than haphazard successions of metrical states.The orderliness of metrical progressions becomes even more apparent when onelocates within a work particular processes affecting one or more states. Suchmetrical processes frequently function as shadings of the basic narratives "C-D-C," "C-D," and "D-C," resulting in subtle links between the basic states of con-sonance and dissonance, and even causing those states to merge gradually intoeach other rather than being bluntly juxtaposed. In the following sections, I in-vestigate a number of metrical processes, categorized as follows: consonance-to-

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Metrical Progression and Processions 87

EXAMPLE 4.1. An abrupt consonance-dissonance motion in the "Pre'amlnde"from Carnaval (mm,


dissonance processes (abbreviated "C-D processes"), processes within a disso-nant state ("D-processes"), and finally dissonance-to-consonance processes("D-C processes").5

Consonance-to-Dissonance Processes

There are two possibilities for consonance-to-dissonance successions: they maybe abrupt, or they may be gradual, in the sense that some foreshadowing of thedissonance may occur prior to its actual establishment. For abrupt establish-ment of dissonance, there are again two possibilities: 1) one or more interpretivelayers that conflict with the existing consonance (usually the primary conso-nance) are superimposed on that consonance; or 2) the layer(s) that formed theconsonance is/are abandoned, and a dissonance consisting of new layers is es-tablished. The former procedure is by far the more common one.

Eusebius interjected, "Most of our dissonant passages do illustrate the first pro-cedure; but on occasion we have used the second, less common one. Your Pream-bule to the Carnaval contains an example, Florestan; from the primary conso-nance of mm. 106-13 you abruptly progress to a dissonance that does notexplicitly contain the metrical 3-layer, namely D2+1 (l=quarter —Example 4.1)."

I refer to the more gradual manner of moving from consonance to disso-nance by the term "preparation." This term is often associated with a particulardissonance type in the pitch domain, namely the suspension; the pitch that is tobecome a suspension is prepared by a prior statement of the same pitch in aconsonant context. Metrical dissonances, too, may be prepared by allusions to acoming dissonance within primarily consonant passages. Metrical preparationgenerally takes the form of the suggestion of an antimetrical layer by just one ortwo pulses — not enough pulses securely to establish a layer and a metrical dis-sonance, but certainly enough to prepare a later appearance of the dissonance.Such preparation is found in Schumann's eleventh Papillon. Early in the piece(Example 4.2a), a single accent on the second eighth note of a measure hints at

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88 Fantasy Pieces

EXAMPLE 4.2. Preparation of dissonance in Papillon no. 11

but does not yet establish the dissonance Dx+1 (l=8th; there is no way of iden-

tifying the cardinality of the layer at this point). This shard of dissonance,placed at the beginning of the first section proper, relates to the later Put lento

section, in which D2 + 1 (l=8th) plays a large role; the dissonance is very strong

in mm. 32 and 41-43 (Examples 4.2b and c), and only slightly weaker (becauseof the lack of dynamic accents) in the measures between those two passages. *«'

Florestan remarked, "Actually, I believe I intended the dynamic accents of m. 32

to continue throughout mm. 32-39. Perhaps I should have written them all out,

tedious though it would have been!"

1 he dissonance D3+1 at m. 27 of the Preambule from Carnaval (Example

2.7) is also prepared by earlier allusions. In mm. 7—8, Schumann begins to hint,by dynamically stressing the second beats, at a displaced 3-layer and hence at

D3+1 (l=quarter). Several consonant measures follow, but in mm. 15—16, the

same suggestion of 103+1 returns. Again, a number of consonant measures fol-

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low (mm. 17-26). In m. 27, the shifted 3-layer appears once more, and the re-sulting dissonance D3+1, prepared by two two-measure allusions, now lasts forno less than sixteen measures (taking the repeat sign into account). Another ex-ample of preparation occurs later in the same movement. In mm. 48, 49, 50, and52 (Example 4.3), Schumann hints at a 2-layer, and hence at G3/2, by inter-spersing left-hand "oom-pah-pah's" with a few "oom-pah's." In mm. 54-61, the

duple "oom-pah's" take over completely while the right hand continues to artic-ulate a 3-layer. Sporadic, intermittent G3/2 prepares uninterrupted, continuousG3/2.

Eusebius remarked, "Our fifth Novellette, op. 21, contains another fine exam-

ple of preparation; the opening measures prepare not one but several later disso-nances. Your dynamic accents on metrically weak eighth notes in mm. 1 and 2(Example 4.4a) foreshadow my extensive use of D2 + 1 (l=8th) in the relatively

placid section at mm. 88—111 (Example 4.4b). Your dynamic accents on the lastquarter-note beats of mm. 1 and 2 prepare the weak, yet audible D6+4 disso-nances within the additional quiet interludes that I contributed to this piece — atmm. 33-35 (Example A.Ac), mm. 52—56, and mm. 205 — 9. (Some of these disso-

nances can be heard as D6—2). The third-beat accents in the opening measuresalso prepare your own more vociferous statement of D6+4 in mm. 153 — 57

(where you create the antimetrical layer with dynamic accents on the thirdbeats)." Florestan remarked, "With the dynamic accents on the second beats ofmm. 3 and 5, I prepare the D6+2 within your quiet second section (mm. 49-51 —

Example 4.4d). Finally, I hint in the first two measures at G6/4; the two V-I pro-gressions, each occupying four eighth-note pulses, and the following two beats ofFit harmony create a weak 4-layer. (I clarify this implicit duple grouping in the re-statement of this material at m. 63, where I highlight the beginnings of the sameduple groups with sforzandos.) The dissonance G6/4 is prominent within yourquiet sections, namely at mm. 33-60 (Example 4.4c) and 209-19."

Florestan proceeded to mention some examples of preparation from theirlater works: "In the second Trio of the third movement of the First Symphony, asingle third-beat dynamic accent in the strings in m. 314 hints at D3+2 (1=quar-ter). This dissonance comes into its own at the end of the Trio (mm. 337—42),where a succession of third-beat accents, and the initiation of harmonies on those

Metrical Progression and Processes 89

EXAMPLE 4.3. Preparation of dissonance in the "Preabbule"from Carnaval, mm. 47—52

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EXAMPLE 4.4. Preparation of'dissonance in Novellette op. 21 no. 5

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Metrical Progression and Processes 91

same beats, creates a more substantial and very prominent stretch of D3+2. (Forharmonic reasons, it can also be heard as D3-1.) In the finale of the Piano Con-certo op. 54, the very extensive G3/2 that we discussed earlier (mm. 188-228) isprepared by a brief hemiola a few measures before (mm. 181—85)." Eusebiusadded, "Another dissonance that we discussed earlier, namely the G9/6 from theend of the first movement of the Piano Trio op. 80 (Example 2.21), is similarlyprepared by a few pulses of an antimetrical layer; in mm. 404-5, then again inmm. 406-8, we group the duplet eighth notes into threes by melodic contour,thus hinting at the 9-layer that will form continuous, though subliminal G9/6 inmm. 410-13."

Eusebius turned back to the manuscript and continued to read. Florestan,however, mused, "My mental and emotional 'dissonances,' like my metrical ones,sometimes arise abruptly, out of the blue. At other times, I can feel the stormclouds forming gradually within me. I know that an outburst is imminent, and Iam powerless to avert it. . . ." When Eusebius began to turn the page, Florestansnapped out of his brown study, begged Eusebius to wait a moment, and quicklyread what the latter had already absorbed.

Processes within Dissonant States

Metrical processes within dissonant passages may adjust a given dissonance, ortransform one dissonance into another. Among the most common "D-processes"are those that adjust the intensity of a given dissonance. These may involve anyof, and any combination of, the factors that distinguish weak dissonances fromstrong — the increasing of the continuousness and quantity of antimetrical ac-cents; the increasing of the number of accent types that form the antimetricallayer; the addition of the particularly powerful accent types mentioned in chap-ter 2 (dynamic or harmonic new-event accents); the reinforcement by groupingof antimetrical layers initially delineated only by accent, or vice versa; the trans-ference of an antimetrical layer initially announced in an inner voice to a moreprominent voice, and so on. These processes may be reversed to create effects ofdeintensification.

A simple example of intensification is found at the beginning of Schu-mann's first Papillon (Example 4.5). In mm. 1-3, density accents within the ac-companiment pattern very weakly establish an antimetrical 3-layer (1 =quarter)and hence the dissonance D3+1; the metrical 3-layer emerges from chordchanges and from the bass attacks. In mm. 4—6, Schumann conjoins the densityaccents with left-hand durational accents, so that D3+1 becomes slightly moreintense. A peak of intensity is reached in the final measure of the first section,where Schumann adds a second-beat dynamic accent to the preexisting types.He maintains this maximal intensity of dissonance during the first two measuresof the second section, then proceeds to deintensify the dissonance by eliminat-ing accent types. In mm. 11-12, he drops the second-beat dynamic accents, andin mm. 13-15, the durational accents as well. (I consider the durational accentsstill to be present in mm. 11—12; although the second-beat notes are not sus-

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EXAMPLE 4.5. Intensification of dissonance in Papillon no. I

tamed, the melody notes beginning on that beat remain in effect for the samerelatively large amount of time as the sustained notes in the preceding mea-sures.) In m. 16 Schumann surprisingly and wittily reminds us of the maximal

thick chords on the 'pah's,' always metrically dissonant? I do not think so." Euse-bius mused, "The author does admit that such a dissonance is very weak. And al-though it seems unconvincing at first to consider the accompaniment pattern atthe opening of our Papillon dissonant, I have no difficulty hearing it that waywithin the context of our gradual intensification process."

A more complex intensification process is found in the second section of

Schumann's sixth Novellette (Example 4.6). Registral accents on the second beat

in the uppermost voice in mm. 17 and 21, and durational accents on the same

beat in the "tenor" voice in mm. 18 and 22, create a sporadic antimetrical 4-

layer (l=8th), so that weak D4+2 emerges. In mm. 25-32, Schumann begins to

Fantasy Pieces92

intensity of the central measures.

Flores tan argued, "Are accompaniment pa t te rns of the 'oom-pah-pah ' form, wi th

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Metrical Progression and Processes 93

EXAMPLE 4.6. Intensification of dissonance in Novellette op. 21 no. 6, mm. 17— .0

intensify this dissonance. The antimetrical 4-layer becomes more continuous in

these measures—only one pulse is missing (in m. 28). A further intensifying fac-tor is the involvement in mm. 25 and 29 of three voices rather than just one inthe antimetrical durational accents. Futhermore, in mm. 25-26, 29, and 32, du-rational accents occur in an outer voice (as opposed to the "tenor" voice of ear-lier measures). Finally, in mm. 27-32, Schumann increases the number of ac-cent types that participate in the delineation of the antimetrical layer; on the

second beat of m. 27 he combines a registral accent with an accent of ornamen-tation, on the second beat of m. 29 a dynamic with a durational accent, on thesecond beat of m. 31 a registral accent with an accent of ornamentation, and on

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94 Fantasy Pieces

the second beat of m. 32 a durational and a harmonic new-event accent. The lat-

ter particularly prominent accent results in a peak of dissonance intensity.

As the opening music of the section reappears in m. 33, the dissonance is

deintensified; multiple accents yield to single accents, and weak-beat durational

accents retreat from prominent voices into an inner voice (compare mm. 32 and

33—34). The intensification-deintensification process is neatly coordinated with

the ternary form of the section; the A subsections contain weak D4+2, and the

B subsection intensifies this dissonance.

Eusebius said, "Another fine example of intensification occurs in the piece

that I named after the bringer of this manuscript — 'Vogel als Prophet.' I weakly

suggest the dissonance D2 + 1 (1 =quarter) in mm. 1—10 (Example 4.7a). The met-

rical layer is clearly audible in these measures, mainly because of the 'oom-pah-

rest-pah' pattern in the left hand, sometimes curtailed to just 'oom-pah.' An

aligned 2-layer is implied, as within any 4-layer, but I do not bring it to the sur-

face as yet. I clearly establish an antimetrical 2-layer, however, by density and

registral accents on the two weak beats of the measures; the thickest chords and

frequently also the highest right-hand pitches occur on those beats. The disso-

nance is absent from mm. 1 1—12, but I bring it back with greater intensity in mm.

13—14 (Example 4.7b), where my placement of the main harmonies delineates a

metrical 2-layer, and where an antimetrical 2-layer is strongly established by dy-

namic accents. The A section ends, as it began, with weak D2+1." Florestan con-

tinued, "In mm. 18—24, however, you take the intensification process one step

further. You keep the metrical 2-layer just barely alive by durationally accenting

the third beats of mm. 19, 20, 22, and 23 (in the right hand) and by the harmonic

changes in m. 22. A prominent displaced 2-layer results from durational, regis-

tral, dynamic and/or harmonic new-event accents on beats 2 and 4; your frequent

combination of numerous accents, including the most potent types, results in

D2 + 1 of unprecedented intensity (Example 4.7c). The term 'Verschiebung' at in.

23 was a witty stroke of yours, Eusebius; it refers, of course, to the soft pedal, but

it also means 'displacement,' which is at its most obvious here. In the final section

you restore the weaker dissonance of the opening and retrace the intensification

process only as far as the dynamically enhanced version corresponding to mm.

13 — 14." They turned to the manuscript and read:

closely related to processes of intensification and deintensification applied

to individual dissonances are those that intensify or deintensify dissonance in

general within a given passage. A particular passage may become successively

more or less dissonant in a variety of ways aside from the manipulation of one

dissonance. Increased duration of dissonance, or increased variety of disso-nance in juxtaposition or superimposition, may play a role in such generalized

intensification of dissonance. A process of this type is found, for example, in the

first sixty measures of the th i rd movement of the Piano Sonata op. 1 1. Schu-


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Metrical Progression and Processes 95

EXAMPLE 4.7. Intensification dissonance in "Vogel als Prophet" from Waldscenen op. 82

mann begins the movement with short bursts of dissonance. In mm. 1-2 (Ex-ample 4.8a) and 4-6, sforzandos on third beats hint at D3+2. In the same mea-sures, repetition of the resultant rhythm "quarter, dotted eighth, sixteenth" inconjunction with durational accents suggests a 2-layer and hence G3/2. In mm.

14-15, Schumann briefly refers to G3/2 dissonance, and in mm. 20-22 and24-25 equally briefly presents D3+2. In mm. 27-32, Schumann allows G3/2 tooccupy a much wider expanse (Example 4.8b); these measures represent an in-termediate step between the initial short bursts of dissonance and the culmina-tion of the intensification process in the first Trio. In this Trio (mm. 51-98 —

Example 4.8c), Schumann not only continues the trend of durational expansionof dissonance, adhering to a dissonant state for no less than forty-eight mea-sures, but also combines (in mm. 51-66) the two dissonances briefly statedwithin the first section (G3/2 and D3+2).

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EXAMPLE 4.8. Intensification of dissonance in the Piano Sonata op. 11, third mvmt.

Florestan said, "The reverse of such generalized intensification is also foundin our works. In my namesake piece from Carnaval, for example, the initial com-

bination of D3+1 and D3+2 (mm. 2 and 4) is subsequently separated out; D3+2

occurs on its own in mm. 5 — 6, and E)3+l in m. 8. The dissection of the initialcompound dissonance results in an effect of deintensification of dissonance."

Eusebius queried, "I wonder about mm. 27—32 of the third movement of op.

11 (Example 4.8b). These measures participate in an intensification process inthe sense that they durationally expand upon earlier allusions to G3/2. On the

other hand, the dissonance in a sense becomes less perceptible in these measures,

for one of its constituent layers—the metrical layer — is not articulated." Florestananswered, "I believe the author addresses this point in the following paragraph."

elated to intensification/deintensification are processes that convert sur-face dissonance into subliminal dissonance, and vice versa. It might seem that a


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Metrical Progression and Processes 97

subliminal version of a given dissonance, lacking articulation of the metrical lay-ers, would be weaker than a version where all layers are clearly perceptible, andthat progressions from surface to subliminal, and subliminal to surface, disso-nance should be regarded merely as special types of deintensification and inten-sification, respectively. The situation is, however, not quite so straightforward.Subliminal dissonances are indeed less intense than surface dissonances in thesense that they do not involve explicit superposition of nonaligned layers. Onthe other hand, they disrupt the normative metrical state in a clearly perceptiblefashion, and in this sense do deserve to be considered "intense" dissonances. Be-cause the relative degree of intensity of surface and subliminal dissonances issubject to interpretation, I prefer to designate processes that interchange sub-liminal and surface dissonance with terms other than intensification and dein-tensification. I apply the term "submerging" when a dissonance begins in a forminvolving explicit articulation of all constituent layers but then, by the elimina-tion of the metrical layer, becomes a subliminal dissonance. I use the term "sur-facing" for the reverse.

A submerging process is shown in Example 2.18. In mm. 45—46, the disso-nance D4+1 is on the surface; the metrical 4-layer is delineated by harmonicchange, the antimetrical layer by durational accents. Beginning in m. 48, how-ever, only the antimetrical layer is clearly articulated, so that the dissonance issubmerged.

The original finale of the Piano Sonata op. 22 (Presto in G Minor) opens withsubmerging and surfacing processes (Example 2.6). G3/2 is initially on the sur-face. The durational accents within the melodic line and a dynamic accent onthe fourth sixteenth-note attack clearly express the metrical layer in mm. 1-2.An antimetrical 2-layer is suggested by a dynamic accent on the third sixteenthnote and a low-point registral accent in the bass on the fifth sixteenth note. Inmm. 3—4, G3/2 is submerged; the metrical 3-layer disappears while the 2-layer,now expressed by successive melodic attacks in both hands, becomes moreclearly apparent. Measures 5-8 reiterate the process of mm. 1-4, as do mm.9-12. In mm. 11-12, however (Example 2.6b), Schumann takes the submerg-ing of G3/2 a step further by using dynamic accents to bring the antimetrical2-layer into greater focus than ever before; the metrical layer remains unartic-ulated. The following cadential measures (mm. 13-14) restore the 3-layer while

passages, the performer should emphasize the otherwise suppressed metricallayer. If the performer does so, however, during works in which a given disso-nance appears in both surface-level and subliminal forms, will not the distinctionbetween those two forms of the dissonance be blurred?" Florestan responded,The distinction, and the sense of surfacing or submerging, will indeed disappear

if the performer overstresses the metrical layer. Performers should not assumethat the metrical layer must be stressed in all pieces. In some of my works I desire

Eusebius inquired, "We earlier agreed that during subliminally dissonant

maintaining the 2-layer, so that G3/2 reappears on the surface.

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98 Fantasy Pieces

an effect of a disjointed dialogue between different meters, rather than one of aunifying, consistently present metrical layer. Much of the opening of this Presto in

G Minor falls into this category; I desire the performer and the listener to behurled back and forth between states of superimposed triple and duple layers(surface-level G3/2 dissonances), states in which the duple layer dominates (sub-liminal G3/2), and states in which the triple layer dominates (metrical conso-nance). Thus, the performer should not attempt to stress the metrical layer dur-ing the subliminally dissonant passages in this piece." Eusebius said, "It would inany case be almost impossible to do so at this speed. The pianist will have his orher hands full with the stresses that you notate!"

Florestan nodded, then remarked, "I must mention a fine example of the sur-facing of a displacement dissonance: the opening of my Intermezzo op. A no. 2 (seeExample 8.7). In mm. 1—9, I form a displaced 6-layer by pattern repetition, bythe attacks of a slow upward arpeggiation (E3-G3-B3-B3-E4) and, in mm. 3—5,by dynamic accents. I initiate the metrical 6-layer by the tonic octave in m. 1, butthereafter hardly articulate it, with the result that the displacement dissonanceD6+5 (possibly heard as D6-1) is here only subliminal. In mm. 9—13, I again ar-ticulate the antimetrical 6-layer by dynamic accents, but now allow the metricallayer to be heard as well; it emerges from the entries of the left hand. Thus D6+5,at first subliminal, moves to the musical surface."

Eusebius added, "We have at times associated the processes of dissonanceintensification and submerging to create an increasing sense of conflict againstthe notated meter across a passage or work. 'Abendmusik' from the Bunte Blatter

op. 99 is a good example. The fanfare-like introduction establishes the primarymetrical 3-layer (l=quarter) by durational accents on the downbeats. The maintheme (mm. 4—12 — Example 4.9a) immediately begins to challenge this layer.Durational accents in the bass fall, with two interruptions in mm. 7 and 11, onthe third beats to form an antimetrical 3-layer, while durational accents in themelody confirm the metrical layer; the interaction of these two layers results inthe dissonance D3+2. In mm. 6—8 and 10 — 1 1, we allude to G3/2; the metrical 3-layer is not clearly articulated in these measures, while the harmonies change attwo-quarter-note intervals, creating an antimetrical duple layer and hence sub-liminal G3/2. In the second section (mm. 12-28 —Example 4.9b), subliminalG3/2 becomes pervasive rather than intermittent. The varied repetition of theopening section in mm. 28—36 involves proliferation of the other dissonance es-tablished at the opening, namely D3+2; the antimetrical layer and the resultingdissonance here proceed without interruption (in the first section there were twogaps). We intensify the antimetrical layer and hence the subliminal dissonanceG3/2 within the varied repetition of the second section (mm. 36—42), expressingthe antimetrical layer not only by grouping (as in the corresponding mm. 12-28)but also by dynamic accentuation. In the new section encompassing mm. 62—86,similar to the Gt major section of your earlier piece 'Grillen' (ct. Examples 4.9cand 2.16), we revert to D3+2 —here probably heard as D3-1 —and submerge itby entirely suppressing the metrical 3-layer; there are no attacks on notateddownbeats until the final cadence of The section. The concluding section restates

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Metrical Proqressions and Processes 99

EXAMPLE 4.9. Intensification and submerging in "Abendmiuik"from Bunte Blatter op. 99

the opening. Up until that return, the durational expansion of dissonances com-bined with increasing suppression of the metrical layer inexorably increases thesense of metrical disorientation. Against this process of metrical decay, I set oc-casional calls to metrical order — the 'all-ottava' utterances at the beginning andending and at mm. 52-53 and 86-87, which counteract the disorientation by du-rationally accentuating the notated downbeats."

As Eusebius spoke, Florestan reflected, "The dissonance that ravages mysoul occasionally comes to the surface in spite of Eusebius's 'calls to order.' But

even when I appear calm and untroubled on the surface, dissonance rages withinme — submerged, but nonetheless intense."

When Eusebius had concluded his remarks, he turned back to the manu-script, and Florestan, too, attempted to focus his attention on the next section:

W e have so far studied D-processes that manipulate a given dissonancewithout changing its identity. There also exist processes that involve alterationof identity, generally from one dissonance to a related one. The simplest of theseare the processes of augmentation and diminution — progressions from lower-level to higher-level, and higher-level to lower-level members, respectively, ofdissonances belonging to the families "Gx/y" or "Dx+n." A passage from the

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100 FantasyPieces

EXAMPLE 4.10. Diminution in the Piano Sonata op. 14, first mvmt., mm. 8-1

opening of Schumann's Piano Sonata op. 14 (Example 4.10) provides a simpleillustration of augmentation and diminution of a displacement dissonance. Mea-

sures 8-1 1 are characterized by D8+2 (l=8th); dynamic, durational, and den-

sity accents on the second beats of these measures create a displaced 8-layer,

while the metrical 8-layer emerges from durational accents (cessation of sixteenth-

note activity) on the downbeats. In the immediately following measures (mm.

12—15), dynamic accents on metrically weak eighth notes result in D4+1, adiminution of the earlier dissonance. (D8+2 continues in a weaker form during

the diminution.) In mm. 16—20, the process is reversed as the material of mm.

8—1] returns.6

In his Study op. 10 no. 2, a transcription of Paganini's Caprice op. 1 no. 6

(cf. Example 3.6), Schumann applies diminution to a dissonance prominent in

Paganini's Caprice, namely G9/6 (where l=a triplet thirty-second note). Schu-mann begins his transcription by emphasizing this same conflict (Example

4.1 la). In mm. 1 and 3, as in Paganini's work, registral accents suggest a 9-layer. Schumann, however, adds a left-hand part in which durational accents

fall on the second quarter-note beat; these accents clearly imply a 6-layer, and

hence render G9/6 more apparent than at the opening of Paganini's Caprice.In addition to intensifying Paganini's G9/6, Schumann transfers that disso-

nance to lower rhythmic levels; his transcription introduces the diminutionsGl.5/1 and G3/2. In mm. 5-9 (Example 4.lib) and 13-15, Schumann superim-poses triplet and duple sixteenth pulses, the latter pulse being the resultant of

the nonaligned right-hand and left-hand eighth notes; these pulses together

form G 1.5/1.

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Metrical Progression and Processes 101

EXAMPLE 4.11. Diminution in the Study op. 10 no. 2

In mm. 19-26, Schumann introduces another diminution of Paganini's 9/6

conflict, namely G3/2. The duple grouping of triplet sixteenth notes is already

implied in Schumann's left-hand figuration at the opening of the work, where

chord members appear at two-triplet intervals. This grouping and the disso-

nance G3/2 become much clearer, however, at m. 19 (Example 4.11c), where a

new oscillatory accompaniment pattern results in a 2-layer, while harmonic

rhythm and right-hand melodic attacks continue the 3-layer. (Pianists will feel

the tug-of-war between the two layers as they play the passage.) G3/2 continues

in the right hand of mm. 27-35, and in mm. 27-35 Schumann combines G3/2and G1.5/l.

Eusebius said, "We treat a displacement dissonance originating in the Pa-ganini Caprice, namely D6+3, in a similar manner in our transcription. The dis-

sonance appears only briefly and weakly in Paganini's work, namely in m. 8,where an antimetrical 6-layer is created by dynamic accents, and in mm. 13-15,

where the same layer is suggested by slurring. We dispense with the displace-

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102 Fantasy Pieces

EXAMPLE 4.12. The final stage of a diminution process in the Piano Quintet op. 44, finale, mm.


ment dissonance in m. 8 of our transcription, but intensify it in mm. 13-15 by ac-

centing the beginning points of Paganini's displaced segments. We add hints atthe dissonance at the beginning of the coda (mm. 46-47), where the left hand'shigh notes create registral accents on the metrically weak eighth notes. Diminu-

tion of D6+3 occurs at several points in our transcription: the staggered eighth-note pulses in mm. 5-9 (Example 4.1 Ib), 13—15, and at similar places, which inconjunction with the triplet sixteenth-note pulse form the dissonance Gl.5/1, cre-

ate the displacement dissonance D3+1.5 in interaction with the right hand's met-rically aligned eighth notes."

Florestan, again engrossed in metrical issues, added, "The Study op. 10 no. 2illustrates that the dissonances involved in diminution are not necessarily contigu-ous; a diminution process may span a large area, its various stages interspersedwith material not involved in the process. Another example of such an extended,intermittent diminution process is found in the finale of the Piano Quintet op. 44.At m. 21, we initiate the dissonance D8+4 (l=8th), and mm. 37—39 contain thesame dissonance. A few measures later (m. 43), the diminution D4+2 appears;harmonic changes and string attacks determine the metrical 4-layer while thepiano's density accents create a displaced 4-layer. (This metrical diminution arisesfrom diminution of the entire earlier passage.) The progression 'D8+4 to D4+2'occurs again in mm. 156—84, where the material of mm. 21—49 is restated. Themusic at mm. 224—47 is the final stage of this diminution process (Example 4.12);the piano's agitated syncopation in eighth notes results in D2+1. The process con-

tributes a great deal to the sense of growing excitement within the movement."The first movement of our First Symphony ends with a broad augmentation

process applied to the dissonance D2+1 (1 =8th). The horns form this dissonancein mm. 432-37 by syncopating at the eighth-note level (Example 4.13a). Thestrings in mm. 439—59, and the winds in mm. 447-59, syncopate at the quarter-note level, resulting in the augmentation D4+2. In mm. 464 and 468-74 (Exam-ple 4.13b), finally, the interaction of layers formed by significant harmonicchange and recurrent bass attacks on the one hand, and by dynamic, durational,and registral accents on the other, results in the further augmentation D8+4. Weplace some reminders of an earlier stage of the process in the string parts at mm.468 — 79, where quarter-note syncopations recall D4+2."

Euscbius chimed in, "Our Second Symphony is even richer in such proce-

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Metrical Progressions and Processes 103

EXAMPLE 4.13. Augmentation in Symphony no. I, first mvmt.

dures. Your second movement ends with striking usages of augmentation anddiminution. In mm. 357—59 you powerfully state D2+1 (l=8th) by placing dy-

namic accents on metrically weak eighth notes in all instruments. The first fewmeasures of the subsequent frantic coda are consonant, but mm. 365-76 are

dominated by the augmentation of the preceding dissonance, D4+2, formedagain by dynamic accents on metrically weak pulses. In mm. 378-81 and 388-89, you bring back the quicker dissonance to generate momentum toward the

final cadence; the antimetrical layer is now formed by accents of density, then du-

ration, rather than by dynamic accents. In mm. 390-93, just before the final ca-dence, you once more state the augmented version of the dissonance by dynami-cally accenting the second beats."

Eusebius continued, "The third movement of the Second Symphony — one ofmy best slow movements —is spanned by an elaborate large-scale augmenta-tion process. The initial accompaniment figure in the violas is syncopated at thesixteenth-note level, creating D2+1 (l = 16th). In the violin melody, I immediatelylaunch the augmentation D4+2; there is almost continuous eighth-note syncopa-tion (durational accentuation of the second eighth note) in mm. 2-19. After abrief consonant stretch, D4+2 appears alone, formed by syncopation in thestrings (mm. 26-30), but I soon reunite it with D2 + 1 (mm. 35-43). Another

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EXAMPLE 4.14. Tightening in the "Landler"op. 124 no. 7

brief consonant passage follows; thereupon, I bring back D4+2 and D2 + 1 and

combine them with another augmentation, D8+4, created by quarter-note synco-

pation in the clarinets in mm. 48—53." Florestan commented, "1 have always ad-

mired how you coordinated this climax of the augmentation process with climac-

tic effects in other domains: in dynamics (poco a poco crescendo), register (highest

pitches in the first violins), and foreground rhythm (trills). But we must finish

this chapter; it is getting very late." They read:

Some D-processes apply only to displacement dissonances. I have made

a distinction between tight and loose displacement dissonnances—those involv-

ing frequent and infrequent contradiction of metrical layers, respectively. The

motion from a given displacement dissonance to a tighter or looser relative re-

sults in processes that I call "tightening" and "loosening," respectively. Tighten-

ing involves the preservation of the displacement index while the cardinality is

reduced by some integral factor. Loosening, on the other hand, involves in-

crease of cardinality with preservation of the displacement index. These pro-

cesses are related to augmentation and diminution; whereas the latter, however,

are based on alteration of cardinality and displacement index, tightening and

loosening involve alteration of the cardinality only.

Tightening is illustrated in the middle section of Schumann's "Landler," op.

124 no. 7 (Example 4.14). In mm. 8-12, during two sequential statements of a

V6/5-I progression (tonicizing V and III, respectively), the third beats of alter-

nate measures are dynamically accented, resulting in D6+2 (1 =quarter). In mm.

12 — 15, Schumann shrinks the sequential segments to a length of three beats by

eliminating the neighboring embellishment of mm. 8 — 12. He continues to ac-

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Metrical Progressions and Processes 105

cent the beginning of each sequential segment; the resulting third-beat accents,

now in each measure, create the tighter dissonance D3+2 (or D3-1). The 6-layersdo not entirely disappear as tightening begins. Our attention, however, focuses

on the 3-layers after in. 12.A similar example is found in mm. 143-68 of the sixth Novellette. At m. 143,

within a passage in which a 4-layer (l=quarter) is formed by harmonic changesat two-measure intervals, Schumann initiates dynamic accentuation of alternate

second beats, resulting in the dissonance D4+1. Displacement by a quarter notecontinues after m. 151 (see Example 2.11), but the cardinalities of the obviousconflicting layers are reduced to 2, resulting in the tighter dissonance D2 + 1. Inmm. 151-57, for example, harmonies change on each downbeat, reinforcing the

metrical 2-layer, and dynamic and durational accents on each second beat cre-ate an antimetrical 2-layer. Tightening of displacement dissonance is matchedby a steady increase in dynamic level, and resolution of D2+1 at m. 169 coin-

cides "with an abrupt decrease in volume.

Eusebius said, "We thoroughly explored the processes of tightening andloosening in our string quartets. I could mention many examples: the tighteningnear the beginning of the finale of the First Quartet (mm. 11—17) from D4+1 to

D2+1 (l=quarter); from D6+2 to D3+2 (l=quarter) in mm. 49-56 of the firstmovement of the Second Quartet; and from D6+5 (or D6-1) to D3+2 (or D3-1;l=8th) in mm. 1—16, 17—25, and 25—48 of the second movement of the Third

Quartet. The exposition of the first movement of the First Quartet demonstratesthat tightening and loosening, like augmentation and diminution, may take placeover broad expanses, the dissonances involved not necessarily being absolutelycontiguous. This exposition is based on an alternation between tightening andloosening, resulting (if I may say so myself) in a pleasing rise and fall of tension.The first theme area begins with D12+3 (l=8th); there are dynamic accents onweak dotted-quarter beats of alternate measures in mm. 36-49 (Example 4.15a).

In mm. 52-55 (Example 4.15b), we tighten the dissonance to D6+3; the celloprovides durational accents on the weak beat of each measure. Loosening (re-

version to D12+3) occurs in mm. 58 — 63 (where the first violin's durational ac-cents and pattern repetitions delineate a hypermetrical 12-layer, while the secondviolin's and cello's durational accents on weak beats of alternate measures resultin a displaced 12-layer —Example 4.15c). We adhere obsessively to D12+3 inmm. 68 — 91, whereupon our placement of dynamic accents on all weak beats inmm. 92-95 again tightens the dissonance to D6+3 (Example 4.15d). We onceagain loosen the dissonance in mm. 95—98, where dynamic accents fall only onalternate weak beats. A consonant patch follows (mm. 99—116), but at the veryend of the exposition, we apply the tightening and loosening processes onceagain to the same motivic dissonances."

Florestan recalled some instances of tightening and loosening from the sym-phonies: "The coda of the finale of the First Symphony illustrates that tighteningmay skip a step, so to speak. In mm. 265-68 (Example 4.16a) and the related

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106 Fantasy Pieces

EXAMPLE 4.15. Tightening ant) loosening in the exposition of the Siring Quartet op. 41 no. I, first


mm. 275—82, the dissonance D8+5 (l=quarter) results from dynamic accents onthe second quarter notes of alternate measures (that is, on the fifth attacks ofeight-pulse hypermeasures). In mm. 285—88 (Example 4.16b), we create D2+1by placing dynamic, then durational accents on second and fourth quarters. Theprogression from D8+5 to the tighter relative D2+1 skips over the intermediateD4 + 1 (which, to be sure, is embedded in D2 + 1). After repeating the progression'D8+5 to D2+1' in mm. 297—312, however, we fill in the skipped step. In mm.313—20, D8+5 returns, again produced by dynamic accents on second quartersof alternate measures. As before, D2 + 1 follows, but this time we place the em-bedded D4 + 1 into relief by dynamically stressing the second quarters of ( all mea-

sures (mm. 320—22 — Example 4.16c).

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Metrical Proqressions and Processes 107

EXAMPLE 4.16. Tightening in the coda of the finale of Symphony no, 1

"A large part of the exposition of the finale of the Fourth Symphony isspanned by successive tightening. The melody of mm. 27-37 is characterized bydescending arpeggiations in each measure. We precede the arpeggiation of every

second measure with an octave leap that delays the arpeggiation by one beat andresults in registral and durational accents on the second beats (Example 4.17a).These accents, reinforced by dynamic stress, interact with the hypermetrical 8-layer created by pattern repetition to form the dissonance D8+1 (l=quarter). Therelated theme in mm. 39-57 (Example 4.17b) is characterized by second-beatdurational, registral, and/or dynamic accents in each bar (with a few exceptions),

which result in the tighter dissonance D4+1. Measures 58-62 are consonant, butwithin their varied repetition in mm. 63—65 (Example 4.17c), we add dynamicaccents on all metrically weak beats, resulting in a further tightening to D2 + 1.

With this broad tightening process," Florestan concluded, "we attempted toimbue this exposition with a sense of heightening tension."

Eusebius remarked, "The author's D-processes are all associated in somemanner with effects of increasing or decreasing of tension. In the case of intensi-fication and deintensification, these effects are obvious. Diminution and tighten-ing, since they involve an increase of speed and in frequency of contradiction of

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EXAMPLE 4.17. Tightening in the finale of Symphony no. 4

metrical pulses, respectively, are appropriate when an increase of tension is de-sired, whereas augmentation and loosening suggest relaxation." Florestan said,"The process of submerging is more difficult to classify in terms of its degree oftension. Since in this process the metrical component of a dissonance disappearsfrom the musical surface, resulting in a decrease in obvioius contradiction of met-rical layers, the overall effect might appear to be one of decrease of tension. Onthe other hand, as the author suggests, because submerging involves suppressionof metrical layers, it is a particularly strong contradiction of the primary conso-nance. It is the latter perspective on submerging that underlies our subliminaldissonances; we expect the performer to ensure that submerged dissonances con-vey an effect of tension rather than relaxation."

Eusebius yawned and said, "Speaking of relaxation, I would very much liketo sleep now." Florestan, however, observed that there was only one more unit inthe chapter, and insisted that they should finish it before retiring.

Dissonance-to-Consonance Processes (Resolution)

Progressions from dissonance to consonance can, following our pitch-to-rhythm

analogy, be termed "resolutions."7 Whereas in tonal music, many dissonances in

the pitch domain arouse the expectation of a particular resolution even out of

context, metrical dissonances do not in themselves imply specific resolutions.

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Metrical Progressions and Proceccess 109

EXAMPLE 4.18. Resolution of dissonance in the "Preambule"from Carnaval

Within a given context, however, particular resolutions may well be implied bythe composer, and expected by the listener. If, for example, a 3-layer is the well-established primary metrical layer, and a 2-layer is for a time superimposed onthat layer, the listener will expect the 2-layer to be abandoned and the triple con-sonance to be restored. When such restoration of earlier consonance occurs,there is undeniably an effect akin to that associated with resolution of pitch dis-sonance — a sense of satisfaction, of a devoutly wished consummation. The term"resolution," in short, seems perfectly appropriate as a designation for disso-nance-to-consonance processes.

Resolution may occur abruptly, or gradually. Abruptness of resolution isalways relative, never absolute, for any juxtaposition of dissonance with conso-nance results in an indirect dissonance between juxtaposed interpretive layers,which endures until the listener's memory of the abandoned layer fades. Thereis thus always a transitional phase between a metrical dissonance and a resolv-ing consonance. Nevertheless, some dissonances resolve relatively abruptly andothers only by stages.

Abrupt resolutions subdivide into two classes: those that occur by theabandonment of one (or more) of the layers of motion contained within the dis-sonance, and those that occur by the establishment of a consonance none ofwhose layers were contained within the dissonance. The latter class of resolu-tions is rare. Such resolution is most likely to occur when a dissonance that didnot contain the primary metrical layer is followed by the primary consonance. Astriking example occurs at the end of the Preambule of Carnaval (Example 4.18).Measures 130—34 are occupied by the displacement dissonance D2+1; the lefthand's "oom-pah's" create one of the constituent 2-layers, the right hand's dy-namically accented attacks form the other. At the end of the movement, as onewould expect, the 2-layers drop out and the metrical 3-layer is reinstated.

Florestan pointed out, "The three final chords cannot entirely erase the 2-layersfrom the listener's mind. And 'Pierrot', in duple time, immediately brings themback, one of them now being the metrical layer. The other, displaced 2-layer ap-pears in the form of forte exclamations at the ends of phrases and, in the middlesection, in the form of syncopations."8

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Much more common is the type of abrupt resolution arising from the

abandonment of: one of the layers contained within the dissonance. This type

frequently occurs in the situation mentioned at the beginning of this section: a

work establishes the primary consonance, the primary metrical layer is joined

for a time by one or more dissonant layers, then the latter are abandoned so as

to restore the primary consonance. Some of the examples from the beginning

of chapter 2 illustrate such resolution. Immediately after the passage shown in

Example 2.1, the displaced layer formed by dynamic accents is eliminated, so

that the primary consonance remains. In Example 2.3, the antimetrical dotted-

quarter layer is abandoned in mm. 3-4, again leaving behind the primary


A common ingredient of abrupt resolutions into the primary consonance is

a dynamic accent that reinforces the initiation of that consonance. I refer to

such accents as "corrective accents." An illustration is found in Example 2.16;

Schumann highlights the end of the subliminal dissonance G3/2 and the reap-

pearance of the metrical 3-layer by placing a dynamic accent on the downbeat

of m. 71. Another example of a corrective accent is found in m. 99 of the first

movement of the First Quartet (Example 4.15d).

Eusebius said, "It is not necessarily the primary consonance that appears

upon deletion of one of the constituent layers. Jn my slow movement of the Ouar-

tet op. 41 no. 2, for example, the section marked Molto pill lento (mm. 64 — 76—see

Example 8.35) is permeated by G3/2 (1 =8th). The cello attacks clearly express a

two-eighth-note layer, while the other instruments maintain the primary 3-layer

by durational and dynamic accents and, to some extent, by their three-note com-

plete neighbor groups. As the Un paco pill vivace section begins (m. 77 —see Ex-

ample 8.34), the 3-layer (the primary metrical layer of the movement) disap-

pears, and the continuing 2-layer forms a duple consonance in interaction with

the eighth-note pulse." Florestan remarked, "One might think of such resolutions

as 'deceptive'; the listener would expect abandonment of the antimetrical layer

during resolution rather than deletion of the metrical layer."

Gradual resolution can take place m a number of ways. Many such reso-

lutions involve D-proccsses that somehow prepare the impending state of con-

sonance. A deintensification process, for example, can lead gradually from a

state of dissonance to one of consonance. The dissonance shown in Example 2.2

is resolved in this manner. D6+2 (l=8th), produced by antimetrical dynamic

and durational accents, endures throughout the Tempo risoluto variation. At the

opening of the following coda (mm. 224–31 —Example 4.19a), dynamic accen-

tuation ceases, so that the antimetrical 6-layer (when it is present at all) is pro-

duced only by durational accents. This deintensification paves the way for the

resolution at m. 232. Schumann maintains metrical consonance in the greater

part of the coda, but concludes the movement with a review of the progression

from dissonance through d e i n t e n s i f i c a t i o n to consonance (Example 4.19b).


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Metrical Proqressions and Processes 111

EXAMPLE 4.19. Gradual resolution by deintensification in the String Quartet op. 41 no. 3, second


The above example involves a form of loosening as well; Schumann drops

attacks of the antimetrical layer in the first seven measures of the coda (though

not in the systematic fashion of other instances of loosening mentioned here).

The process of loosening is another appropriate vehicle for gradual resolution.

It provides an intermediate stage of "dilution" between the original dissonance

and the state of resolution; some antimetrical accents are eliminated, in prepara-

tion for the elimination of all of them. Further instances of loosening leading intoresolution can be found in the first movement of the First String Quartet. Theprogression of D6+3 to D12+3 in mm. 92-98 (Example 4.15d) leads nicely into

the following consonance. The same metrical progression takes place at the be-ginning of the development section (mm. 129-41) and in mm. 193-207.

Resolution of compound dissonances frequently occurs by a gradualshedding of interpretive layers until only one, and thus metrical consonance(visually the primary consonance), remains. The compound dissonance shown

in Example 4.8c resolves in this manner. Both constituent dissonances (D3+2

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112 Fantasy Pieces

and G3/2) remain in place from m. 50 to m. 66. In the latter measure, Schu-

mann eliminates the 2-layer by altering the bass line. A displaced 3-layer,however, remains in effect along with the metrical layer (which continues tobe expressed by the recurring bouncing eighth-note idea).9 In mm. 94 and

96-98, the antimetrical 3-layer, highlighted by dynamic accents, flares up to apeak of intensity, then fizzles out in m. 99, so that D3+2 is at least temporarilyresolved.

Eusebius observed, "My second theme for the first movement of the ThirdString Quartet provides another fine example of gradual resolution of a com-pound dissonance. Deintensification also plays a role within this resolution. Ibegin the theme (Example 4.20a) with a blend of D2+1 (or D2-1) and D12+8(l=8th). The former dissonance arises from the persistent nonalignment of themelody and accompaniment. If I had written the accompaniment chords as af-terbeats, the dissonance would be relatively weak (as in other cases of the 'oom-

pah' type of accompaniment). Since the first accompaniment chord, however,precedes the first melody note, the layer formed by the chords assumes greatprominence. It sounds, in fact, like the metrical layer, and the layer formed by themelody notes sounds syncopated, or antimetrical; the result is a situation of in-tense dissonance. The other component of the compound dissonance, D12+8,arises from my placement of registral and durational accents on alternate second

beats. The metrical 12-layer is, in fact, virtually imperceptible, with the resultthat D12+8 is subliminal. At m. 62 (Example 4.20b), I \veaken the dissonance,expressing the antimetrical 2-layer in the viola alone rather than by chords inthree instruments. This deintensification process foreshadows the complete reso-lution of D2 + 1, which occurs when I entirely eliminate the displaced 2-layer atm. 74. D12+8 remains in effect throughout my resolution of D2 + 1. In mm. 76-80(Example 4.20c), rather than initiating the resolution of the remaining disso-nance, I place durational and dynamic accents on all second beats, thus creatingD6+2, a tighter relative of D12+8. This tightening, associated with a rising chro-

matic sequence, is a deliberate reversal of the relaxing trend of the passage. It is,however, a temporary reversal; immediately thereafter, I return to and completethe resolution process. During the mysterious C#-major arpeggiation in mm.81—83, I eliminate the displaced 6-layer and clearly express the metrical layer bydurational accents. After a few more rufflings of the metrical surface, I close theexposition with secure metrical consonance." Florestan said, "This is indeed afine, imaginative instance of an extended resolution process. And now, Eusebius,

we have only one more paragraph to read!"

As I mentioned earlier, we frequently refer to the most pervasive metricalconsonance of a work as "the meter." The meter in a broader sense, however, in-cludes not only that consonance but also the various conflicts against it, andprocesses such as those that I have descr ibed—in fact, the entire metrical pro-gression of the work. Meter in this sense is not a monoli thic , inflexible grid, but

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EXAMPLE 4.20. Gradual resolution of compound dissonance in the String Quartet op. 41 no. 3, first


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114 Fantasy Pieces

is as organic and expressive as any other component of music.10 The moves

from one metrical state to another in Schumann's music, and his adjustments of

individual states, contribute greatly to the impact of his works; the resultingwaves of tension and relaxation cannot fail to bear us as listeners with them, in

fact to move us.

Florestan closed the manuscript and said, "Now it is time for us to move

from this sofa into our beds, and to resolve in sleep, at least temporarily, the ten-sions that have wrenched us this evening." They bade each other a good night

and went to bed.

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Intermezzo 11

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Metrical Revisions

Florestan and Eusebius arose late the following morning. Clara, who was alreadypracticing busily, had left breakfast for them on the table. They sat down and ateand drank in silence for awhile. The flow of coffee, however, was soon succeededby a flow of conversation. Florestan's eye happened to fall on the shelves stackedwith the manuscripts and sketches for their works, arranged in tidy bundles andbound volumes, and he said to his companion, "I recall your reference in Eupho-nia to my 'mutation' of your idea for the first Trio from the Piano Sonata op. 11.It seems to me that such revisions of metrical structure occurred frequently dur-ing our compositional travails."1 Eusebius, thoughtfully sipping coffee, said,"They did indeed. Most of them involved your addition of metrical dissonance topassages that I had conceived in consonant form. Sometimes you inserted disso-nant segments into my consonant contexts. In my early version of the original fi-nale for the Piano Sonata op. 22 as well as in my later fair copy, the dissonanceG3/2 (l=triplet 16th) that now occupies mm. 99—106 (Example 2.6c) was notpresent. When you revised the fair copy, you placed crosses and alphabetical la-bels at m. 99 and corresponding measures, and wrote the material to be insertedon similarly labeled loose pages. In an even later manuscript of the completesonata, you included the dissonant passage at m. 99 and at several later points."2

Florestan interjected, "I recall that we had some arguments then about whetheror not to let the passage stand (the movement was rather long even without it).You crossed it out, but I, too captivated by its beauty to relinquish it, insisted onits inclusion. You finally relented, and permitted me to write 'gilt' in ink besidethe passage."3

Eusebius went on, "I recall a similar revision in the Second String Quartet.In the completed finale, you included a four-measure passage in which all metri-


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118 Fantasy Pieces

EXAMPLe 5.1. String Quarted op. 41 no. 2, fourth mvmt., mm. 90-9

cally weak eighth notes are dynamically accented, resulting in D2+1 (l=8th; Ex-

timple 5.1). In my first draft, these measures were absent."4 As he spoke, Euse-

bius rose from the table, drew the folder containing the quartet sketches from the

shelf, opened it to the page that he was discussing, and pointed out to Florestan

that the present m. 89 was originally followed by a double bar, then by the pres-ent m. 94. As they continued their reminiscing, they constantly interrupted their

breakfasts to remove another manuscript from the shelves, and the open folders

and volumes gradually formed a rampart around their dishes.Florestan observed, "More often than inserting dissonant measures into your

consonant passages, I added new voices that were metrically dissonant against the

existing material. My revision of mm. 25—27 of the Preambule from Carnaval comesto mind. In your early sketch of the passage—here it is on page 16 of our "musical

diary"5 — an emphatic, octavc-doubled statement of the main motive in both hands

was succeeded by two measures of soft repeated chords, then by a restatement of

the motive in the left hand alone. I later followed the octave-doubled motive directly

with a left-hand restatement and added to it a right-hand imitation (Example 2.7).

The entry of the imitated motive on beat two of m. 27 already created D3+1, whichdissonance I further intensified by dynamically accenting the beginning of the imi-

tative entry. In the following measures (28—30, also 32—34), 1 added an 'oom-pah'

accompaniment pattern whose pairs of quarter notes interacted with the continuingthree-quarter-note motive to form G3/2. Thus, I clad your consonant passage in two

types of dissonance by the addition of textural layers."Similar examples abound in our chamber music," Florestan continued. In

your draft of mm. 8 ] -88 of the first movement of the Second String Quartet, you

originally notated only the second violin part, which quotes the consonant open-ing theme in the dominant key.6 In the fair copy I added a first violin and viola

counterpoint in mm. 81-84, and open fifths simulating the drone of a bagpipe in

the cello in mm. 84–87. Both the counterpoint and the drone durationally accen-

tuate the eighth-note pulses just before the downbeats of the theme, resulting inthe dissonance D6+5 (or D6-1; Example 5.2)7 And do you remember, Eusebius,how we agonized over mm. 162 — 74 of the first movement of the Piano Trio op.

80 — a contrapuntal spinning out of a portion of the second theme? There arethree crossed-out attempts at this passage in our first draft . 8 Missing in all drafts,

however, was the piano bass which, in mm. 165-70 of the final version, has dy-

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Metrical Revisions 119

EXAMPLE 5.2. String Quartet op. 41 no. 2, first mvmt., mm. 80-88

namic accents on the third and sixth eighth notes of the bar, resulting in D3+2(Example 5.3). I added that voice and that dissonance in the fair copy."9

Eusebius, helping himself to a second roll and filling his coffee cup, said, "Asthe passage that I mentioned in Euphonia illustrates, you sometimes created met-rical dissonance by adjusting the alignment of existing textural layers rather thanby adding new ones. My first brief sketch of this first Trio from the third move-ment of the Sonata op. 11 shows that I originally conceived of its melody as beingin accord with the notated meter; the melody's durational accents consistently fellon the notated downbeats (Example 1.6a). In your later, more detailed sketch(Example 1.6b), you sh*tted the melody backward to create the dissonanceD3+2. You revised mm. 46 — 53 of the finale of the Piano Sonata op. 14— the Con-

cert sans orchestre — in a similar manner. In your beautifully conceived final version(Example 5.4a), the triplet sixteenth-note figuration is composed of three voices,two moving by step and one reiterating a single pitch. The attacks of the lower

and more prominent of the linear voices, each of which carries a 'new-event' ac-cent, are not aligned with the eighth-note pulses of the two-four measures." Flo-restan interposed, "Furthermore, whereas most of the chords arpeggiated during

the sixteenth-note figuration are passing chords, the second-to-last sixteenth notein each measure sounds like a strong harmonic arrival. The accents created bythese new harmonies and those created by the melodic new-event accents thatyou have mentioned result in displacement dissonance on two levels." Eusebiuscontinued, "In my rather tame early sketch for part of the passage (Example

EXAMPLE 5.3. Piano Trio op. 80, first mvmt., mm. 165— 70, piano part

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EXAMPLE 5.4A. Piano Sonata op. 14, fourth mvmt., mm. 46-50

5.4b), the various voices were aligned on the metrical eighth-note pulses, with nohint of dissonance.10 Your revised version is a brilliantly colored butterfly thatemerged from the humble chrysalis of my idea."

Florestan pulled the third sketchbook off the shelf and opened it to page 109,saying, "Here is a rather different and particularly interesting example of my in-jection of dissonance into one of your consonant ideas. In your sketch, appar-

ently intended for violin and piano (Example 5.5a), a 2-layer (l=quarter) arosefrom the durational accents within the reiterated 'four-sixteenth-note, quarter-note' figure and from the dynamic accents in mm. 8-10. This layer interacted

with a 4-layer produced by harmonic change to create the primary metrical con-sonance." As he turned to page 38 of the same sketchbook, he said, "Now look at

my radical reworking of your material (Example 5.5b), which in every respect,including key, time signature, and instrumentation, much more closely resemblesthe ultimate destination of the passage—the second section of the Intermezzo op. 4

no. 5. From m. 5 of this second version onward, your 'four-sixteenth-note, quarter-note' motive, already announced in the initial measures, becomes particularlyprominent. As in your earlier version, the durational accents within the motiveform a 2-layer. Within my revised metrical context, however, this layer results in

metrical dissonance; it conflicts with the primary metrical 3-layer, which I estab-lish in the initial three bars by durational accents and repetition of the note D,and which I uphold in mm. 6—7 by the harmonic rhythm." Thus, I created met-

EXAMPLE 5.4B. Sketch for the ,same passsage, Arcbiv (der Gesellscbaft der Musikfreunde in Wien,

A285, p. 2, br. 7

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Metrical Revisions 121

EXAMPLE 5.5A. Sketch destined to be absorbed into the Intermezzo op, 4 no. 5, Universitats- and

Landesbibliothek Bonn (ULB Bonn), Manuscripts Division, Schumann 15 (Sketchbook III),

p. 109, br. 1, mm. 5-10

rical dissonance by importing a layer that was originally in alignment with themetrical layer into a new metrical context with which it conflicts."

Eusebius, spreading plum jam on his roll, said, "We have so far mentionedonly your revisions involving the addition of new dissonance to my consonant pas-sages. I believe, however, that most of your metrical revisions involved the manip-ulation of dissonances that already existed in my first versions (for not all of my ini-tial sketches were devoid of metrical conflict!). Sometimes your manipulationstook the form of altering the dissonance type that I had chosen.12 More frequently,however, you simply enhanced the dissonances that I had already sketched."

EXAMPLE 5.5s. Sketch for Intermezzo op. 4 no. 5, ULB Bonn, Manuscripts Division, Schumann

15, p. 38, br. 1-2

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122 Fantasy Pieces

"Or," said Florestan, "that / had sketched. For instance, in my final revisionof the 'mutated' version of the first Trio of the third movement of the Sonata op.11,1 added even more dissonance (compare Examples 1.6b and 4.8c); I made thebass hop back and forth between the tonic and dominant notes, rather than

woodenly reiterating the tonic note. By pattern repetition and low-point accents,this activated bass established a 2-layer (l=quarter), which resulted in the addi-

tion of G3/2 to the existing D3+2, and in the conversion of a simple dissonanceinto a compound dissonance."13 Eusebius noted, "My contribution to the finalversion was the elimination of the second version's inner-voice dynamic accents;I felt that listeners might find it difficult to absorb your added grouping disso-

nance if the displacement dissonance were too prominent."Eusebius continued, "More often than adding layers to create compound dis-

sonances, you merely intensified my simple dissonances, usually by adding dy-namic accents.14 Your fine-tuning of accentuation is evident even in our earliestworks. In an early draft for op. 2 no. 8 (Example 5.6), 1 included a hint at D6+4(1 =8th) in the form of an inner-voice tie linking the third beat of m. 24 to the first ofm. 25. In the final version, I eliminated this antimetrical durational accent; you, onthe other hand, added dynamic accents on the third beats of mm. 24, 25, 27, 29, and31, thereby greatly intensifying D6+4. Another early example of added accentua-tion is found in the ninth Impromptu, op. 5. I already suggested the dissonanceD3+1 in my first version by writing durational and registral accents in the left hand

(Example 5.7).15 In both published versions, your added dynamic accents on thetreble and bass notes played by the left hand significantly enhance the dissonance."

EXAMPLE 5.7. Sketch for the opening of Impromptu op. 5 no. 9, Scbunann-Haus Zwickau

4648-A I, recto, br. 4

Schumann 15 (Sketchbook III), p. 96, br.I

EXAMPLE 5.6 PapillonDraft of op.2 no. 8, mm.25-26. ULB Bonn, Manuscripts Division,

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Metrical Revisions 123

EXAMPLE 5.8A. Draft of String Quartet op. 41 no. 1, first mvmt., mm. 20-23, Deutscke

Staafobibliothek zu Berlin —PreufcherKulturbesitz, Musikabteilung mit Mendelssohn-Arcbiv,

Mus. ms. autogr. R. Schumann 19, p. 3, br. 5- 6

Florestan, pouring some more coffee for both of them, said, "My practice of

adding dynamic accents continued to be frequent in later works. Compare yourdraft of mm. 20—22 of the first movement of the First String Quartet (Example

5.8a) with my final version (Example 5.8b). In the former, registral accents in thefirst violin part (mm. 21—22) and two dynamic accents on a metrically weak six-teenth note (mm. 21 and 23) already resulted in a hint of D2 + 1 (l = 16th). In myfinal version, mm. 20—22 contain numerous dynamic and some registral accentson metrically weak sixteenth notes, resulting in more intense dissonance. Simi-larly, in your sketch of mm. 47—51 of the finale of the Third Symphony, the

weak-beat dynamic accents of my final version (Example 2.18) were lacking.16

Whereas your consistent antimetrical durational accents already suggested D4+1(l=quarter), my reinforcement of the durational accents by dynamic accents re-sulted in much stronger dissonance."

Eusebius observed, "May I remind you that occasionally it was I who inten-sified dissonances that existed in your first versions? I did so, to be sure, by re-

moving dynamic accents rather than by adding them." In the booklet of sketchesrelating to the String Quartets, op. 41, he turned to the beginning of the Scherzomovement of the second quartet and said, "The original version was typical of

EXAMPLE 5.8B. Final version of the passage

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124 Fantasy Pieces

EXAMPLE 5.9A. Draft of String Quartet op. 41 no. 2, third mvmt., mm. 1-3, Deutsche Staatsbit

liotbek zu Berlin —Preufiuchcr Kullurbcjitz, Miuikabteilitntj mit Mendelssobn-Arcbiv, MM. nu

autogr, R. Schumann 19, p. 27, br. 3

your style; you insistently contradicted the notated meter by placing density ac-cents, harmonic new-event accents, and some dynamic stresses on the upbeats(Example 5.9a). When I copied your version out, I initially left its metrical struc-ture unchanged, except that I transformed pairs of your three-four measures intomeasures of six-eight (since 1 felt that eighth notes better suggested the fleet-footed character of the movement). Subsequently, however, I revised the passage

by crossing out all of your dynamic stresses on weak beats and adding downbeatstresses in m. 4 and in the corresponding m. 12; we agreed to publish the passagein this revised form (Example 5.9b).'7 Whereas your draft, with its offbeat

stresses, looked strongly dissonant, I realized that the dissonance would hardly beevident to listeners. One of the layers involved in the apparent dissonance — themetrical layer — was virtually imperceptible. Most listeners would likely have

heard the layer of motion resulting from the dynamic stresses as the metricallayer, and would have perceived no conflict against it. My final version incor-porates features that clearly convey the metrical layer—the added downbeatstresses, and retains others that establish a displaced 6-layer — the density andharmonic new-event accents, with the result that a conflict between nonalignedlayers becomes much more clearly apparent."

Florestan said, "I recall that you advocated a similar revision at the opening ofthe finale of the Piano Sonata op. 11. As Meister Raro pointed out yesterday, the

EXAMPLE 5.9B. Final version of the passage, mm. 1 — 5

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Metrical Revisions 125

EXAMPLE 5.10. Piano Sonata op. 11, finale, mm. 1-4

opening theme of this movement involves a clear duple grouping of quarter-notebeats that conflicts with the notated three-four meter (Example 5.10). In my earlyversion of the opening, virtually identical to the final version in terms of pitches anddurations, I had emphasized the 2-layer by placing dynamic accents on the first

and third beats of the first measure, a tenuto marking on the second beat of m. 2,and similar tenuto markings in mm. A and 6.18 I did not realize at first that since thiswas the opening of a movement and the notated meter had in no way been estab-lished, this version, in spite of its appearance, did not sound dissonant, but gave theimpression of undisturbed duple meter (with a larger triple grouping). Your elimi-nation of the dynamic accents in the final version gave the notated three-four meter

a fighting chance of becoming audible; the pianist, not told to accent the attacks ofthe duple layer, was now at liberty to give some subtle accentuation to the notateddownbeats so as to render audible the conflict between the metrical 3-layer and thebuilt-in 2-layer. But please refresh my memory, Eusebius: why did you not excise

the corresponding accents during the restatements of the opening theme in mm.49-57, 190-205, 238-46, and 381-96?" Eusebius responded, "I felt that at theselater points, the listener would have sufficiently grasped the notated triple meter,

would be able to maintain it during the theme, and, in spite of the accents, wouldperceive the dissonance G3/2 rather than duple consonance."

Florestan, wiping some jam from his hand, said, "Your revisions, Eusebius,notwithstanding the two movements that we have just discussed, generally resultednot in intensification but m deletion or deintensification of dissonance. At times you

persuaded me to eliminate dissonant passages entirely. The fourth piece in our firstedition of the Impromptus op. 5, for example, contained much displacement disso-nance. When we prepared the second edition, you recommended the elimination ofthis variation and its replacement with a metrically consonant one of livelier char-acter. Similarly, I planned to include in the slow movement of the Piano Sonata op.14 a variation in six-eight time in which the second eighth notes of numerousgroups of three were dynamically accented, creating D3+1 (Example 5.11). Onyour advice, I omitted this intensely dissonant variation." Eusebius responded, "Istill think I advised you well. Displacement dissonance was already prevalent inseveral of the other variations, and also permeated the remaining movements of thework. I felt that some relief from this conflict would be appropriate."19

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Eusebius continued, "More frequently than I eliminated entire dissonantsections, I modified accentuation so as to weaken your dissonances. The manu-script of the Davidsbundlertanze, for instance, shows that you originally intendedthe middle section of no. 13 to be dissonant; under a right-hand part identical to

the present one, you initially notated a syncopated bass line.20 I crossed out thisline and pasted the present nonsyncopated bass over it. My elimination of anti-metrical durational accents resulted in a virtually consonant middle section."

Florestan said, "You revised my original conclusion for the Papillons (corre-sponding to mm. 63—92 of the finale) in a similar manner. You recall that the left-

hand statement of the horn-call-like opening theme yielded in this early versionto a chromatic progression in contrary motion, moving in steady quarter notes.My strategy within this progression was to replace an increasing number of thequarter-note pulses with silence — a strategy that I was also employing withinthe melody. After four measures of unbroken quarter-note motion, I suppressedthe downbeats of four successive measures, then eliminated every second quarter-note attack (Example 5.12). The suppression of downbeats resulted in weak

D3+2 (since durational accents occurred on the third beats), and the duple layerformed by the elimination of alternate quarters conflicted with the underlyingprimary metrical 3-layer to create G3/2." Eusebius observed, "In my final ver-sion, I retained your weak D3+2 (mm. 74-88), but dispensed with the morestriking G3/2, so that dissonance in the passage is markedly less strong."21

He continued, "You have mentioned your addition of G3/2 to the passage

that we eventually used as mm. 20—26 of the Intermezzi op. 4 no. 5 (see Example

EXAMPLE 5.12. Sketch for the conclusion of Papillons, ULB Bonn, Manuscripts Division, Scbu

126 Fantasy Pieces

EXAMPLE 5.11. Sketch far a variation intended for the slow mvmt. of the Piano Sonata op. 14, ULB

Bonn, /Manuscript,' Division, Schumann 2, p. 3,br. 4, mm. 5— 7

mann 15 (Sketchbook III), p. 53, br.1 - 2

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Metrical Revisions 127

EXAMPLE 5.13. Intermezzo op. 4no. 5, mm. 20—26

5.5). But I later reshaped the passage once again, eliminating the dissonance(Example 5.13). I excised a dynamic accent and a tie across the bar line—that is,an antimetrical durational accent — that contributed to the establishment of thisdissonance (compare m. 3 of Example 5.5b and m. 25 of Example 5.13). Afterthe cadence in m. 26, I dispensed with the imitation of the 'four-sixteenth-note,quarter-note' motive, thereby eliminating durational accents on alternate beatsthat had also participated in the formation of G3/2."

Florestan remarked, "In connection with op. 4 no. 5, you have mentioned theremoval of a dynamic accent. I believe that you most frequently accomplished theweakening of my metrical dissonances by this method." Eusebius agreed, saying,"Striking examples of my removal of dynamic accents are found in the tenth Pa-

pillon. In your earliest version of the third section (Example 5.14a) — so early asto be in the 'wrong' key—you had only very weakly expressed the primary met-

EXAMPLE 5. MA. Early sketch for Papillon op. 2, no. 10, mm. 25-29, ULB Bonn, Manuscripts

Division, Schumann 15 (Sketchbook III), p. 88, br. 4—5

EXAMPLES.MB. Later sketch for the passage, ULB Bonn, Manuscripts Division, Schumann 15,p.53, br


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EXAMPLE 5.15. Piano Quintet op. 44, first in mvmt., reconstruction of the subsequently revised open-

ing measures of the recapitulation (mm. 207-1O), ULR Bonn, Manuscripts Division, Schumann 5,

p. 13, br. 1

ncal 3-layer by registral accents resulting from the high points and low points

within the left-hand accompaniment pattern. Your melodic new-event accents aswell as occasional dynamic accents on third beats resulted in a prominent dis-placed 3-layer and hence in strong D3+2 (or D3-1). In my later version in thesame sketchbook (Example 5.14b), in the 'correct' key of C major, I almost elim-

inated the dissonance by doing away with all antimetrical dynamic and new-event accentuation. The durational accents on the third beats (within the accom-paniment pattern) kept the dissonance alive, but only as a shadow of its formerself." Florestan pointed out, "Your weaker dissonance actually sounds muchmore like 133+2 than D3-1; with the disappearance of my anticipatory ties, thereis no longer a sense of 'backward' displacement." Eusebius went on, "In our finalversion of this passage (Example 2.8), we stood by the elimination of the origi-nal syncopation but, with my approval, you reinstated and in fact multiplied theantimetrical dynamic stresses. The dissonance became considerably more intense

than in the second version, but, because of the absence of melodic syncopation,remained weaker than in the first."

Florestan, "I must mention one more of your deintensifying revisions."

He opened the fair copy of the first movement of the Piano Quintet op. 44 to thebeginning of the recapitulation. "Here, Eusebius, you see that I originally in-tended the recapitulation to begin with strong metrical dissonance (Example

5.15). I gave the right hand of the piano part an eighth note accompaniment pat-tern— a continuation of the pattern from the end of the development section. Inthe first two bars of the recapitulation, this counterpoint included new-event har-monic, registral (high point) and dynamic accents on the eighth notes just beforethe metrically accented points, resulting in the dissonance D4+3 (or D4-1;l=8th). In the third and fourth measures of the recapitulation, I changed theright-hand pattern, retaining the steady eighth note rhythm but placing dynami-cally accented double notes, anticipating the following harmonies, on metricallyweak eighth notes. The dynamic, new-event, harmonic and density accents car-ried by these double notes resulted in a prominent antimetrical 2-layer, and in atightening of the dissonance of the preceding two measures from D4+3 to D2 + 1

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(or D4-1 to D2-1)." Eusebius interposed, "The manuscript clearly shows my re-vision of the passage; I crossed out (in red ink) all of the piano's metrically weakeighth notes and most of the antimetrical accents from m. 207 onward. (The re-tained antimetrical accents are inactive because the notes to which they pertainare deleted.) I rewrote the dynamic accents on the somewhat revised half notechords in red ink so that the metrical layer remained very clear; the antimetricallayer, however, was removed." Florestan added, "I did persuade you to leave onevestige of the dissonance in place, namely the sforzando on the last eighth note ofm. 206, which highlights the beginning of the recapitulation."22

The door opened, and Clara walked into the room. When she saw the jampotin precarious proximity to the beautifully bound manuscript of the Piano Quin-tet, and a coffee cup perched on the open third sketchbook, she threw up herhands in horror and shrieked, "Robert! How can you eat and drink amidst yourmanuscripts! Do you not realize how much value these documents will have forlater generations ? Put them away immediately!" Eusebius said, "Now, Chiarina,do not excite yourself. The manuscripts are unharmed. Florestan and I have beenconsulting them while we have ruminated about our frequent revisions of metri-cal structure. Pray have a seat and let us show you some of the interesting exam-ples that we have recalled."

Although his strange manner of speaking pained her, her interest in the sub-ject was aroused and she joined him at the table. Eusebius tenderly put his armabout her and said, "First it is necessary to share with you what we have recentlylearned about metrical conflict." He explained to her the various types of metricaldissonance and the labels associated with them, and the processes within whichthese metrical states can be employed. She listened raptly, delighted by the lu-cidity of his exposition and captivated by the material. Florestan proceeded toshow her some examples of metrical revision. She soon interrupted him, saying,"I would be very interested to hear for what reasons you made these changes."

Florestan mused, "Some of these revisions lie in the distant past; neverthe-less, I believe we can recall the reasons for most of them. Sometimes the reasonwas internal to the given passage. My first sketch for the third section of thetenth Papillon (Example 5.1 4a) was frankly rather ugly; the displaced melodic at-tacks resulted in unpleasant dissonances against the accompaniment pattern."23

After briefly surveying the sketch, Clara pointed out, "There are also concealedparallel octaves in the first two measures of the sketch, where the succession 'B-Ct' is duplicated, with displacement, in the outer voices." Florestan grimaced andsaid, "You are right. Eusebius's revision eliminated these problems. On the otherhand, some passages conceived by Eusebius were originally rather bland, and myadditions of metrical dissonance provided a pleasing pungency. This was thecase, for example, in the development section of the first movement of the PianoTrio op. 80. The passage at m. 165 consisted, in Eusebius's original version (for-give me, my friend), of rather pedestrian imitation. My added displacement dis-sonance, created by offbeat accents in the piano part, rendered the passage vastlymore distinctive (Example 5.3). Sometimes I added or intensified dissonance inorder to avoid monotony-within the recurrence of an earlier passage. In m. 25 of

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130 Fantasy Pieces

the eighth Pupil/on, for example, my third-beat accents at the second appearance

of the D1-major theme (which were not present in Eusebius's first sketch —

Example 5.6) lend the restatement a sense of novelty."

Eusebius said, "The explanations for most of our metrical revisions, how-

ever, are to be found not within the given passages alone but within their con-

texts. Some of the revisions arose from our consideration of the function of a

passage within the form. For example, I persuaded Florestan to eliminate the dis-

placement dissonance at the beginning of the recapitulation of the first movement

Piano Quintet op. 44 (Example 5.15) because I felt that the tensions of the de-velopment section should here be resolved." Clara interjected, "Some of the revi-

sions that you have shown me occur near the ends of works or movement. Did

you perhaps feel that metrical dissonance might detract from an effect of clo-

sure?" Eusebius responded, "Yes; I eliminated the duple groups of quarter notes

in Florestan's original ending for the Papillons, for instance (Example 5.12), pre-

cisely for that reason. Further examples of my enhancing of closure by the dein-tensification of dissonance arc found in the Davidsbundlerlanze, for example, in the

coda of the sixth piece. The manuscript had dynamic accents on the fifth eighth

notes of mm. 87—88 and 91-96, resulting in strong D6+4 (1 =8th). I eliminatedthese accents between the manuscript and the first edition. At the end of the thir-

teenth Davidsbundlertanz, my deletion of the dynamic accents on the syncopated

notes in the right hand weakened the dissonance and allowed the final metricallyconsonant chords to fulfill their resolving function in a more satisfying fashion."24

Florestan drained his cup, rose from his chair, and took Chiarin's arm, say-

ing, "1 need some fresh air; let us go for a walk. We can continue our discussion

as we do so." Although she felt that she should return to her practicing, she

agreed to come along. They put the various manuscripts back onto the shelves,

donned their coats and hats, and left the house. It was a cool but fine day, and

Florestan suggested that they make for the Rhine (he found himself irresistibly

drawn toward the river in those days). As they walked, he picked up the thread

of their conversation, observing, "A number of our metrical revisions were moti-vated by our desire to clarify the form, either by intensifying contrast between

sections or by highlighting formal boundaries. The dissonant measures that I in-

serted at the beginnings of restatements of the second theme in the original finalefor op. 22 (Example 2.6c), for instance, help to articulate this important formal

boundary. The revisions of the third section of the tenth Papillon illustrate the en-hancement of sectional contrast. I conceived the highly dissonant first version,you remember, as the opening of a piece (Example 5.14a). 25 By the time Euse-

bius wrote his virtually consonant second version (Example 5.14b), we were at

the stage of searching for an appropriate larger context for the passage. When wemoved this second version into its ultimate location, that is, after two metrically

consonant sections, we immediately realized that its very weak dissonance pro-

vided insufficient contrast to the foregoing material, and we agreed to restore

some of the original dissonance."As they walked onto the bridge not far from their house, Clara inquired,

"Would your extensive revision of the second episode of the second movement of

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Metrical Revisions 131

the Piano Quintet have arisen from similar considerations? The first episode al-ready involved the pervasive grouping dissonance of triplet quarter notes (in thepiano) against groups of four eighth notes (in the strings), and the dissonance inyour first version of the second episode was very similar. Your decision to basethe second episode on a contrasting dissonance type (D4 + 1 at the quarter-notelevel) was a wise one. In the final version of the movement, each section has adistinct metrical character." Florestan agreed with Clara's assessment of this re-vision, and Eusebius added, "Another instance of metrical revision that enhancedthe contrast between sections was my elimination of displacement dissonancefrom the middle section of the thirteenth Davidsbundlertanz; since the outer sec-tions contained a fair amount of such dissonance, I decided that respite from thatdissonance in the middle section would be desirable."

As they stopped on the bridge and gazed down at the mighty Rhine, swollenby the winter rains, Eusebius continued, "A number of our revisions were in-tended to create relationships to other passages rather than to create contrasts.Since we wrote many of the early piano pieces by gluing together existing frag-ments, it was important to create some links between the various fragments, andmetrical revision was one means to that end.26 The tenth Papillon illustrates thisreason for revision in addition to the other reasons that we have mentioned. Inthe process of eliminating the unpleasant features of the first version, I had ren-dered the original dissonance virtually imperceptible, and had thus removed asignificant connection between this passage and other Papillons that feature D3+2."Clara interjected, "You mean the fourth (mm. 19-22), the sixth (mm. 32-33)and the eighth (mm. 24—31)." Eusebius nodded and continued, "Florestan's rein-statement of the dissonance in the final revision was motivated in part by the de-sire to restore this connection." Florestan said, "My addition of third-beat dy-namic accents in the eighth Papillon (Example 5.6), of course, also contributed tothe network of connections between the movements."

Clara said, "You showed me how you added D3+1 to mm. 27—34 of thePreambule to Carnaval. Surely you did so in part because you wished to create aclear link to the first section, where this dissonance is foreshadowed at two pointsby accents on the second beats (mm. 7-8 and 15-16)." Florestan and Eusebiusagreed, and the former added, "The G3/2 formed at m. 28 by my new accompa-niment pattern, on the other hand, created links with later passages (mm. 48—62and 99—109) in which 'oom-pah' accompaniments similarly form G3/2." Eusebiuscontinued, "Florestan's addition of displacement to the idea at m. 46 of the finaleof the op. 14 Sonata (Example 5.4) not only rendered the passage intriguinglybeautiful, but resulted in a relationship to the opening theme of the movementwhere similar, though more intense, displacement dissonance occurs.27 And tomention once more the first Trio from the third movement of op. 11, Florestan'saddition of D3+2 and G3/2 to that originally consonant passage resulted in clearconnections to the first section of the movement, where both dissonances alreadyoccur."

Clara now urged that they should return home. As they turned to leave thebridge, she asked, "Were any of your metrical revisions motivated by a desire to

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create the kinds of metrical processes that you mentioned to me earlier?" Flo-restan responded, "Yes, I recall several such examples. One revision that resultedin a process, albeit of small scale, was that in the introduction of the First StringQuartet (Example 5.8). The opening motive of the completed introduction al-ready contains a registral accent on the third sixteenth-note pulse of the measure.In later measures there are similar but successively stronger accents; the intervalsby which the highest note is approached increase in size (from a minor second inm. 1 to a fourth in m. 3 to an octave in m. 11), resulting in ever more perceptibleD8+2 (1 = 16th). At m. 9, my dynamic accent on the third sixteenth note furthercontributes to the intensification process. In m. 10, the strongest registral accentoccurs on the third sixteenth note of the second beat; taken together with thesimilar accent on the third sixteenth note of the following measure, this accent re-sults in a tightening of D8+2 to D4+2. The sforzandos in mm. 20-22 (Example5.8), which I added in the fair copy, create D2 + 1.28 This dissonance, besidesbeing a diminution of the earlier D4+2, completes a process of successive reduc-tion of cardinality. The proliferation of dynamic accents, furthermore, completesthe intensification process initiated at the beginning of the introduction."

During his remarks, they had noticed an acquaintance — Julius Tausch,Robert's successor as conductor of the Dusseldorf Musikverein — walkingquickly toward them.29 They would gladly have avoided him, but, aside fromleaping off the bridge, there was no possibility of doing so. Tausch came up tothem and said, "Herr Doktor Schumann, Frau Schumann, how glad I am to meetyou!" without the slightest acknowledgment of Herr Tausch's presence, Euse-bius continued the discussion of metrical revisions, while Florestan with diffi-culty restrained himself from hurling into Tausch's smiling face the vituperativeepithets that boiled up within him, and while Clara stood there tight-lipped andflushed with embarrassment. Herr Tausch spoke softly to her during Robert'sdisquisition: "/ have just called at your home to invite you to our bouse t h i s afternoon. An-other instance of small-scale process achieved by a series of revisions (youscheming scoundrel!) is found in the first Papillon (see Example 4.5). Several

members of the Verein will be there, and we shall have chamber music and tea! The inter-mediate stages of the processes of intensification and deintensification (you hyp-ocritical hound!) were not present in our first two versions of the piece. In both,the inner-voice durational accents of mm. 4 — 6 were absent. Come if you can—both

of you. In the first version, moreover, the second beats of mm. 9—12 were all dy-namically accented. The gradual additions and deletions of accents that renderthe metrical process in the final version so elegant were not fully worked out untilour fair copy of the work (you snivelling sycophant!)."30

When Robert finished, Clara thanked Herr Tausch with all the grace thatshe could muster and accepted his invitation. With a sidelong glance at the nowsilent figure next to her, he raised his hat in farewell and strode swiftly back intothe town. Following more slowly, Clara and Robert returned to their house andwalked upstairs, where Clara, after embracing him, ran tearfully from the room.

Florestan and Eusebius sat down once more at the table, and the formcrsaid, "I remember some interesting examples of revisions that resulted in metrical

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Metrical Revisions 133

EXAMPLE 5.16. Metrical 'dissonance in the "Fandango"draft, Arcbiv der Gesellscbaft 9er i

freunde in Wien, Ms. autogr. R. Schumann A283

processes of larger scale. One of these occurred during the composition of ourPiano Sonata op. 11." Fetching and opening a manuscript that was labeled 'Fan-dango/ he continued, "We began this draft, destined to become the opening of

the exposition of the first movement, with the dissonance D4+2 (1 = 16th — Exam-ple 5.16a).31 In the first sixteen measures (corresponding to the present mm.54 — 70), we consistently displaced the bass and/or inner voices by two sixteenthnotes with respect to the melody (whose durational accents corroborate the met-

rical layer). We abandoned the dissonance in mm. 17—42 of the draft (most of thethird through sixth staves), where the motivic rhythm, its long durations still co-ordinated with the metrical beats, took over the entire texture."

Kusebius pointed to mm. 43—46 (corresponding to the present mm. 106—9),and said, "In this climactic passage, syncopation in an inner voice, dynamic ac-cents on the final eighth notes of measures and left-hand new-event accents on

the second eighth notes together resulted in a return of the initial D4+2 (Exam-ple 5.16b). In the continuation of this section (the last two bars on page 1), thedissonance was maintained by a syncopated inner-voice melody. The following

section (mm. 52—62 — the first two staves of page 2) reverted to the obsessive,metrically consonant opening rhythm (of. mm. 123—39 of the final version).Thereupon we gradually phased out this rhythm, first relegating it to the bassalone (on the third staff of page 2), then abandoning it entirely as we initiated asecond theme in steady eighth notes (corresponding to mm. 140—74 of the finalversion)." Florestan said, "Metrical dissonance appeared only once more withinthe draft, namely at mm. 64 — 68 (the first five measures on the third staff of page2), where quarter note syncopation in the upper voices resulted in D8+4, an aug-mentation of the initial D4+2. The 'Fandango' draft, in short, began with a

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EXAMPLE 5.17. Metrical dissonance in the exposition of the Piano Sonata op, II, first mvmt.

prominent metrical dissonance and returned to it occasionally, but did not de-

velop it in any coherent manner."32

Eusebius observed, "How different was the published exposition, completedfour years later! Here you added many more statements of the initial dissonance.In mm. 76-86 (the second of three Ftt-minor statements of the opening theme),

you created, by dynamic accents and by registral accents resulting from the lefthand's excursions into high altitudes, the dissonance D16+10 (1 = 16th), a looserelative of D4+2 (Example 5.17a)."33 Florestan interposed, "The dynamic accentswith which you reinforce the meter at mm. 89—92 in the final version are not pres-ent in the draft. 1 suppose you felt them to be necessary only after I had addedthe metrical dissonance in the immediately preceding measures." Eusebius nod-ded, and continued, "In mm. 94 — 106 (the third Ftt-minor statement and its after-phrase— a passage that in the draft consisted of reiterations of the metrically con-sonant motivic rhythm), you added a great deal of D4+2. In mm. 94-95, thedissonance arises from new dynamic accents (Example 5.17b), and in mm. 99-1 06from antimelrical slurs and harmonic new-event accents. (In the latter passage,

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Metrical Revisions 135

the dissonance could be heard as D4-2.) Finally, you added inner-voice syncopa-tion and hence D4+2 within the second theme in A major (mm. 150-51 of thefinal version). In the completed exposition, then, D4+2 is much more significantas a unifying feature."

Florestan added, "Furthermore, whereas in the draft there were no interme-diate stages between the initial D4+2 (Example 5.16a) and the more intensestatement of mm. 43—46 (Example 5.16b), we engage D4+2 in a process of grad-ual intensification in the final version. Significantly, you slightly weaken the firstappearance of D4+2 in comparison to the beginning of the draft, thus crouchingthe better to spring; at the opening of the exposition (mm. 54 — 57 — of. Examples5.17c and 5.16a), you conceal the displaced layer in inner voices, rather than im-mediately placing it in a prominent outer voice. The migration of the displacedlayer to an outer voice in m. 56 already creates an effect of intensification. In mm.62 and 66, we offer subtle hints at the manner in which D4+2 is to be further in-tensified: in the former measure, we initiate a new harmony (B minor, replacingB major) on the second eighth note, and in the latter, we place a dynamic accenton the same eighth note in the bass. Neither hint is present in the draft."

Eusebius gleefully observed, "The significance of these hints begins toemerge at mm. 94 — 95, where we intensify D4+2 by dynamic accentuation. Inmm. 106—18, the climactic region of the exposition (corresponding to mm. 43—46of the sketch — Example 5.16b), we state D4+2 in an equally intense manner. Wecreate it here by a blend of the techniques hinted at in mm. 62 and 66: new-eventharmonic accents appear on the second eighth-note pulses, and dynamic accentson the fourth eighth-note pulses of each measure. In mm. 110—13, we again formD4+2 by antimetrical dynamic and new-event harmonic accents; the dynamic ac-cents are your addition to the corresponding draft measures."

Florestan remarked, "The gradual intensification of D4+2 is only one compo-nent of a general, not exclusively metrical intensification process that spans thefirst forty-five measures of our completed exposition. Another important elementin the process is the rise in register across the aforementioned three statements ofthe opening theme: the first statement (Example 5.17c) remains quite low, the sec-ond one (mm. 74 — 92 — Example 5.17a) begins to champ at the registral bit withits momentary left-hand leaps into a higher register, and the treble part of the thirdstatement (mm. 94-98 —Example 5.17b) is an octave higher than that of the first.This gradual registral rise is lacking in the draft, in which the left hand does notreach over the right, and in which even the third statement remains within itsoriginal low register. In the completed exposition, an increase in dynamic level inmm. 85 through 94 adds to the overall effect of intensification; this crescendo, too,is missing in the draft. A generally static character was acceptable for a little fan-dango, but we felt that in a sonata exposition a greater sense of controlled processwas necessary. By means of judicious metrical revision as well as by the additionof the other features that I have mentioned, we accomplished the transformationof a character piece into a dramatic sonata exposition."

Eusebius rose and brought another manuscript to the table. As he turned toits first page, he said, "Another work that comes to mind in connection with re-

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EXAMPLE 5.18. Metrical dissonance in the "Exercice " (draft for the Toccata op. 7), the Robert Owen

Lehman Collection, on deposit in the Pierpont Morgan Library

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Metrical Revisions 137

vision for the sake of large-scale metrical process is our Toccata op. 7. My firstversion of this work from 1830, entitled 'Exercice,' was in many ways quite dif-

ferent from the published Toccata, completed in 1832.34 For example, my notationwas originally predominantly in eighth notes rather than sixteenths.35 There aresignificant harmonic differences between the versions as well; the key of 111, forexample, reached at m. 14 in the final version, was already attained at m. 8 in my'Exercice.' The sonata-allegro form of the work became much clearer in the pub-lished version; my first version already contained a section in the dominant, butthe contrasting theme that highlights the dominant area in the final version wasbarely suggested."36

Florestan took over: "In addition, I made many changes in the treatment ofmetrical dissonance. Your first version already contained many of the displace-ment dissonances that are significant in the final version. Allusions to D8+2(l = 8th) in the form of accents on the third sixteenth- or eighth-note pulse ap-peared in mm. 1, 29 (Example 5.18a) and 59 (Example 5.18b); in m. 1 the anti-metrical accent is registral, and in the other two measures, it is dynamic. At thevery end of the development section, you suggested D8+2 by placing registral ac-cents on those same pulses in a few consecutive measures (Example 5.18c).D8+7 (l = 16th, which corresponds to the eighth-note pulse used on the otherpages of the 'Exercice') occurred at mm. 11–14, where the last left-hand six-

teenth note of each measure was tied over the bar line, resulting in a series of du~rational accents. You suggested D4 + 1 (l=8th) by the slurring at mm. 29-30 ofthe exposition (see Example 5.18a), and at various other points by left-hand du-rational accents. Another 4-displacement, D4+2 (l = 16th), appeared at mm.17–22 of the exposition, where the displaced layer resulted from registral ac-cents, then more briefly at mm. 54–55 (l=8th), where the displacement was cre-ated by dynamic accents (Example 5.18d). D4+3 (l = 16th) appeared briefly in m.15, created by ties from the fourth to the first sixteenth in two groups (Example5.18e). You broached D2 + 1 (l=8th), finally, with antimetrical slurs at variouspoints, for instance, in mm. 27-28 (Example 5.18P) and 48 — 50. All of your dis-sonances occurred only relatively briefly, most of them weakly, and — forgive mefor saying so—with little semblance of order."

Florestan continued, "In the final version, I enhanced all of these disso-nances, using them as a means for unification, and as distinguishing features forindividual sections. My elevation of D8+2 (l = 16th) to motivic significance is al-

ready initiated in the opening measures of the second version. I establish the dis-sonance by placing durational accents on the second eighth notes of the two in-troductory measures (Example 5.19a). In the first theme area (mm. 3-24), thebass continues these durational accents on second eighth notes (Example 5.19b)while harmonic changes reinforce the metrical 8-layer; I thus maintain D8+2throughout that section, with interruptions only in mm. 18 and 20. D8+2 returnsat the dominant harmony that heralds the second theme area (mm. 42-43).Large portions of the development section are occupied by the same dissonance(mm. 100-110, 121-39), as is the first portion of the recapitulation (mm.149 — 72)." Eusebius said, "You coordinate most of the appearances of the disso-

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EXAMPLE 5.19. Melrical dissonance in the final version of the Toccata op. 7

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EXAMPLE 5.19. (continued)

Metrical Revuiotu 139

nance with significant formal junctures: the opening, the cadence leading into thesecond theme, the opening of the development section, and the opening of the re-

capitulation. The comparison with my sporadic and haphazard statements ofD8+2 in the first version is striking indeed."

Florestan continued, "I similarly advance the status of D4+3 in the revisedversion. I first hint at it in mm. 61–62, where slurs initiate groups on the final six-teenth notes of two successive beats (Example 5.19c). At mm. 69–71 (Example5.19d) and 75 — 79, I state the dissonance somewhat more strongly, creating it bydurational accentuation rather than mere grouping. (At these points, the disso-nance could be heard as D4-1.) D4+3 reaches the height of its prominence at theend of my version. In mm. 229-37 (Example 5.19e), the melodic framework (C-D (or three measures, then E-F for one measure, all repeated an octave higher)articulates the metrical 4-layer. Significant harmonic changes, however, occur onthe fourth sixteenth notes of mm. 229-30, on the fourth and final sixteenth notes

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in m. 231, and on the fourth sixteenth of m. 232, resulting first in intermittent,then constant D4+3 (or D4-1). The same is true of mm. 233-37. In mm. 237-42,then at greater length in mm. 250-55 and 260-80, I create the antimetrical 4-

layer of D4+3 (or D4-1) by durational accents in the highest voice and by har-monic changes.

Another dissonance that appears much more frequently in my final versionis D2+1. I allude to it in mm. 38, 40, and 112, then allow it to pervade the coda

of the work (mm. 213-81). In mm. 213-37 (Example 5.19f), the significantmelodic notes (the chord tones) consistently articulate the metrical 2-layer, butharmonic changes and density accents occur on the intervening sixteenth-note

pulses." Eusebius interjected, "You recall that in my sketch of the passage in themusical diary, the density accents and harmonic changes reinforced the metrical2-layer, so that the passage was virtually consonant."37 Florestan went on, "At m.

237, I submerge D2 + 1 (and D4+3); nothing supports the notated meter exceptthe notation!"

Eusebius interrupted, "Did you intend the pianist to articulate the notatedmeter in this passage?" Florestan responded, "This is another of those excep-tioniil situations where 1 would not advise the pianist to do so. I doubt that it is

possible for human hands to bring out both metrical and antimetrical layers dur-ing this frantic passage. I would suggest that the pianist abandon the metricallayer until m. 250, and generate the tension of the passage by physical attitude,by the high speed, and by the indirect dissonances that occur at the points of

abandonment and reinstatement of the metrical layer." He continued, "At m. 250both of the conflicting 2~layers are operative; the uppermost two voices state sig-

nificant members of the prevailing D harmony (A and D) at eighth-note inter-vals, while the attacks in the lowest voice in the right hand establish a displaced2-layer. The culmination of my development of D2 + 1 occurs at mm. 256 — 59 (Ex-

ample 5.19g), where the vehement chordal attacks of the left and right hands cre-ate metrical and antimetrical 2-layers, respectively."

Eusebius inquired, "Do these chords not simply merge into a series of ac-

cented sixteenth-note pulses, so that the effect of dissonance is minimal?" Flo-restan said, "The registral space between the two chordal layers prevents them,at least at first, from merging into a single pulse. By the end of the passage, to be

sure, the hands are very close together, and the dissonance becomes weak. Butthis deintensification is precisely what I desired here; it paves the way for themurmurous mm. 260–80 (Example 5.19h). You obviously had a hand in thesemeasures, Eusebius, for D2+1 here assumes a relatively serene guise. As in m.250, the uppermost two voices articulate the metrical 2-layer by stating signifi-cant members of the prevailing harmony (E and G) at eighth-note intervals; this

layer is reinforced by the 'tenor' statement of the second theme. The attacks inthe lowest voice in the right hand, meanwhile, establish a displaced 2-layer. D2+1is fully resolved only by the final cadential chords in quarter notes (mm.281-83)." Eusebius observed, "Your treatment of D2 + 1 again demonstrates theelevation of a dissonance that 1 used only briefly in my first version to a pervasiveand highly significant role."

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Metrical Revisions 141

He continued, "Even more remarkable than the proliferation of certain dis-sonances, and hence the intensification of dissonance in many passages, is the in-creased involvement in your second version of dissonances in logical processes.The dissonances in my first version — I admit it freely—are like players in a teamwithout a captain; they mill about without a plan of action. In your version, theplayers are organized and made to work together. First, I notice in your Toccata

an overall progression from displacements of large cardinalities to displacementsof small cardinalities. Just over half of the work (mm. 1-172) is dominated by 8-displacements. After m. 172, you abandon them, shifting to 4-displacements andfinally to the 2-displacement (sometimes with larger displacements superim-posed) . This large progression is nicely foreshadowed by the first portion of yourmetrical progression (D8+2 to D4 + 1 to D2 + 1 in mm. 1-40). At times, the pro-gression from a larger to a smaller displacement involves a more specific process,for example, diminution (the progression from D8+2 to D4+1 at m. 25) or tight-ening (the progressions from D4+3 to D2 + 1 in mm. 25 — 38, from D8+7 to D4+3in mm. 67-71 and 72-79, and from D8+2 to D4+2 in mm. 121-48 and 149-80).

"You also subject individual dissonances to interesting processes," Eusebiuswent on. "For example, as you mentioned earlier, you abandon the pervasive dis-sonance D8+2 briefly at two points within the first theme (mm. 18 and 20). Theseinterruptions neatly presage your longer departure from D8+2 in m. 25. The ex-pansive treatment of D2 +1 in the coda is briefly foreshadowed in mm. 38 and 40,•where the uppermost voice states displaced eighth-note pulses. The long passagedominated by D2+1 at mm. 213-80 contains some subtle processes which pre-vent it from becoming monotonous. The antimetrical 2-layer is at first not ab-solutely constant. In mm. 213—28, dominant-tonic progressions at the ends of allmeasures strongly assert the metrical layer (Example 5.19F). It is difficult toimagine the antimetrical 2-layer continuing through these progressions; the ton-ics on the downbeats are so clearly the more strongly accented of the two chords.At m. 229 (Example 5.19e), you deemphasize the downbeat tonics, subsumingthem within sustained dominant notes. D2 + 1 thus remains uninterrupted, in con-trast to mm. 213–38. In the central portion of the coda, you gradually add fur-ther metrical colors to D2 + 1: intermittent, then constant D4+3 beginning in m.229, and D8+3 in mm. 237—41. (One might just as well say that by adding ac-cents at particular points, you gradually render explicit certain displacements al-ready implicit within D2 + 1.) None of these processes is present in my first ver-sion. You m effect turned my 'Exercice' in piano technique into a thoroughgoingstudy in displacement dissonance."

Florestan smiled smugly, then rose and said, "Shall we continue our readingof the Prophet Bird's manuscript?" Eusebius agreed with alacrity. After puttingthe "Fandango" and "Exercice" documents away, they mounted the stairs to thetop floor of the house, Eusebius's light treads and Florestan's heavy footfallsforming the dissonance D2 + 1.

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Interactions of Metrical Dissonance

with Pitch Structure, Form, and

Extramusical Elements

Florestarn and Eusebius settled on their sofa, opened the manuscript, and read:

The upper portion of Figure 6.1 shows the metrical structure of Schu-

mann's transcription, or rather recomposition, of Paganini's Caprice op. 1 no. 6

(published as the second of the Concert Etudes op. 10). At the very top of the

figure, I have summarized the formal and harmonic events of the composition;

the remainder of the figure is a metrical map of the type described in chapter 4.

The figure makes clear that meter and pitch interact in interesting ways in

Schumann's piece. Significant large-scale harmonic events coincide with metri-

cal resolutions; the beginning of the retransitional dominant prolongation

(m. 36) coincides with the resolution of G3/2 and D6+1.5, and as the dominant

moves to the recapitulatory tonic, the remaining dissonance, Gl.5/1, is resolved

as well. The process of harmonic stabilization and resolution that heralds the

end of the study is beautifully matched by a gradual casting off of veils of met-

rical dissonance. Harmonic events of smaller scale are no less carefully co-

ordinated with metrical states. For example, Schumann associates each of three

sequential passages within the central section with a unique dissonant state: the

first (mm. 19—26) with the combination of G9/6 and G3/2, the second (mm.

27—31) with the continuation of those dissonances along with intermittent

Gl.5/1 and D3 + 1.5, the third (mm. 32-35) with a blend of G3/2, Gl.5/1, and

D6+1.5. The sense of increasing instability and tension produced by the pro-gressive curtailment of the sequential cells (shown by the slurs at the top of the

figure) is enhanced by an overall increase in amount of metrical dissonance m

mm. 19-35.

The coordination between metrical structure and form in the transcription



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Interactions of Metrical Dissonance 143

FIGURE 6.1. Comparison of interactions of metrical structure, form, and pitch structure in

Schumann's Study op. 10 no. 2 and Paganini's Caprice op. 1 no. 6

is no less remarkable than that between metrical structure and harmony. Schu-mann ends the first section (mm. 1-18) by resolving all dissonances. He reiniti-ates G9/6 and also establishes the new diminution, G3/2, at the beginning of thesecond section (m. 19). He resolves Gl.5/1 precisely at the point of recapitula-tion (m. 39) and marks the beginning of the coda (m. 46) with the same resolv-ing gesture.

Such concern for coordination between metrical structure and pitch andform is evident in many of Schumann's other works. In the first part of thischapter, 1 offer further examples of the interaction between form and meter, andbetween pitch and meter. The second part of the chapter begins with a discus-sion of relationships between metrical structure and text in Schumann's vocalworks. This discussion provides a springboard into some speculations on possi-ble meanings of metrical dissonance in Schumann's instrumental music.


Among the ways in which Schumann associates metrical states and form is thehighlighting of a formal boundary by a change in metrical state.1 Resolution ofmetrical dissonance, for example, frequently coincides with the close of a formalunit, be it a low-level unit such as a phrase or a period, or a higher-level unitsuch as a thematic section of a sonata form. "Eusebius" from Carnaval providesa simple example of the former situation. The second and third measures of the

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EXAMPLE 6.1. "Grillen" from Phantasicstucke, mm. 1 — 8

first two phrases (mm. 2—3 and 6 — 7) contain the low-level dissonance of septu-

plets against quarter notes. In the final measures of these phrases, however,

Schumann dispenses with the dissonance, replacing the right-hand septuplets

with normal eighth notes. The first eight-measure phrase of "Grillen" from the

Phantasiestucke (Example 6.1) begins with metrical consonance, but in m. 3 a

suggestion of dissonance (D3+2, 1 =quarter) appears in the form of a dynamic ac-cent on the third beat. The phrase becomes more dissonant as it proceeds; m

mm. 5 — 6, dynamic and duralional accents on the second beats result in intense

D3 + 1. No dissonance, however, disturbs the succeeding cadential measures; asin "Eusebius," Schumann associates the close of a formal unit with resolution of

dissonance. In the first piece from Kreisleriana, the initial displacement disso-

nance 132 +1 (l=8th), created by the nonalignment of right-hand arpeggiatedharmonies and left-hand attacks and, in mm. 11—12, by dynamic accents on met-

rically weak eighth notes, is brought up short at the strongest cadences, where

the two hands come together (for instance, at mm. 7-8 — Example 6.2).

Eusebius said, "At the final cadence of the agitated first section (mm.21—24), we allot more time to the state of consonance than at m. 8, as if to suggest

that the section ending with which it is associated is a more significant formal

boundary than the earlier one." He continued, "A good example of similar coor-

dination is found at the end of the second theme of the first movement of op. 80

EXAMPLE 6.2. Kreislcriana op. 16 no. I, mm. 7–8

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Interactions of Metrical Dissonance 145

EXAMPLE 6.3. Piano Trio op. 80, first mvmt., mm. 78-86 (piano part only)

(mm. 78-85 —Example 6.3). In mm. 78-81, we produce D6+3 (l=8th) by verypowerful accents, namely new-event harmonic accents in conjunction with dura-tional and sometimes dynamic accents. In mm. 82—84, the measures leading intothe final cadence of the second theme, we significantly deintensify the disso-nance. The accents that form the dissonance become much weaker than in thepreceding measures; in m. 83, there is a dynamic accent in just one voice (the

cello) and a density accent in m. 84, as opposed to the earlier full-texture dy-namic and harmonic new-event accents. Immediately after the cadence, we rein-tensify the dissonance, thus setting off the cadence with weaker dissonance." Flo-restan added, "The coordination with pitch structure is interesting here as well;

the final phrase of the second theme is quite heavily chromatic during the metri-cally dissonant portion, but as the dissonance is weakened, the harmony becomesdiatonic (mm. 83–85). It is this sense of simultaneous relaxation in three do-mains that renders our cadence so beautiful."

Eusebius continued, "There are plenty of additional examples of coordina-tion between phrase ends and metrical resolution in our works. In the finale of

the Sonata op. 11, the first theme (see Example 5.10) is permeated by subliminalG3/2 (l=quarter), but temporary resolutions of the metrical dissonance occur atthe two main cadences of the theme (at mm. 8 and 16). In the first movement ofthe First String Quartet, we associate important cadences at the end of the ex-position (m. 137a) and the recapitulation (m. 334) with resolution of D6+3

(l=8th). At the end of the fourth movement of that quartet, resolutions of met-rical dissonance — of low-level three-against-four dissonance plus D8+4 (l=8th),and D8+4 alone, respectively — coincide perfectly with phrase ends (mm. 294 — 98

and 310—14). I see that the author comments further on this movement." Theyread:

At times, Schumann employs a particular dissonance as a "marker" at for-mal dividing points. In the finale of the First String Quartet, D8+4 (l=8th) per-forms such a function. This dissonance, created by antimetrical dynamic ac-cents, first appears at the end of the exposition (mm. 71-72). Allusions to D8+4open the development section (mm. 77 and 81), and at m. 148—just before thesomewhat confusing recapitulation begins — D8+4 appears once again. The oc-currence at m. 200, corresponding to that of m. 71, heralds the delayed return ofthe opening theme at m. 213.

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EXAMPLE 6.4. Papillon op. 2 no. 11, mm. 1-3

Eusebius pointed out, "None of these statements of D8+4 was present in my first

draft of the movement.2 You inserted them later, to aid listeners in orienting

themselves within the unusual form and tonal structure of this finale, in which

the second theme group is recapitulated in F major before the first group returnsin A minor.

Instead of highlighting formal boundaries by particular metrical events,

Schumann sometimes associates an entire section with a particular metrical

state, thereby setting the given section apart from its context and clarifying the

form. There are many examples in the piano works. The Papillon op. 2 no. 11,for instance, begins with a brief introductory passage, which leads into the mam

body of the piece in in. 3 (Example 6.4). The introduction is permeated by

D2 + 1; dynamic and durational accents convey the metrical 2-layer while har-

monic new-event accents create an antimetrical 2-layer (l=8th). At the end ofthe introduction, the latter 2-layer disappears, resulting in a state of consonance

(except for the references to D2 + 1 shown in Example 4.2). The introduction is

thus clearly set apart from the beginning of the main portion of the piece.A larger-scale instance of the association of an introductory passage with

metrical dissonance is found at the opening of the Fourth Symphony (Example

6.5a). There is some conflict against the metrical 6-layer (1 =8th) at the outset;

the initial dominant note occurs on the upbeat, and when Schumann emphati-

cally jerks the wandering harmony back to the dominant in m. 5, he does so on

EXAMPLE 6.5A. Symphony no. 4, first mvmt., mm. 1–

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Interactions of Metrical Dissonance 147

EXAMPLE 6.5B. Sketch for a fugue subject, Dcutsche Staatsbibliotbek zu Berlin —Preufsischer

Kulturbesitz, Musikabteilung mit Mendelssohn-Archie, Mus. ms. autogr. R. Schumann 36, no. 10,

recto, st. 5

the second beat. Most of the dissonance, however, occurs at lower levels. In

many measures of the introduction there is a conflict between 2- and 3-layers.

In mm. 1—3, for example, the eighth-note pulse is grouped not only notationally

but also by harmonic events, into threes; the 3-layer is set into motion by a

chord change after the first three eighth notes, and the listener tends to main-

tain that layer in subsequent measures,

Eusebius interjected, "Do you remember a fugue subject in D minor that you

sketched in 1845 — a subject very similar to the opening of the Fourth Symphony

(Example 6.5b)? In that sketch, you more obviously realized the potential for

triple grouping of the eighth notes; you couched the theme in three-eight time,

with a note stating that six-eight is an alternate metrical possibility."

Later measures of the symphony's introduction render the 3-layer even more

prominent; in mm. 13—14 and 18, for example, large leaps between the third

and fourth eighth notes in the first violin part clearly demarcate two triplegroups per measure, and articulation changes in most instruments halfway

through each of mm. 18, 19, and 20 have the same effect. The metrical 2-layer,

on the other hand, is articulated by harmonic change in mm. 4–5 (see Example

6.5a) and by the voice exchanges between the first violin and bass parts in m.

21. This layer is also implied by dynamic accentuation of the third quarter-note

beat in mm. 2-3, 6-9, and 11—12, and by the surface-level attacks of the outer-most voices in mm. 7—10.

At m. 22, where the surge toward the actual exposition begins, Schumanndrops the 3-layer while clearly expressing the metrical 2-layer with bass neigh-

boring motion. In m. 25, he imposes a 4-layer upon the 2-layer (i.e., he alters the

meter from three-four to two-four) and begins to increase the tempo. These

changes, combined with the elimination of the 3-layer, herald the exposition ofthe movement, which is based on the consonance 4/2. The metrical resolution atthe boundary of introduction and exposition contributes significantly to the

sense of "getting down to business" that is appropriate for this point of the form.Schumann employs distinctive metrical states for many formal situations

other than introductions. In many of his short ternary forms, he enhances con-

trast in the middle section by allotting to it a metrical state significantly differentfrom that of the outer sections. In the "Scherzino," op. 124 no. 3, a piece writtenaround the time of the Papillons, the outer sections are consonant, whereas the

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middle section is dominated by G3/2 (1 = 16th). In "Wichtige Begebenheit" from

the Kinderscenen, the outer sections contain subtle grouping dissonance; most ofthe attacks of an underlying stepwise descent in the melody take place at two-

quarter-note intervals, resulting in a 2-layer (l=quarter) that conflicts with thesubliminal metrical 3-layer. In the middle section in the subdominant key (mm.

8-16), however, the 2-layer disappears and the downbeats receive durational

and dynamic accents, so that metrical consonance reigns. The outer sections of

the first piece of the Kreisleriana, as was mentioned above, are rich in displace-ment dissonance. The middle section, however, is virtually consonant; only a

few stabs of accentuation on the third sixteenth notes of triple groups ruffle the

placid metrical surface.

Florestan remarked, "Our distinguishing of sections by means of metricalstructure is not restricted to works in ternary form. In 'Grillen' which is in rondo

form, we assigned a different metrical progression to each of the three different

sections. The A sections (mm. 1—16, 44 — 60, 96—1 12, and 140-56—see Example6.1) twice move through the metrical progression 'consonance—133+1 (^quar-

ter)— consonance.' The B sections (mm. 16—44 and 112—40) begin with D12+1 1,

or D12-1 (produced by dynamic accents on every fourth upbeat), and move to

the tighter dissonance D3+2 at the first double bar and back to the original

D12 + 11 at the second double bar. We perfecdy coordinate the tightening and

loosening procedure with the subsections of the B section. In my C section (mm.

60-96), I tighten the initial D6+5 (or D6-1) to D3+2 (or D3-1), then loosen toD6+5 again (at the subsection boundaries — mm. 72 and 80, respectively). In ad-

dition, I throw in the dramatic incursions of subliminal G3/2 that we discussed

yesterday" (Example 2.16).

Eusebius said, "We use metrical dissonance in a similar manner to set off

the sections of our later larger forms. In many of our sonata forms, we assign

clearly distinguishable metrical states to particular thematic areas. In the firstmovements of the First and Second String Quartets, displacement dissonances

in the closing themes effectively distinguish those sections from the preceding

consonant material." Florestan interposed, "These dissonances were absentfrom, or very weak, in your first drafts; I added them in part because I wished to

set apart the closing themes."3 Eusebius continued, "Another relevant example isthe second theme of the first movement of the Third String Quartet, which ispermeated by a combination of two displacement dissonances as yet unused inthe movement (Example 4.20). In the second theme of the opening movement ofthe Third Symphony, we follow the opposite procedure; in contrast to the first

theme, which is dominated by G6/4 (l=8th), the second theme area (mm.

95—165) is almost entirely metrically consonant (with the exception of the last

few measures)."Florestan pointed out, "As we discussed this morning, metrical dissonance

can serve not only to separate sections from each other, but also to create linksbetween sections, be they adjacent or nonadjacent. We often allow a metrical

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Interactions of Metrical Dissonance 149

dissonance established in one section to reappear in an entirely different guise ina later contrasting section, so that the dissonance provides a subtle but audiblelink to the earlier section. In our conversations about metrical revision, we men-tioned a number of works in which we employed metrical dissonance as a link

between sections. Additional examples include the Intermezzo op. 4 no. 5, the

first two sections of which are connected by their usage of D6+2 (1 =8th; cf. Ex-amples 8.9a and 5.13), and 'Vogel als Prophet' in which the thinly textured Asection and the fuller, chorale-like B section are linked by D2 + 1 (see Example4.7)." Eusebius added, "In some works, we employ related rather than identicalstates to provide a connection between contrasting sections. In the sixth Novei-

lette, you vociferously announce the dissonance D2 + 1 (1 =8th) in the first section(mm. 9—12), and I take up its augmentation, D4+2, in my calmer second section(see Example 4.6)."

The door opened and Clara's head appeared. "Robert," she urged, "it is time

to leave for the Tausches!" When she encountered his abstracted gaze, she knewthat she would be going alone that day. She came to him, kissed his brow, andrushed off. Florestan and Eusebius continued their reading.

A number of the above remarks with regard to form have already broachedthe subject of coordination between metrical and pitch structure. When metri-cal dissonance is associated with a formal dividing point, it is likely also to belinked with a significant harmonic event (a cadence). The relationship betweenmetrical dissonance and pitch, furthermore, has already been addressed in priorchapters, where it became obvious that pitch structure has a significant impacton the establishment of layers of motion. Here, I investigate some additionalpossibilities for the interplay of metrical structure and pitch structure.

The analysis of Schumann's study in Figure 6.1 illustrates one way

in which pitch and metrical structure can interact. In mm. 19-35, a passage thatis tonally unstable is metrically dissonant (i.e. unstable) throughout; thus, metri-cal dissonance is coordinated with an analogous pitch state. Schumann associ-

ates tonal and metrical instability in numerous works. In the first Papillan (Ex-ample 4.5), the unstable, sequential measures that initiate the second half areassociated with strong D3+1. As the sequence makes its way back toward the

tome, the dissonance is weakened and resolved. Measures 9—12 of the fifth Pa-

pillan illustrate a similar pitch/meter coordination; an unstable, sequential sec-tion is associated with displacement dissonance, the dissonance being resolvedas harmonic stability, in the form of the tonic, reappears.

Florestan recalled, "Pitch and meter were not originally thus coordinated in thefifth Papillon; in our first version, metrical dissonance appeared at the pointwhere the sequence ended (m. 12).4 The achievement of coordination between

metrical structure and other musical aspects is certainly another common moti-vation for our metrical revisions."

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Numerous pitch states other than instability can be considered analogous tometrical dissonance and can therefore logically be coordinated with the latter

state. Pitch dissonance is the most obvious of these. Metrical dissonance and

pitch dissonance are frequently associated in Schumann's music, with the result

that effects of tension generated individually by the two classes of dissonance

are magnified. Suspensions and retardations, both involving displacement dis-

sonance in conjunction with pitch dissonance, are simple examples of such coor-

dination. Some of Schurtumn's combinations of displacement dissonance with

pitch dissonance, such as the first of the impromptus op. 5 and the fourth Davids-

biindlerlaiiz, consist primarily of straightforward suspensions or retardations.Other associations of displacement and pitch dissonance are related to the sus-

pension idea in the sense that they project potentially congruent harmonic

planes that have been shifted out of alignment — for example, the passage atmm. 9—14 of the finale of the Piano Sonata op. 14 and the opening of the first

piece of Kreisleriana.

Fascinating though they are, the above passages cannot be regarded as de-

liberate coordinations of dissonance in two domains, for within suspensions or

retardations, pitch and metrical dissonance are by definition inseparable. We

look now at a few instances of coordination of dissonance in the two parametersthat are not based on suspension or retardation and that therefore suggest a

conscious effort on Schumann's part to synchronize events within the domains

of pitch and meter.The third section of the tenth Papillon (see Example 2.8) follows two sec-

tions that are virtually consonant both with respect to pitch (aside from domi-

nant seventh chords and momentary passing notes) and meter. Within the thirdsection, Schumann associates D3+2 with some harsh pitch dissonance (espe-

cially in mm. 34—36, not shown in Example 2.8). In the displacement-ridden

opening theme of the first movement of the Piano Sonata op. 14 (Example

4.10), numerous outer-voice sevenths and ninths coincide with the accents that

produce the displacement dissonance. The following metrically consonant sec-

tions, on the other hand (mm. 22-26, 26-38, 38-46), are significantly moreconsonant with respect to intervallic structure as well; the outer voices of mm.

26–38, for example, move primarily in tenths.

Intermezzo II from the second piece of Kreisleriana illustrates a well-crafted

coordination of intensification of pitch and metrical dissonance. The Intermezzois in rounded binary form. The A section begins with D6+2 (l=quarter— mm.91–95), then presents the tighter dissonance D3+2 (mm. 95-96), the antimetri-cal layer arising mostly from durational accents in the bass. The final measures

of the section (mm. 97-99) are metrically virtually consonant. The metrically

dissonant measures contain occasional prominent pitch dissonances (the A/B)clash in m. 93 and the G/F in m. 95), whereas the metrically consonant final

measures are entirely consonant in terms of pitch. Most of the B section is per-meated by intense 1)3+1 in addition to weaker D3+2; D3+1 is initiated by thedynamic accent on the second beat of m. 99 and is maintained by similar accents

in mm. 100 — 106, and D3+2 arises from durational accents on third beats (Kx-

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EXAMPLE 6.6. Kreisleriana no. 2, mm. 104—11

ample 6.6). In mm. 107—8, Schumann abandons all of the 3-layers and establishestwo conflicting 2-layers, one by regularly reiterating D minor harmony, theother by dynamic accents. These 2-layers create indirect and subliminal G3/2 aswell as D2 + 1. Because D3+1 is the diminution of the A section's D6+2 andhence involves more frequent contradiction of metrical pulses; because disso-nances are created to a greater extent by dynamic accents; and because the met-rical layer is strongly contradicted by subliminal dissonance (in mm. 107—8),the B section is metrically much more intensely dissonant than the A section.Exactly the same is true of pitch dissonance; the outer voices in mm. 101-8 ob-sessively state sevenths and ninths. In mm. 107—8, where contradiction of theprimary metrical layer reaches an apex, pitch dissonance is particularly violentas 'well; both measures contain parallel ninths. In the final two measures of theB section (mm.109—10), all metrical dissonance is resolved. Simultaneously, theouter voices begin to state consonant intervals and, in m. 110, merge into a sin-gle octave-doubled voice!5

Florestan muttered, "An interesting example, to be sure! We do not, how-ever, always coordinate intervallic and metrical dissonance in this manner. In thefirst movement of the Faschingsschwank, for instance, some of the passages thatare metrically most dissonant are completely consonant in terms of pitch, such asthe subliminally dissonant passage in mm. 87-126 (Example 2.14). The same istrue of the displaced passage comprising mm. 340-56 of that movement (Exam-ple 8.24c); the chords in this passage, with the exception of those built on F# in

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EXAMPLE 6.7. Faschingsschwank aus Wien, first mvmt., mm. 357—62

mm. 342—43, are either consonant or relatively mildly dissonant (dominant and

diminished sevenths)." Ensebius countered, "In the following section, however

(mm. 356 — 62 — Example 6.7), you do associate the continuing displacement dis-

sonance with strikingly dissonant chords." Florestan said, "You are right, but 1

wished to indicate that the association of pitch and metrical dissonance does not

always take the most obvious form." They continued their reading.

A Schenkerian perspective suggests additional interesting ways to associ-

ate metrical dissonance with in analogous pitch state. In the eleventh Papillon,

the relinquishing of the primary tone on the middleground level—a yielding of

middleground melodic stability to instability — is associated with metrical disso-

nance. The primary tone A is embellished on the middleground level until m. 10

by repeated downward octave coupling. At the end of m. 10, a middleground

linear progression, already foreshadowed on the foreground during the first

beat, is inititited. Precisely at the point where the primary tone is dislodged,

Schumann brings the indirect metrical dissonances G3/2 and G4/3 into play by

interjecting a measure of common time.

Florestan impatiently remarked, "I do not understand most of the terminol-

ogy in the paragraph that we just read." Eusebius agreed, "1, too, do not under-

stand it completely. It seems to me, however, that this 'Schenkenan' theory has to

do with layers or levels in the domain of pitch." They read on:

In the "Landler," op. 124 no. 7, Schumann associates an unstable melodic

event of another kind, namely interruption, with metrical dissonance. The pri-

mary tone is Fl. In the first section, two linear progressions (F#-E-D) prolong

the primary tone. After the double bar (see Example 4.14), the background de-

scends to the second scale degree, which is then prolonged by octave coupling

until the return of the opening in m. 16. The prolongation of scale degree 2, un-

stable in terms of the background level, is coordinated with displacement disso-

nance. As the primary tone returns, the dissonance resolves.

The f if teenth piece from op. 124 (sec Example 7.3) involves a more unusual

type of instability in the pitch domain: Schumann leaves the fundamental line in-

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Interactions of Metrical Dissonance 153

complete. The primary tone is scale degree 5 (El), and descents as far as scale

degree 3 (C) occur a number of times (mm. 1-4, 5-8, and in the final phrase).

The line, however, never reaches full repose on the tonic. Schumann parallelsthis large-scale melodic instability by allowing the metrical dissonance D3+2 (orD3-1), -which is active through most of the piece, to remain unresolved at the

end.Early nineteenth-century composers sometimes organize passages and

even entire works around a rivalry between two keys.6 The analogy betweensuch a tonal conflict and conflict between two or more layers of motion is obvi-ous, and Schumann does occasionally coordinate these analogous states. Thefifth Intermezzo from op. 4 no. 5 provides an example. (Portions of this work areshown in Examples 5.13, 8.9, and 8.10.) The governing tonal conflict between

the keys of F major and D minor is exposed during the initial section (mm.1—19), which begins in F major but at m. 13 moves into D minor. A similar shiftfrom F to D takes place within each recurrence of the opening music. Furthermanifestations ot the F/D conflict are found in the second section. In mm.32—34, a rising root progression by fifths connects the contending tonics (D toF), whereupon the music returns to D minor. Whereas the first ending remains

in the latter key and leads to its dominant, the second leads to the dominant of

F. The section at mm. 37—45 (see Example 8.9b) contributes to the D/F conflictby prominently presenting references to the enharmonically equivalent dyadsC/Ctt and C/DI>, the former suggesting the key of D, the latter suggesting andindeed leading into the key of F/ The "Alternativo" section arrives powerfullyon V of D minor (m. 135), but V of F is immediately set against it as the open-

ing music returns. The key of D minor ultimately wins the tonal battle.

An important component of the tonal conflict is the rivalry between twocontenders for primary tone status, one per key. The apparent primary tone atthe beginning is C, that tone being solidly established by an upward octave cou-pling in mm. 2—6. In mm. 13—20, C moves to C#. Since C# is the enharmonicequivalent of the Dl that acts as an upper neighbor to C within the F-major

portion of the opening theme, the large C to C# motion in mm. 13-20 not onlycontributes to the modulation to D minor, but in a broader sense encapsulatesthe overall D/F conflict. In mm. 20-36, the C# resolves to D, but above that Dthe new primary tone F appears (mm. 21-26 and 30-32). This tone, like theinitial C, is coupled upward (mm. 21-30); Schumann's similar treatment of Fand C corroborates the apparent equality of these two primary tones. It is Fthat assumes ultimate primacy; the final descent of the piece emanates from this

pitch (mm. 204-5). In a strict Schenkerian sense, then, F is the true primarytone of the work.

How does Schumann coordinate metrical conflict with the conflict betweenthe tonics of F and D? First, it is obvious that the piece exhibits a large amountof metrical dissonance; m broad terms, we can state that Schumann has chosento suffuse a piece governed by tonal conflict with conflict in the metrical domainas well. But there are more specific pitch/meter coordinations as well. For ex-ample, striking metrical dissonances highlight significant points within the D/F

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conflict. Strong displacement dissonance at m. 21 (see Example 5.13) is coordi-nated with the first appearance of the final key and the actual primary tone F.The passage comprising mm. 32—36, in which Schumann so clearly traverses apath from one tonic to the other, is permeated by subliminal G3/2. In mm.

37-38 (see Example 8.9b), intense D2 + 1 (or D2-1) highlights the C/C# andC/D\ dyads that embody the D/F conflict.

The contending primary tones, too, are highlighted by metrical means. Atthe opening, Schumann contributes to the pretense that C is the primary toneby presenting it in a metrically stable manner; he places it on the downbeats ofmm. 2, A, 10, and 12. The true primary tone, F, on the other hand, is metricallydisplaced at its first arrival at mm. 21—24. Schumann subtly foreshadows, by

metrical means, the outcome of the battle of the primary tones; he lets the "pri-mary tone" C migrate onto an accented third beat at m. 6, whereas the true pri-mary lone F migrates from its initial displaced position onto a downbeat atm. 32.

"Well, Florestan," said Eusebius, "were you aware of all of that?" Florestanresponded, "To be honest, I never thought about these matters in such detail. Idid, however, sense that we were creating interesting parallelisms between tonaland metrical conflict in this piece."

In the preceding paragraphs, we have seen several exiimples of Schu-mann's use of metrical dissonance in order to highlight a significant point withina tonal conflict. Such highlighting is by no means restricted to situations of

tonal conflict; metrical dissonance can emphasize any significant pitch-relatedevent.8 In the Intermezzo op. 4 no. 5, metrical dissonance draws attention notonly to important moments within the F/D conflict, but also to events not di-

rectly involved in that conflict. For example, the melodic line of the Bl-major

"Alternative" section is characterized by an upward-striving motion—a reaching-over, in Schenkerian terms — the ultimate aim of which is to couple D4 to D7.The first wave of the reaching-over begins with the D4 in m. 69 and attains B4at mm. 79—82 before dropping back to D-4. The second wave retraces the samepath (to m. 100), but a third wave moves beyond B4 as far as Bt5 (mm.

101-13). A final wave breaks through the latter barrier at m. 131 and reachesD7 at m. 132. Each of the three registral crests is allied with metrical dissonance(which, since the "Alternativo" is otherwise virtually consonant, stands outclearly from the context). The arrival at B4 in mm. 79-82 is highlighted byD3+1 (inner-voice durational accents) and D3+2 (dynamic accent in m. 82).The approach to Bt5 (see Example 8.9c) features a compound dissonance com-posed of G3/2, D6+2, and D6+5. Both the ascent to the final registral peak andthe recession from it are associated with particularly intense metrical disso-nance, the ascent with G3/2 (mm. 129-31—see Example 8.10b), the descent

with the augmentation G6/4 (l = 8th).Schumann sometimes coordinates not only analogous states, but also anal-

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ogous processes, in the domains of pitch and meter. We have already touchedupon this matter in connection with earlier examples in this chapter; we havenoted, for instance, the simultaneous intensification of pitch and metrical disso-nance in the second piece of Kreisleriana, the simultaneous resolution of disso-nances, and the coincidence of significant large-scale harmonic resolutions (ca-dences) with resolutions of metrical dissonances. I mention only two moreexamples of process coordination here.

A metrical process that occasionally coincides with a parallel pitch processis preparation. One pitch process that is analogous to metrical preparation isthe preparation of modulatory goals by single prominent pitches. Schumannsometimes links such a process with the preparation by one or two antimetricalpulses of a coming metrical dissonance. In "Grillen," for example, the first hintat metrical dissonance — the dynamic accent on the third beat in m. 3 (see Ex-ample 6.1) — prepares D3+2, a metrical dissonance to be featured prominentlyin the Gl major section (especially mm. 72—80). Interestingly, the harmony towhich the preparatory accent in m. 3 is affixed is V7 of Gl>, which prepares thelater prolongation of Gk

In "Vogel als Prophet," Schumann employs gradual intensification of met-rical dissonance in conjunction with the equally gradual seeping of a particularpitch, namely El>, into deeper levels of structure. The metrical process — intensi-fication of D2+1 —was traced in an earlier chapter (see Example 4.7). The cor-responding pitch process begins in mm. 1—3, "where D2 + 1 is weak. Here, El>acts as a lowly neighbor-note (enharmonically respelled to D# in m. 3). A fewmeasures later, El> is promoted to membership in two significant harmonies; itbecomes the seventh within a prolonged dominant harmony (mm, 8—10), thenthe third of a C minor triad that acts as a cadential goal (m. 12). These steps inthe promotion of El> occur just before a passage in which D2+1 is greatly inten-sified— mm. 13-14. The final step in the pitch process occurs at the end of the Bsection, that is, during the section that is metrically most intensely dissonant; E!>here attains its highest status: that of the root of the main modulatory goal of thework (mm. 24-25).9

Florestan said, "A most interesting example! I can think of even more waysin which we coordinated pitch structure with metrical consonance and disso-nance. One of these has to do with harmonic parentheses—passages that brieflydeviate from the main harmonic argument. We have at times coordinated suchparentheses with 'metrical parentheses'—with metrical states that deviate tem-porarily from the prevailing state. An example occurs in the first movement ofthe Third String Quartet (mm. 81-84 —see Example 4.20c). From m. 76 on-ward, near the end of your metrically dissonant second theme, you arouse the ex-pectation of a cadence to E major. Instead of providing this cadence, however,you move ever farther away from the expected E major triad, first elaboratingthe closely related C# minor triad (mm. 76-80), then surprisingly landing on C#major harmony. The C# major passage sounds parenthetical not only because it is

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so remote from the expected goal of E major, but because you use an etherealhigh register, a low dynamic level, and a slower tempo. During this harmonicparenthesis, you resolve the dissonance D6+2 which had prevailed at the end ofthe second theme. When the harmonic progression regains its bearings in m. 84

(where it arrives at a six-four chord embellishing the E major triad), the disso-nance D6+2 returns; the second beats of mm. 84 and 85 are emphasized by a du-rational and a registral accent, respectively."

Florestan went on, "At times we associated passages that were related interms of pitch structure with the same metrical dissonance. The Intermezzo op. 4no. 5 furnishes some good examples. We have just read that mm. 1—4 (Example8.9a) and 37 (Example 8.9b) feature the enharmonically equivalent dyads C/DIand C/C#, respectively. This pitch relationship between the two passages is par-alleled by a metrical one: both passages are associated with the metrical disso-nance D2 + 1. The dissonance is, to be sure, much stronger in the latter passage.Both mm. 33—35 and mm. 109-11 (Example 8.9c) involve the rising progressionby fourths, G-C-F; the bass states it in the former passage, and the melody in thesecond. Both passages are also characterized by G3/2, a dissonance that is oth-erwise rare in the piece." They turned back to the manuscript, and read:

t he lower portion of Figure 6.1 shows the metrical structure of the Pa~ganmi Caprice on which Schumann based his study. Comparison of the twoparts of the figure reveals that in Paganini's work there is much less coordina-tion of metrical dissonance with formal and harmonic structure. The disso-nances do resolve at the most significant cadence points in the first section, atthe recapitulation and at the very end of the work, and the point where the met-rical conflict is most obvious (mm. 32—35) coincides with the harmonically un-stable passage preceding the retransitional dominant. Schumann, however, setsup many more, and much more sophisticated correspondences between form,pitch structure, and meter.

Florestan remarked, "1 knew by the time I composed this study that 1 wouldnot be able to emulate Paganini as a virtuoso. It was some solace to me that I wasable not only to emulate but to outdo him as a composer, specifically as an inge-nious and resourceful manipulator of metrical dissonance."

Eusebius, who had looked ahead to the next section of the manuscript, said,"I am pleased that the author is granting some attention to our vocal works(which so far have hardly been mentioned)." They continued to read with re-newed interest.


I laving studied interactions of metrical structure with other musical features in

Schumann's works, we now turn to an investigation of associations between

metrical states and extramusical features. 1 begin by considering the ways in

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which metrical states are linked with text in Schumann's vocal works. I restrictmy investigation to his songs, which are by far the richest source of metrical dis-sonance within his vocal oeuvre. By studying Schumann's use of metrical disso-nance in the Lieder, we may not only discover the ways in which metrical disso-nance relates to text in specific songs, but also begin to understand themeanings that this device carries in his instrumental works.

Florestan said, "The author indicates that our choral works contain less metricalconflict than our Lieder. He is right, and there is a good reason why this is so. Ihave conducted choirs,10 and I know that choristers, many of whom are not pro-fessional musicians, have difficulty with rhythmic complexities. In our choralmusic, I therefore curbed my penchant for metrical intricacies." Eusebius added,"It seems to me that, in general, you indulged your metrical fancy most freely inour piano music and in our chamber works. In our symphonies, your metricaldissonances are slightly less numerous, and slightly less bold." Florestan said,"Yes; I have always felt that passages of metrical conflict were more likely to beperformed properly by soloists and small ensembles than by large groups." Theycontinued their reading:

Schumann's songs, though they contain more metrical dissonance than hislarger vocal genres, are a less fruitful source of metrical dissonance than the in-strumental works; not only does metrical dissonance appear less frequently inthe songs, but it generally appears more briefly and in a more limited number offorms. Schumann may have felt that complex metrical superpositions woulddistract the listener from the text. Furthermore, involvement of the vocal part ina dissonance could have posed problems of declamation; the necessity of adher-ing to the poetic accentuation precluded the freedom with which antimetricallayers can be established in instrumental music. (Significantly, Schumann gen-erally avoids declamation problems by using metrical dissonance within un-texted portions of songs, or by placing antimetrical layers within the piano part;we shall, to be sure, encounter a few exceptions.) The metrical dissonances thatdo exist in Schumann's songs, however, are well worth investigating, particu-larly in terms of their relation to poetic content. In the following paragraphs Iinvestigate various textual factors that may have impelled Schumann to bringmetrical dissonance into play.

At a climactic moment of the ballad "Die Lowenbraut," the lion feels slightedbecause his beloved mistress is about to desert him in favor of a husband, and hemakes his displeasure known in no uncertain terms with bloodcurdling roars. Thethick, accented chords in the interlude after the words "Er im Zorn den Ausgangwehrt" ("in his fury he prevents egress"), displaced by a sixteenth note with re-spect to the half-note beats (Example 6.8), are surely intended to imitate the un-predictable fluctuations in sound that are characteristic of a lion's roar. Pitch dis-sonance and low register collaborate with metrical dissonance to achieve thedesired effect. Considering that Schumann probably never heard a lion's roar, this

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EXAMPLE 6.8. The roars of the lion in "Die lowenbraut" op. 31 no, 1

is not a bad imitation! Schumann's song output contains numerous similar in-

stances of the attempt to mimic with metrical dissonance particular sounds or ac-

tions mentioned in the poem. In "Warte, warte, wilder Schiffsmann" (Example6.9), Schumann abruptly displaces the vocal line by a quarter note when the text

mentions the action of shuddering. Displacement dissonance at a quick tempoevokes the regular oscillations of a shiver. Furthermore, the deliberate contradic-

tion of textual accentuation caused by the vocal displacement suggests the un-

controlled diction associated with shuddering.11

Florestan offered a few more examples of metrical mimicry: "In 'Lied eines

Schmiedes" (op. 90 no. 1), our superposition of two nonaligned, accented halfnote layers suggests the blacksmith's hammer blows and their echoes. In 'Die

wandelnde Glocke' (op. 79 no. 17), a similar metrical dissonance evokes the os-

cillations of a tolling bell. In the orchestral introduction of the third ballade fromVom Pagen und der Konigstochter, op. 140 — a duet between the queen and a mer-

man— the low strings, clarinets, horns, and tympani articulate the metrical layer

(the dotted quarter-note beats of twelve-eight time). The violins, flutes, andoboes, however, state a displaced layer, resulting in the dissonance D3+2 (l=8th).

This dissonance suggests the lapping of the waves to which the opening of the

text alludes."

EXAMPLE 6.9. The shudder in "Warte, warte, wilder Schiffsmann" op.24 no. 6

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EXAMPLE 6.10. The answer to the riddle in "Rathsel" op. 25 no. 16

Rathsel" (Riddle), op. 25 no. 16 (Example 6.10), illustrates a differenttext-related function of metrical dissonance in song, namely that of marker orhighlighter for especially significant portions of the text. The answer to thepoet's riddle — the letter H — is supplied at the very end of the poem, not in thetext but in musical notation: Schumann not only ends the vocal line on the noteB (H in German) but, even more dramatically, reiterates syncopated B's in thepiano part immediately after the parenthetical question "was ist's?" (What isit?). Syncopation has hardly occurred m the song thus far.

Eusebius interjected, "There is a single syncopated B during the piano interludeafter the word 'Philosophic'—a hint at the solution of the riddle that was absentfrom our first version."12

1 his displacement dissonance, then, stands out from the context andstrongly marks for consciousness this crucial point in the song. The listenerwould surely solve the riddle during that striking series of metrically displacedB's

Florestan observed, "Yes, assuming that the listener understands German, hasperfect pitch, and that the song is being performed at the notated pitch level!"

Another good example of the highlighting of particularly significant textby metrical dissonance is found in "Waldesgesprach" (op. 39 no. 3). The turn-ing point of the text is the moment at which the protagonist recognizes that thelovely maiden with whom he has been dallying is the evil enchantress Lorelei.Schumann associates this point with a dramatic superposition of the displace-ment dissonances D3+1 and D3+2 (l=quarter; Example 6.11). The former dis-sonance, created throughout the man's E-major music by syncopation in theupper voice of the left hand, is formed at "Gott steh' mir bei" by a durational ac-

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EXAMPLE 6.11. The turning point in "Wadesgesprach" op. 39 no. 3

cent on the second beat of the voice part (at "bei") and by the piano's imitation

of the voice's dotted motive at the distance of one quarter note. Schumann also,

however, places a dynamic accent on the third beat of the measure. The latter

accent and the resulting superposition of a new dissonance upon the existing

one highlights the moment of truth.

Eusebius remarked, "Our use of D3 + 2 at this point also reflects the forcible re-

onentation within the man's psyche brought about by his sudden awareness of

the true significance of the encounter. By adhering to D3+2 during the final state-

ment of the man's E-major music in the postlude, where the left-hand ties begin

on the third rather than the second beat, we suggest that the man's life has been

permanently and chillingly changed by his encounter with the Lorelei." Florestan

added, "The shift in the music associated with the protagonist from D3+1 to

D3+2 was not part of our initial strategy; we originally employed D3+2 at the

opening as well as in the postlude."13

in some of Schumann's songs, conflicting layers of motion appear to de-

note different levels or dimensions of some textual attribute, for example, of re-

ality (the apparent versus the actual), or of time. In "Zwiehcht," op. 39 no. 10,

displacement dissonance is concentrated within one stanza, that which pes-

simistically mentions the potential treachery of friends; no doubt Schumann

meant the two layers to suggest the apparent and the true nature of the


Florestan pointed out, "Some of the displacement dissonances in our opera Gen-

oveva have a similar meaning. Displacement frequently coincides with words or

events that highlight Golo's treachery. His entry into Genoveva's chamber near

the beginning of Act: 2, for example, is accompanied by syncopated quarter-note

chords. We associate his blatant vilifications of Genoveva before Drago with

D4+2 and D2+1 ( l=quarter) . A very dramatic displacement dissonance occurs

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just after Siegfried's naive assertion that Golo was always loyal to him; here, achromatically descending progression in the orchestra is festooned with dynamicaccents on weak beats."

The text of "Es treibt mich Kin, es treibt mich her" (op. 24 no. 2) alludes to

the slow, unruffled flow of clock time and to the poet's eagerness for a ren-

dezvous with his beloved. Schumann initiates allusions to D3+2 (or D3-1) dur-

ing a reference to the languid passing of time (at "behaghich trage" and "gah-

nend") and intensifies this dissonance with dynamic accents in the postlude.

The metrical layer might well represent the ineluctable progress of clock time,while the displaced layer, anticipating the notated downbeats, suggests the ex-

pectant lover's desire to move time forward.By far the most common function of metrical dissonance in Schumann's

songs, however, is the reflection of emotional or psychological states, particu-

larly those of a violent nature; the dissonance in these cases suggests the loss of

control associated with such states. The emotional states may be of a positivecharacter. In "Es treibt mich hin," metrical displacement, besides representing

two times, suggests the lover's excitement. Continuous low-level displacement

in the third song of Dichterliebe ("Die Rose, die Lilie") has a similar function. In

the first song of Schumann's little-known Justinus Kerner cycle, op. 35 ("Lust

der Sturmnacht"), continuous displacement by a sixteenth note and occasional

accentuation of the final two sixteenth-note pulses of a measure contribute sig-

nificantly to the representation of a lover's exhilaration and exultation; the con-

sistent use of low-level displacement dissonance results in a sense of excitement,

and the jabs of weak-beat accentuation suggest the spurts of adrenalin associ-ated with being happily in love.

Eusebius added, "In Genoveva, we sometimes associate the unsavory joys of the

villains with displacement dissonance. We suggest Golo's excitement just before

kissing Genoveva by eighth-note syncopation in the strings. Similarly, in the fi-

nale of Act 1, Golo's passion and Margaretha's gleeful anticipation of her revengeon Siegfried are both associated with D2 + 1 (l=quarter), created by dynamic ac-

centuation of both weak beats of common-time measures."

Schumann employs metrical dissonance more frequently in connection

with negative states. Example 6.12 shows an association between displacementdissonance and insanity; just as Heine's poem refers to "Wahnsinn" (madness),the piano launches into low-level displacement dissonance—an appropriate rep-resentation of a mind going awry.14

In a number of the passages mentioned above, metrical dissonance is asso-ciated with poetic passages that are rife with tension, the lion's roar, the shud-

der, and the moment of truth in "Waldesgesprach" being obvious examples.

Since metrical dissonance is a tensional combination of conflicting or non-

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EXAMPLE 6.12. The setting of "Wahnsinn"in "Scbone Wiege" op. 24 no. 5

aligned pulse groupings, its association with emotional conflicts and tensionsmentioned in a text is appropriate. The resolution of a metrical conflict, on theother hand, can aptly represent the resolution of textual conflicts, or sensationsof relaxation in general. Such usages of metrical consonance and dissonance arevery common in Schumann's songs. A simple but lovely example is found nearthe end of "Mondnacht" (op. 39 no. 5). During the words "als floge sie nach,"the vocal line and the piano bass project a 2-layer (l=8th) against the continu-ing 3-layer of the right-hand part. The resolution of the resulting metrical dis-sonance precisely at the word "Haus" elicits an appropriate sensation of "home-coming"— of settling into a sale and familiar place.

Eusebius noted, "The syncopation in voice and bass that makes this effect of

relaxation possible was an afterthought; I added it to ray inked manuscript inpencil."15

in Dichterliebe, Schumann deploys displacement dissonance over a widemusical expanse in order to reflect the increasing tension within the protago-

nist. The first songs of the cycle, in which the poet's love affair seems to beprogressing smoothly, contain virtually no metrical dissonance. Later songs,in which it becomes increasingly clear that the affair has gone sour, involvefrequent use of displacement by one eighth or sixteenth note. In the tenthsong ("Hor" ich das Liedchen klingen"), D4 + 1 (l = 16th) is prominent through-out (Example 6.13a). The dissonance is tightened to D2 + 1 in the postlude.The eleventh song ("Ein Jungling liebt ein Madchen") also exhibits D4 + 1(l=8th —Example 6.13b) and the same tightening.16 In the last song of thecycle, Schumann appropriately coordinates a prominent resolution of D2+1(l=8th) with textual references to the end of the poet's tormented love. Thethrobbing syncopated chords that underlie the question "Do you know whythe coffin is so large and heavy?" yield to metrically aligned music in the lastline, during which the text states that the poet has buried his love and pain.

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EXAMPLE 6.13. Metrical Dissonance in Dichterliebe op. 48

Eusebius added, "Our resolution of D6+1 in the seventh measure of thepostlude is also meant to suggest the end of the poet's inner turmoil."

Florestan said, "There are numerous similar examples. In 'In der Fremde'(op. 39 no. 1), we suggest by pervasive displacement dissonance, created by dy-namic and density accents on the metrically weak beats as well as by quarter-

note syncopation, the disquiet of the protagonist and her dissatisfaction with herenvironment.17 As she ponders the peace that will soon come to her in death('Wie bald, ach wie bald kommt die stille Zeit'), we resolve the dissonance. Dur-ing the first statement of the phrase 'da ruhe ich auch,' the dissonance reappears,

suggesting a final spasm of unrest, but we again resolve it during the repetition ofthe phrase.18 In 'Stiller Vorwurf (op. 77 no. 4), the anonymous poet recalls thepain that his beloved caused him; we set this portion of the poem with frequentD4+2 and some D2+1 (l=8th), frequently creating the former dissonance byplacing piano chords on the weak beats of measures (Example 6.14a). At theend, where the poet states that he cannot help forgiving the woman, we presentpiano chords on the strong beats, thus resolving D4+2 (Example 6.14b)." Euse-bius countered, "D2+1, however, is still in effect at this point; the word 'kann' ap-pears one eighth note later than expected, suggesting that some residual pain oranger remains in the poet's heart."

Florestan said, "D2+1 does resolve before the song concludes. Occasionally,when textual conflicts are unresolved at the end of a poem, we conclude our set-tings with unresolved metrical dissonance. The Lenau song 'Der schwere Abend'(op. 90 no. 6), is a good illustration. The text deals with the parting of unhappylovers on a sultry, starless night. The final line, in which the poet wishes that he

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EXAMPLE 6.14. Metrical dissonance and resolution in "Stiller Vorwurf" op, 77 no. 4

and his beloved were dead, does not relieve the prevailing tension. Throughoutthe song, we express the poetic tensions with grouping dissonance; quarter note

duplets in the voice conflict with the piano's three quarters per measure. Brief al-lusions to displacement dissonance (D3+1 and D3+2, l=quarter) during pianointerludes, suggesting flashes of lightning, add to the tension (mm. 8, 28, 48). Weexpand upon D3+2 in the piano postlude (Example 6.15), where we place dura-

tional, then harmonic new-event accents on the third beats rather than on down-beats. (Where harmonies are initiated on the third beats, the dissonance can beheard as D3-1.) The final chord of the song does fall on a downbeat, but that sin-

gle chord does little to counteract the displacement of the earlier ones. Metricaldissonance hangs over the end of the song like the brooding clouds mentioned in

Lenau's text.Eusebius remarked, "'Der schwere Abend' brings up another kind of rela-

tionship between metrical dissonance and text—a relationship that has to do notwith poetic content but with poetic meter. When we initiated our text-setting ac-tivity by reading the poem, its metrical irregularities inevitably caught our atten-tion, and in some cases influenced the anomalies in the musical meter. In 'Derschwere Abend,' the only irregularity occurs in the penultimate line ('wiinscht ichbekiimmert beiden'), which disrupts the straightforward iambic meter of the re-mainder of the poem. Now a succession of iambs suggests a duple grouping ofpulses, while a dactyl like 'wunscht ich be-' suggests a triplet, taking the time ofone duple group. (Other rhythmic settings of these poetic feet are, of course, pos-

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EXAMPLE 6.15. Metrical dissonance at the end of "Der schwere Abend" op. 90 no. 6

sible, but the ones I mentioned are the most obvious.) The suggestion within a textof such indirect two-against-three dissonances might well have influenced our de-

cisions with regard to metrical dissonance in the musical setting, all questions ofpoetic content aside. In the case of 'Der schwere Abend,' the poem contains theseed of our pervasive grouping dissonance." Florestan said, "Your remarks also

apply to another of our Lenau songs, 'Meine Rose' (op. 90 no. 2). The content ofthe text does not justify our pervasive metrical dissonance. The poem contains,however, three 'triplets' amidst its many duple groups: 'reich ich den,' 'still meine,'and 'Konnt ich dann.' These irregularities in the poem influenced our decision tosaturate the setting with G3/2 (1 =8th). I see that the author is about to discuss 'Esleuchtet meine Liebe,' one of the songs that we excised from Dichterliebe, whichalso illustrates my point. Its text, like most of Heine's poems, is primarily iambic,but there are numerous triplet disruptions; they increase in frequency as the poemprogresses — two in the first stanza, three in the second and third, four in thefourth. We even expand upon Heine's disruptions in the fourth stanza by repeat-ing one of the irregular lines ('es stolpert der Riese nach Haus'). The two-against-three dissonance of the music, then, grows out of the meter of the poem." Eusebius

observed, "In this case, however, the content of the poem also suggests metricaldissonance, as I am sure the author will mention." They read:

To summarize the ideas presented thus far in this chapter, I present a metri-cal analysis of Schumann's setting of Heine's "Es leuchtet meine Liebe" (op. 127

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FIGURE 6.2. Interaction of metrical structure, form, pitch structure, and text in "Es leuchtet meine Liebe"

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Interactions of Metrical Dissonance 167

no. 3). Heine's poem "Es leuchtet meine Liebe" opens with an analogy between

the poet's love and a tragic and somber fairy tale, then shifts abruptly to the nar-

ration of just such a tale. The tale begins innocuously enough: two lovers walk

silently in a magical garden, surrounded by the nightingale's song and by shim-

mering moonlight. The knight kneels down before his beloved, who stands still asa statue. This nocturnal tableau is rudely disrupted as the "giant of the wilder-

ness" appears.19 The maiden flees, and the knight and the giant engage in an af-

fray (which is not explicitly mentioned in the poem, but is brought to life in Schu-mann's setting by a stormy piano interlude). The grim fairy tale concludes with

the knight falling bleeding to the ground and the giant stumbling homeward. In

the final line, the two planes of the poem — the poet's discussion of his love, and

the fairy tale — merge; the poet's statement that the tale will be over when he is

buried suggests that he is himself the wounded knight of the fairy tale.Figure 6.2 shows the metrical and formal structure of the song, as well as

one aspect of pitch structure — the locations of intense pitch dissonance. It is ob-

vious from the figure that changes in metrical state contribute to clarification of

form. Resolution of metrical dissonance occurs at the beginning of the B section

(m. 7). The return of the A section in the subdommant key (m. 19) is marked bythe resolution of two dissonances. In a transitional passage (mm. 22—25), G3/2

is weakened, to be restored to its former intensity precisely at the point where

the goal of the passage, the A section in the tonic, is reached. The coda (mm.

30—38) begins with resolution of dissonance and remains virtually consonantthroughout.

The figure also reveals that metrical dissonance is coordinated with pitch

dissonance. Those passages characterized by the strongest pitch dissonances(semitone dissonances, sometimes taking the form of clusters) are precisely

those in which metrical dissonance is most pervasive (mm. 1—6, 15—18, and

26-29). In mm. 7-14 and 30-38, where, with few exceptions, pitch disso-

nances are restricted to the mildest ones (dominant and diminished seventhchords), metrical dissonance is hardly in evidence.

Both form and pitch structure clearly correspond to the poetic form andcontent. The A sections m the tonic are coordinated with the external narra-

tive— the poet's remarks about his love—while the B section sets the fairy tale

that allegorically represents the circ*mstances of that love. Intensity of pitch

dissonance changes at poetic dividing points. Since both pitch structure and

form, then, are influenced by the text, the observation that metrical dissonance

is coordinated with pitch structure and form indirectly implies that metrical dis-sonance is coordinated with the text.

But the coordination of metrical structure and text is more directly in ev-

idence as well. The most prominent of the several dissonances, G3/2 (l=8th), isclearly intended as a musical symbol for the evil giant (who, in turn, personi-

fies the conflicts that bedevil the poet's love). This dissonance is established at

the very beginning (Example 6.16a). The pianist will likely emphasize everythird eighth-note pulse in the right hand, in accordance with Schumann's timesignature, thus immediately establishing the metrical 3-layer. From m. 2 on-

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EXAMPLE 6.16. Metrical dissonance in "Es leuchtet Heine Liebe " op. 127 no. 3

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Interactions of Metrical Dissonance 169

EXAMPLE 6.16. (continued)

ward, the left-hand part of the piano introduction more obviously articulatesthe 3-layer. A conflicting 2-layer is expressed, however, by the grouping of the

right-hand chords — by the recurrent patterns "consonance-dissonance" and"tonic-dominant." When the voice enters, its durational accents (which coin-cide with poetic accents) join the piano bass in articulating the 3-layer, while

the 2-layer continues in the right hand.The association of metrical dissonance with the textual conflict becomes

very clear at mm. 15-18, where the evil giant rears his ugly head (Example6.16b). Metrical consonance, which has reigned since m. 11, is appropriately

replaced with G3/2 at this point. While the voice part continues to articulatethe metrical 3-layer, the piano expresses two 2-layers in mm. 15—18. One of

these is formed by implied accents on the first notes of the slurred groups(which can be played and heard as appoggiaturas and their resolutions), andby the simultaneous syncopated repeated notes played by the right hand (El>,F, and finally G). The other 2-layer, shown by the upper 2's in the example,arises from subsurface new-event accents on the second bass notes of theslurred groups, which together form a rising stepwise ascent through a fifth ineach measure. The non-aligned 2-layers result in D2+1 in addition to G3/2. Thesforzandos on the final eighth notes in mm. 16—18 create yet another disso-nance (D12 + 11, or D12-1). The sudden pileup of dissonances in mm. 15—18

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effectively mirrors the shattering of the lovers' nocturnal idyll by the entranceof the giant.

Eusebius remarked, "Your mm. 15—18 are somewhat similar to my mm. 9—10; thetwo passages both make use of slurred duple groups. Since your measures containso much additional metrical dissonance, however, they give the impression of adistortion rather than a mere restatement of mine. This effect of metrical distor-tion contributes to the musical depiction of disruption of the earlier idyllic state."

in the fortissimo piano interlude in mm. 19—21, the struggle between theknight and the giant is musically suggested by a continuation of G3/2. (Theother two components of the compound dissonance are abandoned after theirfunction of dramatizing the giant's entrance is served.) Although the 2-layertakes over the entire texture in m. 19, G3/2 remains in effect subliminally. Inmm. 20—21, while the 2-layer continues to be expressed by grouping in theright hand, the piano bass clearly asserts the metrical 3-layer by accentuation ofdotted quarter-note beats. The dissonance G3/2 is maintained during the narra-tion of the succumbing of the knight (mm. 22 — 23) and, albeit weakly, as thevictorious giant stumbles home (mm. 23—26); in the piano part of mm. 23—25,recurrence of individual pitches (F# in mm. 23–24 and D in m. 25) suggests a 2-layer while textual accents and contour repetition articulate the metrical 3-layer(Example 6.16c). The giant's stumbling is further suggested in in. 25 by anothersubtle dissonance; the descending diatonic framework of the passage is de-ployed m such a way that two of its members, the C natural and B flat, appearon the third eighth notes of metrical groups, resulting in a hint at D3+2.

Florestan looked up and said, "1 recall that when Chiarina played the piano partof this song, she placed subtle stresses on the Fit's and D's that form the 2-layer,so that the stumbling of the giant became more audible. I found this enhance-ment of a dissonance that is hardly evident in the score very appropriate. Luckythe singer who has a pianist like Chiarina at his or her side!" Eusebius agreed,then remarked, "We had better finish the chapter. It is growing quite dark!"

I he dissonance G3/2 continues and in fact becomes more intense as theopening material returns in m. 26 and as the text comes to a close; the subtle dis-placement dissonance of m. 25, however, resolves in m. 26 as the giant makes hisexit. The partial resolution in m. 26 is not the only example of text-inspired reso-lution in the song; there are two significant resolutions of the mam dissonance,G3/2. Schumann eliminates the 2-layer, and hence the dissonance, during mostof the first part of the fairy tale (mm. 7—14). This resolution corresponds to atemporary reduction in poetic tension. The first part of the fairy tale appearsquite idyllic; it does not yet possess the "ACL and somber" quality announced atthe beginning of the poem. G3/2 appears briefly at mm. 9-10 — perhaps as a sub-

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tie indication that the peace of the initial portion of the fairy tale is illusory — butconsonance then reigns again until m. 14. More significant, Schumann resolves

G3/2 at the end of the song; he abandons the accompaniment pattern based onchords grouped in pairs, and writes new material, characterized by ominous ris-ing octaves, that clearly expresses the metrical 3-layer. With this permanent res-

olution of metrical dissonance, Schumann reflects the content of the final line,"When I am buried, the tale will end" (that is, the conflicts surrounding the pro-tagonist's love will be resolved, definitively though not happily, by his death).

In sum, in "Es leuchtet Heine Liebe" Schumann effectively coordinates

states of metrical dissonance and their resolutions with pitch structure andform. Furthermore, his metrical dissonances beautifully evoke particular as-

pects of the text. The song contains examples of many of the types of connec-tions between metrical state and text that were mentioned earlier: the use ofparticular metrical states to mimic an action mentioned in the text (the giant's

stumbling in m. 25), to highlight a crucial point in the poem (the appearance ofthe giant at m. 14), and to represent a textual conflict and its resolution.


The very frequent occurrence of metrical dissonance in his music, demonstratedby the large number of examples cited in this and earlier chapters, might leadone to conclude that Schumann delights in this state for its own sake — that theeffect of metrical dissonance appealed to him just as certain chord types or cer-tain rhythms might appeal to other composers. Our investigations of metricalprocesses, however, suggest that his interest m metrical conflict arises fromsomething more than aesthetic preference. The fact that he does not merelytreat metrical dissonances as exciting coloristic effects, but rather developsthem in a variety of ways, makes clear that he is interested in the exploration ofthe potential of these states as musical ideas. (Of course, his selection of theseparticular ideas confirms that he did enjoy them as "colors" as well.)

For Schumann, however, metrical dissonances are more than musical col-ors and ideas. Our study of metrical dissonance in Schumann's songs suggeststhat they carried particular extramusical meanings for him — meanings, infact, that were deeply relevant to his life and his personality. Dietrich Fischer-

Dieskau suggests, for example, that when setting "Es leuchtet Heine Liebe,"Schumann identified himself with the poet (and the knight), Clara with themaiden, and Wieck with the giant. He surmises that Schumann may alsohave been thinking of Wieck as he set "Die Lowenbraut"; like the lion, Wieck,about to lose his precious daughter to an interloper, became vicious in hisjealousy and disappointment.20 If Schumann related these poems to the con-flicts within his own life, then the fact that he prominently or pervasively em-ployed metrical dissonance when setting them suggests that he consciouslyor subconsciously linked that device with his personal conflicts. It is not far-fetched to assume that in Schumann's instrumental music, too, metrical dis-

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sonances frequently represent the conflicts that he was working through inhis life.

Schumann was, even more than most artists, riven by internal conflicts and

faced with external ones. Among the internal conflicts are the famous Florestan-

Eusebius duality; the conflict between the poet and the musician; the conflict

between Biedermeier and Bohemian (which could be generalized to "normal

versus abnormal"); the conflict between the objective self and the subjectiveself; and so on. Among Schumann's external conflicts were the struggle againstthe Philistines of the musical world in which he engaged through the Neue

Zeihicbrift; and the famous protracted battle with Wieck, which also broughtwith it painful tensions in Schumann's relationship with Clara.21

These manifold dualities and conflicts inevitably impinged on Schumann's

music in a variety of ways: in the dialectic bet-ween the esoteric and the accessi-ble that animates the -works of the late 1840s,22 in the manifold juxtapositions of

Eusebian and Florestaman sections, but surely also in the frequent use of met-

rical dissonance. The metrical layers within a particular dissonance are apt sym-

bols for normality, for order, for the objective self, and for the Eusebian side of

Schumann, whereas antimetrical layers suggest the abnormal, the irregular andthe disorderly, the subjective self, or the Florestaman side.

\Ve can never, of course, be certain precisely what Schumann might have

"meant" by particular instances of instrumental metrical dissonance. We shall

not be far off the mark, however, if we interpret them as representing inner or

outer conflict, and their resolutions as expressing a desire to come to terms with

conflict — for as Dieter Schnebel points out, in his music, unlike in his life,

Schumann was able to resolve all conflicts if he so wished.23 "I1*

Florestan mused, "Thus ends the chapter. The author is certainly on the right

track when he emphasizes the connection between metrical dissonance and trie

various conflicts in our lives. Some of our instrumental metrical dissonances, how-

ever, have connotations other than conflict. With displacement dissonances at a

very fast tempo, we sometimes express fear, panic, and breathlessness, for exam-ple, in the finale of the Piano Sonata op. 14,M and in the Scherzo in F minor excised

from that same work. Some of our dissonances are humorous in intent; the unex-pected association of disparate elements that underlies metrical conflicts certainly

has comic potential. The subliminally dissonant passage beginning at m. 188 of thefinale of our Piano Concerto is one of my humorous examples. It is certainly a

good joke on the conductor, who is forced to wave his arms in accordance with ameter that has very little to do with the music that the performers are playing!"25

Eusebius smiled, then went on, "I have occasionally employed metrical dis-

sonance in a manner that suggests neither conflict, panic, nor comedy, but ratherevokes a suspended, dreamlike, hovering state. Do you recall the little 'Im-

promptu 'that 1 dashed off in 1838, and that we recently included in our ALbwn-

blatter op. 124 (Example 6.17)? In this piece 1 superimposed three layers of mo-tion, none of which possesses obvious primacy. The 2-laycr (l=8th) that ispurportedly the metrical layer is in fact the least strongly articulated in the music.

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EXAMPLE 6.17. "Impromptu " op. 124 no. 9, mm. 1 — 4 and 8—12

It is difficult for listeners to come to a convincing metrical interpretation for thispiece; they will likely find themselves hovering deliciously and dreamily betweenmeters."26 Florestan nodded and added, "These dreamlike pieces of yours per-haps come closer to liberating music from the 'tyranny of meter' than my moreviolent and impassioned dissonant passages."

Eusebius haltingly continued, "Sometimes the metrical dissonances in ourinstrumental works symbolize insanity. Moritz Hauptmann, as I pointed out inEuphoma, associates meter — that is, metrical consonance—with health. Whatbetter means than metrical dissonance to represent ill health — a mind goneawry —than metrical dissonance? Insanity is a theme that has recurred in ourlives and in our music. Have we not always feared it? Have we not often felt itsshadow fall upon us?"27 Florestan nodded slowly and responded, "In 1840,when the struggle with Wieck loomed large on our horizon, I equated the giantin 'Es leuchtet Heine Liebe' with him. But now I identify the giant with the in-finitely more frightening black cloud that hovers over us, that stretches its mistytentacles out for us, that threatens to engulf us. . . ." They sat in brooding silencein the gathering dusk of the winter afternoon. Their room was now lit only bythe moon, which filtered through the shrub-enshrouded windows.

The door opened and Clara entered. "Robert, you were sorely missed at theTausches," she lied. He gazed at her and murmured, "When I am dead, the tale

will be ended." She came to him, stood before him, and embraced him. He leanedhis head against her breast, and thus they remained, motionless, in the shimmer-ing moonlight.

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Intermezzo 111

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Performing Metrical Dissonances

On a rainy morning in April 1854, Clara Schumann sat down at Robert's desk.A wave of depression seized her as her eye fell on his effects—the inkwell andpen from which had flowed such a wealth of music, the well-thumbed copyof Flegeljabre, the well-organized folders of his manuscripts. . . . With a sigh,she picked up his pen, took a sheet of paper from one of the drawers, and be-gan to answer a letter from her former student and friend Martha von Sa-binin, which had arrived early in February and had lain on the desk unan-swered ever since.'

She wrote:

Dear Martha,I must apologize for my long delay in responding to your letter, which ar-

rived at a very bad time — indeed the worst time. My poor Robert's health cameto a crisis in February. He had demanded for some time to be consigned to aninstitution, but I postponed that dire step until the dreadful day 'when he at-tempted to end his life. I have not seen him since he was taken away to Dr.Richarz's asylum at Endenich, and do not know when I shall be permitted to doso. He is very ill.

Only now that the horrid flurry of activity associated with his removal ispast am I again capable of attending to my correspondence. I particularly wel-come the opportunity to respond to your query about the execution of passagescontaining metrical conflict; my response will enable me to think about Robert'smusic and thereby to feel close to him.


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Robert was fascinated with metrical conflict — in fact, he spoke at length to

me on this subject shortly before the catastrophe — and conflicted passages oc-

cupy a prominent position in his works. You have, therefore, focused on one of

the most profound problems that faces performers of his music. There are two

broad issues that you must consider in preparing yourself to play such pas-

sages: first, metrical conflicts and their resolutions must be conveyed to the lis-tener in the clearest possible fashion; and second, not only the letter but also

the spirit of conflicted passages must be communicated. I can offer you a few

suggestions about each of these issues. My remarks refer specifically to Robert'spiano music, but they are to a large extent also relevant to works for other in-struments.

In order to play metrically conflicted passages properly, you must knowprecisely where they begin and where they end. Hence, you must take the time

to analyze with some care the work that you are preparing. Many metrical con-

flicts are obvious from Robert's scores; visual signals such as recurring accents

at points of the measure other than the downbeat, or ties and beams that persis-

tently cut across measure and beat boundaries, will alert you to the existence of

a conflict against the meter. Other conflicts are more concealed because theyare built into the melody and harmony of the work; these reveal themselves only

after careful listening.

You must discover not only where the conflicted passages are, but also howthey are constructed, that is, you must search out the various layers of which

they are composed. The following exercises will clarify for you the nature of the

components involved in a given conflict, and will at the same time tram yourfingers to negotiate them. If the passage involves the superposition of unequal

layers — superimposed triple and duple layers are particularly common in

Robert's music — begin by playing the layers separately, using the fingering that

you will need to use in the end. Then combine the layers while attempting to

preserve their individual character. In Robert's piano music, each hand gener-

ally plays one layer; in such cases this exercise is not difficult to perform. Some-times, however, Robert assigns more than one layer to one hand, as in the Trio

of the Scherzo in F Minor (see Example 8.18a), and in the first Trio from the

Scherzo of the Piano Sonata op. 11 (see Example 4.8c). At other times, a given

layer might be formed by a combination of events in both hands rather than

being localized within one hand. At the opening of the Presto in G Minor, for in-stance (which was the original finale for the Piano Sonata op. 22), a duple layerresults from the succession BI>-C-D in the left hand, each note occupying two

sixteenth-note pulses, but also from the dynamic accent on the third sixteenth-

note pulse in the right hand (see Example 2.6a). The separate practicing of lay-ers becomes more difficult when layers are scattered across the texture (and

across the two hands) in this manner, but it will clarify for you the role of eachfinger in conveying the metrical conflict within the passage. In passages con-taining three different layers, playing the layers in pairs is a useful exercise as

well. Playing all layers together will be much less difficult after these prelimi-

nary steps.

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Performing Metrical Dissonances 179

EXAMPLE 7.1. Metrical realignment of the opening of the finale of the Piano Sonata op. 14

Where conflicts result from equivalent but non-aligned layers — a secondtype of conflict that frequently occurs in Robert's works — it is helpful to re-shape the conflicted passage by aligning the layers. Play the passage in the re-vised form, and observe how its sound and its effect are altered. For example, atthe opening of the finale of the Sonata op. 14 (Example 7.1), increase the dura-tion of the notes marked sforzando to eighth notes and place them on the beats.Similarly, at the opening of Kreisleriana move the bass octaves and chords backone eighth-note pulse (Example 7.2). After playing your revised version, playthe actual passage again. This procedure will bring the character of the passageas Robert wrote it into focus for you.

Once you have discovered the metrical conflicts in a work, and completedthe preliminary familiarization exercises, you must consider how to render theconflicting layers audible. The meter of anything that you play, and particu-larly of any conflicted passage that you play, is to a large extent in your handj.

The placement of weight or stress, and the amount of stress that you allot to in-dividual notes or chords in such passages, will to a large extent determine howthe listener perceives the meter. You must decide, then, which layer or layersyou need to "bring out" by stress. Robert generally associates his "antimetrical"layers with accents of various kinds; hence it is rarely necessary for the per-former to stress these layers. Doing so might, in fact, render the conflict in-audible. It is frequently necessary, on the other hand, to apply subtle stressesto the metrical layers, particularly to the notated downbeats, when they arecontradicted. Sometimes, the downbeats are sufficiently accented within themusic, by virtue of register, density, harmonic change, etc., and thus require no

EXAMPLE 7.2. Metrical realignment of the opening of Kreisleriana

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EXAMPLE 7.3. "Walzer"op. 124no. 15, mm. 1-4

extra effort on the part of the performer. For example, in mm. 14—16 of theScherzo from op. 11, a passage in which a duple layer conflicts with the metri-cal triple layer, harmonic changes take place on the downbeats so that the met-rical layer is perfectly audible without any additional emphasis. In the initialtheme of the finale of the same sonata, on the other hand (Example 5.10), atthe beginning of the Scherzo movements of the Second String Quartet (Ex-ample 5.9b) and of the Piano Quintet, and in similar passages in which themetrical layer is musically highlighted in no obvious way, I would suggest avery slight stressing of the notated downbeats. Since in these passages all ac-cents within the score contradict those downbeats, only such subtle stress on

the downbeats will render audible the conflict that Robert's notation suggests.(I recall that Robert spoke about having eliminated antimetrical accents fromcertain passages so as to leave room for the performer to articulate the notated


The stresses on downbeats must always be subtle; strong stressing of all

downbeats would be intolerable! And there are cases where downbeat stresswould be entirely inappropriate. Among these are the Scherzo in FMinor, whichwas originally part of Robert's Concert sand orchestre (the Piano Sonata op. 14),

and the aforementioned Presto in GMinor. Both works are based on a constantand rapid alternation between passages that support, and passages that contra-dict, the notated meter. The breathless excitement within these works stemsprecisely from this alternation; they would lose much of their effectiveness if the

performer rendered the metrical layer audible at all times. It would at any ratebe virtually impossible, given the breakneck speed of these two works, for a

pianist to convey the antimetrical aspects of Robert's notation (accents andbeams) while also providing subtle downbeat stresses.

In some of Robert's works, the stressing of downbeats is impossible toranother reason: the notated downbeats are entirely suppressed for many suc-cessive measures, in the sense that no attack is associated with them. Amongsuch passages are the initial and final sections of the "Walzer," op. 124 no. 15(Example 7.3), and mm. 86-101 of the first movement of the Fcschingsschwank

aus Wien (Example 7.4a). In such passages, beats other than the notated down-beats easily usurp the role of downbeats, in which case an effect of metricalalignment or "consonance" arises. This must not be allowed to happen! If

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EXAMPLE 7.4A. Faschingsschwank aus Wien, first mvmt., mm. 86— 88

Robert had desired such an effect, he could easily have written the passages in

an aligned manner. I am convinced that he chose the more complex notation

because he wished the performer somehow to make audible the conflict that

was optically evident within the score. I know that Robert worked very hardto achieve the clearest possible visual representation of the sounds that he

heard in his mind or conjured up at the keyboard, and all of us will do well to

trust his notation. In connection with metrical issues, this means especially thatwe should not ignore his time signatures and bar lines, even if they are contra-

dicted by all aspects of the music.

How can such optical conflicts be communicated? In symphonic music,conductors assume a particular significance during such passages, for they dis-

play the notated meter to the audience and hence render the conflict in the score

visually if not aurally perceptible. (The famous passage from the finale of the

Piano Concerto is a good example!) Communicating such conflicts in noncon-

ducted music is somewhat more difficult, but not impossible. First, it is impor-

tant that you continue to feel the notated downbeats, even if you cannot articu-late them. Doing so will create a sense of tension and frustration within you,

which is bound to be transferred to the audience.3 A slight pressing downward

during suppressed downbeats, though it "will have no audible result, might assist

you in feeling the downbeats. Second, the notes and chords that articulate the

antimetrical layer must not be overstressed; overstressing would very quickly

lead the listener to hear those notes and chords as downbeats (particularly sincethey are already highlighted by various musical means.) Third, certain physical

signals can be employed to convey conflicts within passages in which only an-

timetrical layers are articulated. I have, for example, heard chamber musiciansand soloists inhale sharply but softly on some (not all!) suppressed downbeats.

As long as such breaths do not become overly obtrusive, I find them quite ap-propriate. A slight leaning forward during fully displaced passages might alsosuggest tension; leaning back and perceptibly relaxing would be appropriate at

the points where the displacement is resolved. But I should not like to prescribe

specific gestures; you must do what comes naturally to you. Performance wouldbe a sorry business if all players moved in precisely the same manner at givenpoints of a work!


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EXAMPLE 7.4B. The effect of deley at in. 86 of Faschingsschwank aus Wien, first mvmt.

A final remark regarding such fully displaced passages: it is important toavoid delay at their inceptions. Displacement depends upon placement, that is,on the positioning of accents in relation to the established metrical frame-work. If one waits even a moment too long when embarking on a displaced

passage, the displacement becomes distorted; the constituent layers (metricaland antimetrical) may even become confused, the displaced layer sounding-like a continuation of an established metrical layer. Here, for example, is howthe aforementioned portion of the Faschingsschwank would sound if the pianistwere to delay its beginning (Example 7.4b); the chords assume the function ofdownbeats, which is antithetical to the score.

Entirely different technical problems are posed by the execution of pas-sages containing more than two conflicting layers (which are quite common

in Robert's works). Such passages, not particularly problematic in ensemblemusic, become quite difficult when they are written for piano. Pianists will,however, after suitable practice, be able to articulate clearly the numerous lay-ers in Robert's passages of this type.4 Robert knew very well what he couldand what he could not demand of fellow pianists. Close inspection of hismany-layered passages generally reveals that he has facilitated the pianist's

task in particular ways. First, as I mentioned, he writes many layers clearlyinto the music, for example, by manipulating density, register, and duration.These layers take care of themselves; one need not worry about "bringingthem out" by added stresses, and can thus concentrate on those layers that do

require reinforcement. (The pianist must, of course, determine which layers do,and which do not, require stressing.) Second, when Robert wishes one hand toarticulate two layers, he generally separates those layers by register, so that theyare played, respectively, by the "lower" and "upper" parts of the hand. For ex-ample, in the aforementioned passage from the first Trio of the Scherzo fromop. 11 (Example 4.8c), two registrally distinct nonaligned triple layers areconveyed by the "lower" and "upper" parts of the right hand (the "lower"being the thumb and index finger, the "upper" being the remaining fingers).The same is true of the Trio of the Scherzo in F minor (Example 8.18), whereRobert assigns the metrical sextuple layer to the fifth finger of the left hand,the metrical triple layer to its "upper" fingers, and two registrally separatedduple layers to the corresponding parts of the right hand. Any accomplished

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pianist will be adept at such "split-hand" playing, which is a basic keyboardtechnique.

A piece that illustrates the pianistic challenges of multiple metrical layers isthe charming "Impromptu," op. 124 no. 9. It is important to recognize that thispiece is written in the style of a string quartet (Robert wrote it in 1838, when hewas beginning to explore the string quartet medium.)5 In the A sections (mm.1-8, 12-20, 24-32 — see Example 6.17a), a melodic motive is imitated betweenthe three "upper strings." Those "instruments" not stating the motive accom-pany it with reiterated syncopated pitches (the "cello" does so throughout thesesections). In the harmonically more mobile B sections (mm. 8—12 and 20—24 —see Example 6.17b), statements of the motive in the "viola" and "second violin"are answered by outward-moving scale passages culminating in registral anddynamic peaks.

This harmonically and formally uncomplicated piece is metrically of greatcomplexity; the score suggests at least four metrical layers. The metrical sextu-ple layer (l = the eighth note) is not only implied by the bar lines but is articu-lated by Robert's dynamic accents on downbeats. The syncopations in the ac-companying voices create an antimetrical duple layer. A triple layer emergesfrom registral and durational accents within the opening motive, and is rein-forced by registral and dynamic accents at the aforementioned peaks within theB sections. Finally, the three-four time signature suggests a duple layer alignedwith the metrical sextuple layer.

It might seem that two human hands could not possibly convey all of theselayers. But as I suggested earlier, it is not necessary to invest effort into bringingall of them out. The sextuple layer will be audible if the dynamic accents in theA sections are observed. The nonaligned duple layer, too, cannot fail to becomeaudible, as the syncopated attacks that create it continue almost uninterruptedthroughout the piece. The triple layer will emerge from registral and durationalaccents. The only layer, in fact, that the performer must actively reinforce is themetrical duple layer, which will otherwise be completely overshadowed by theantimetrical duple and triple layers. Again, the meter is in your hands. If youstress those notes of the opening motive that are already accented by registerand duration, the piece will sound as if it is in six-eight time (with a conflictingduple layer provided by the syncopated notes). If you overemphasize the syn-copated notes, they will sound like downbeats of a conflicted three-four meter(the three-eighth-note layer generating the conflict). Neither of these mannersof performance would do justice to Robert's notation. Only a subtle stressing ofthe quarter-note beats of his notated three-four meter will permit that meter —the result of the interaction of the sextuple layer and an aligned duple layer—tobecome audible.

Such stressing need not be maintained consistently throughout thepiece. It is vitally important at the beginning, so that the listener is "trained"to hear Robert's meter. Later in the piece, however, other layers could behighlighted. As in so many of his works, Robert allows us to play, and the lis-

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tener to hear, his most striking and lovely passages more than once. You havethe opportunity, then, to shape the meter differently when a passage returns— to allow the listener to hear it from a new perspective. You could, for in-

stance, give primacy to the metrical duple layer at the opening by applyingsubtle stresses on alternate notes of the motivic statements from the first noteof m. 1 onward. At m. 12, where the opening music returns, you could give

slightly more weight to the triple layer, thus making the listener wonderwhether the piece might not be in six-eight time after all. In the final A section,the initial manner of execution should return, so that the meter that Robertnotated retains the greatest overall prominence. The result of such a flexibleperformance would be a certain amount of confusion for the listener. In someworks, confusion should create a sense of tension and frustration. In this "Im-promptu," however, the confusion should be delightfully intriguing rather thanoppressive.6

I move on to my second major point. It is not enough to convey the letter

of metrical conflicts; you must also attempt to penetrate and to communicatetheir spirit, that is, their meaning. To a certain extent I have already ad-dressed this issue by referring to tension and relaxation, confusion and am-

biguity. Metrical conflict almost invariably results in an increase in tensionwithin the music, and that is an important aspect of its meaning. Such con-flict can arouse a sensation of almost physical discomfort in the performer

and listener, partly because of the coming apart or going awry of layers ofmotion that were previously aligned, partly because of the ambiguity andconfision that it generates. Metrical realignment, on the other hand, createsa sense of relaxation, of security, of homecoming. Learn to feel the waves oftension and relaxation that Robert creates so skillfully in his works. Listenfor subtle hints at coming tensions, in the form of isolated accents that con-

tradict the meter; for the full fruition of the foreshadowed tensions; and, fi-nally, for their dispersal. If you feel these waves, your listeners will likely feelthem as well. Again, I must stress the importance of analysis; if you do not

know where the metrical conflicts are, from the smallest hints to the broadestconflicted expanses, you will not be able to feel and to convey the tensionthat appertains to them. You might wish to prepare a diagram of the metricalstructure, a kind of "metrical map," as an aid in tracing the curves of tension

and relaxation.You might find it easier to perform metrical conflicts in a meaningful man-

ner if you allow the rise and fall of tension associated with them to suggest toyou a specific narrative, an image, or an emotional state (or a succession ofthese). Robert certainly associated metrical conflict with particular emotional ormental states, as is amply demonstrated in his songs. In his instrumental music,too, we should think about what he might have intended to convey by in-dividual conflicted passages. You cannot, even I cannot know precisely whatmeaning a given metrical conflict had for Robert, and we might well arrive atinterpretations that diverge from his own. No matter; a performance that con-vincingly suggests a certain narrative, image, or emotional state, even if they

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differ from those that the composer had in mind, will always be more moving

and compelling than a cold, detached performance.

The "Impromptu" that I mentioned earlier, with its continuous and com-

plex, yet languid motion, suggests to me the following image: a bough sus-

pended in a stream, its many leaves waving gently in the current. Robert told

me that he used to spend hours staring at such boughs while lying on the river-

banks around Zwickau. Although I have no idea whether he had this image in

mind when writing the piece, the image helps me to achieve the "tender execu-

tion" that Robert demands, and prevents the metrical confusion from generat-

ing a tension that is certainly inappropriate.

The images and narratives that Robert's more Florestanian conflicted pas-

sages suggest to me are quite different. Lately, understandably, the narratives

that occur to me often have to do with Robert's present state. I give you one ex-

ample: the finale of the Piano Sonata op. 14. The initial theme suggests to me

the discourse of an individual on the verge of a breakdown. He painfully,

breathlessly attempts to whisper into the ear of his beloved the thoughts that

chase each other at breakneck speed through his mind. At m. 6, he cries out in

frustration and pauses to catch his breath, then continues his incoherent mur-

murings. At m. 15 (where the metrical layer begins to assert itself), the beloved

attempts to quiet him, and succeeds to a certain extent; the poor man's babble

does not cease, but becomes less agonized and breathless.

Most of the rest of the movement alternates between states of pronounced

and more subdued panic (in metrical terms, states of very obvious and less ob-

vious displacement). One moment stands out for me as a very special one. Mea-

sures 176-77, which lie between a restatement of the frustrated outcry first

heard at m. 6 and a resumption of the mad, misaligned, murmuring sixteenth

notes, are in themselves entirely without metrical conflict; the two hands sud-

denly line up and collaborate in an almost comically simple cadential gesture.

These measures are like a gleam of good humor shining through brooding

clouds of despair. Such moments in Robert's music remind me so much of him

as he has been during the last few years. In the midst of some disquieting, even

terrifying monologue, he blurts out a remark reminiscent of the old, healthy

Robert – some ingratiating, witty epigram that, however, elicits not laughter but

tears. So it is with this passage.

The conclusion of the movement represents to me the overcoming, at least

temporarily, of madness and terror. The offbeat accents disappear at the final

cadence (mm. 350 — 51), and the final measures involve coordinated arpeggia-

tion in the two hands, a gesture unprecedented in the movement. The shift to

the major mode, of course, contributes significantly to the new, more positiveemotional state.

That is my story for this finale. I would not wish to impose it on anybody

else; some other narrative might work equally well. I cannot imagine, however,

that one could play this movement without having in mind an image relating to

feverish, frenetic mental or physical activity.

Writing this letter has, as I anticipated, enabled me to feel close to him who

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is far away. And the remembering of his music has given me hope that perhapshis mind shall, like the meter at the end of op. 14, return to a healthy state. Ihope that all is well with you, and I look forward to remaining in communica-tion with you.

With many friendly greetings,Clara Schumann

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When the caretaker left, Florestan flung the tray of food that he had brought outof the window, narrowly missing one of the gardeners, then stared, trembling, atthe woods and fields of Endenich. There had just been a rather violent con-

frontation with the caretaker, whose attempts to calm him, assisted by Eusebius,had been without avail. Florestan was silent now only because his prolonged

screaming had exhausted his vocal cords. Shrieks continued to bubble up withinhim, and when Eusebius came up behind him and put his hand on his shoulder,one of them burst from him as a hoarse moan. Eusebius drew him away from the

window with a pitying sigh and succeeded in settling him on the sofa. He satdown beside him and drew his attention to the manuscript that he held in hishand. "Look, Florestan, what I have found at the bottom of my trunk!" he said.

"There is still one chapter that we have not read. It promises to be diverting; itstitle and subtitles allude to several of our compositions." Florestan made no re-sponse, but sat quietly as Eusebius began to read to him.1


The music of Hector Berlioz is by no means as replete with metrical dissonanceas that of Schumann. Whereas Jacques Barzun ranks Berlioz as one of thegreat rhythmic innovators of the nineteenth century, the novelty of his rhythmsseems to be based more on irregularity, both at low and high levels, rather thanon the interaction of nonaligned regular layers of motion.2 Nevertheless, Berliozwas capable of employing such interactions with great finesse. The beginning of"Scene aux champs" from the Symphonic, fantastique (which Schumann cites in


luisa balaguer

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his famous review of that work) is a good example.3 The movement begins withthe displacement dissonance D3+1 (l=8th); most of the durational, registral,and dynamic accents in the initial woodwind dialogue are one eighth note re-moved from the nofated strong beats. This dissonance is not perceptible at firstbecause the metrical layers are not yet established. Durational accents in mm. 2,

4, 6, 8, and 9, however, begin to suggest the metrical 3-layer. The entry of the vi-olas on the downbeat of m. 11, very soft though it is, contributes its mite to theestablishment of the metrical 3- and 6-layers. Thereafter, new-event harmonicand dynamic accents in the violas reinforce the metrical 6-layer, while dynamicaccents in the woodwinds continue the antimetrical 3-layer. The initial sublim-inal dissonance thus gradually surfaces as the initial section of the movement

unfolds. The dissonance resolves as the next section begins in m. 20, to be re-called only by occasional durational and dynamic accents on the second eighthnotes of measures (for example in mm. 22 and 35).

The metrical structure of the second movement of the Symphonic fantastique isalso worth investigating. A short summary addressing the questions listed in chap-ter 2 is followed by a discussion of the most salient metrical features and processes

of the movement. (It is impossible to mention all interesting metrical features.) Thesame format is used for all analyses of complete works within this chapter.


\. Main recurring dissonances: G6/4, D6+2, and D6+4 (1 = 16th).

Families of dissonances operative in the movement: "G6/4."Recurring juxtapositions or superpositions: G6/4 and the diminutionG1/.67.

4. Proportion of primarily consonant and primarily dissonant passages:mostly consonant with brief incursions of dissonance, especially at ca-dences and in the coda.

5. Amount of subliminal dissonance: there are numerous instances of sub-liminal G6/4, brief enough that the metrical 6-layer can be maintained by

the listener.6. Frequency of change of metrical state: generally infrequent change, with

greater frequency in the coda (for added excitement).7. Basic metrical narrative: preparation of two main dissonances in the in-

troduction followed by their development.

It is the latter point that I wish to discuss at some length. The movementopens in a metrical haze (Example The barely audible initial tremolo isnoncommittal with regard to meter, and the following cello and bass arpeggia-tion continues the metrical ambiguity. Whereas Berlioz's placement of the firsttwo statements of the tonic note within the arpeggiation supports the notatedmeter, the dynamic and registral accent on C in m. 4 suggests two distinct dis-sonances against the metrical 6-layer (1 = 16th). The hint at the displacement dis-sonance D6+2 is obvious. In addition, the accentuation of C hints at a parti-tioning of the arpeggiation into pairs of eighth notes, and hence at a 4-laycr and



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EXAMPLE 8.1. G6/4 in "Un bal" from Berlioz's Symphonic fantastique

G6/4. The same hints recur in mm. 7-8, 13-14, and, more weakly because of

the lack of a sforzando, in mm. 17—18.Within the final cadence of the introduction (mm. 30—31—Example 8.1b),

G6/4 assumes greater prominence: the arpeggios of the second harp divide into

pairs of triplets on the basis of pattern repetition, creating a 4-layer, while the

metrical 6-layer is articulated by the solid chords of the first harp.

Later in the movement, Berlioz maintains the association of G6/4 with ca-dential passages. At mm. 78—84 (Example 8.1c), where a cadential dominant isprolonged, the first violins' sixteenth notes are grouped into fours by contour,the leaps functioning as dividers. Dynamic accents in the winds, meanwhile,continue the metrical 6-layer. During the cadential portion of the central idee fixe

statement (mm. 152—55), the melodic new-event accents in the flutes and clar-

inets create a 4-layer while the 6-layer is subliminally maintained. A similar sub-liminal dissonance is found at the prolonged dominant immediately precedingthe return of the A section (mm. 171—73). The coda, an expanded cadence to

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EXAMPLE 8.2. G3/2 in "Un bal"

the movement as a whole, opens with G6/4 (mm. 256-63 — Example 8. Id); theviolins establish a 4-layer by durational accents (eighth notes) and by pattern

repetition, while the metrical 6-layer continues subliminally. At the climactic ca-

dential six-four chord at mm. 298-301, Berlioz creates a link to an earlier verysimilar event, namely to mm. 30a—31 (Example 8.1b), by again giving repeated

groups of six triplet sixteenths (forming a 4-layer in terms of the nontriplet six-

teenth-note unit) to the harps. The flutes reinforce that layer with a repeating

four-sixteenth-note pattern. Meanwhile, the 6-layer is subliminally maintained

in mm. 298-99 and, in mm. 300-301, explicitly expressed by new-event melodic

accents in the strings. One more cadential passage involving G6/4 initiates the

rush toward the conclusion (mm. 320—25); the metrical layer is again sublimi-

nal, and the 4-layer results from new-event melodic and harmonic accents in the

flute, oboe, first violin, harp, cello, and bass parts.4

Aside from these literal usages of the grouping dissonance suggested during

the introduction, Berlioz uses two diminutions. The diminution G3/2 occurs par-

ticularly frequently. The mam theme of the movement, whose accompanimentdelineates a 2-layer, hints intermittently at a 3-layer; in the first violin part in mm.

40-41, 45, 49 (and in corresponding later measures), the measure's six sixteenth

notes divide on the basis of melodic contour into two groups of three. The 3-layer is particularly clear in the precadential measures (45 and 53) because a rel-

atively large central leap (a fourth) creates a registral accent on the fourth six-

teenth note, and because a three-sixteenth-note chromatic neighbor-note pattern

is repeated. During the coda, Berlioz expands upon the specific instances of

G3/2 that are characteristic of the opening theme. In the melody of mm. 288-90

and 293, for instance (Example 8.2), he repeatedly uses reiterated neighboring-figures separated by leaps to create a 3-layer, while the accompaniment persists

in its eighth-note "oom-pah-pah" pattern. Similar passages are found in mm.

340-42 and 348-50; slurred three-note figures separated by leaps establish a 3-layer in the melodic voices, while the accompanying voices (harps) articulate the

metrical 2-layer. These allusions to specific versions of G3/2 from the main theme

contribute immensely to the coda's success as a summary of the movement.Further diminution of G6/4 (G1/.67) occurs in the second harp part at mm.

30-31 (Example 8.1 b), between the first violins and all of her instruments at m.

61, between the harp and the strings during the restatement of the main themeat mm. 183-86, and intermittently, then steadily during the coda (from m. 258

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EXAMPLE 8.3. G6/4 and its double diminution in "Un bal" (mm. 298-99)

onward). The combination during the cadence at mm. 298—301 of G6/4 with itsdouble diminution contributes significantly to the excitement of the moment(Example 8.3).

The displacement dissonance suggested during the initial measures of themovement, D6+2, begins to play a role in mm. 107—13, where density accents(harp and string chords) occur intermittently on the second eighth notes ofmeasures. The antimetrical 6-layer arises from curtailment of a metricallyaligned "oom-pah-pah" pattern, split in mm. 94—105 among the strings, harps,and winds, respectively. Deletion of the winds' final "pah" after m. 105 turns thesecond-beat "pah" of the harps into a durational accent. At mm. 233-45 and248-51, Berlioz employs D6+2 during a statement of the opening theme, albeitrelatively weakly: registral accents and, in m. 245, a dynamic accent in thestring parts emphasize the second beats.5 More intense statements of D6+2occur within the coda; in mm. 265-68 (Example 8.4a) and the correspondingmm. 281-84, there are dynamic and/or density accents on the second beats,while the harmonic rhythm and durational accents maintain the metrical layer.

EXAMPLE 8.4. D6+2 in the coda of "Un bal"

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In mm. 331-33 (Example 8.4b), dynamic accents again appear on the secondbeats, while downbeat statements of the principal harmony of the passage (16)enable the metrical layer to remain in effect. Thus is this fine "Valse francaise"permeated by the metrical dissonances introduced at its opening.

Florestan, much calmer now, said, albeit still hoarsely, "Hector was a re-markable composer. It was good to see him in Euphonia." Eusebius agreed, thensaid, "I see that the next section of the chapter discusses one of our early works,the Intermezzi op. 4." He read:



1. Main recurring dissonances: D6+2 and G6/4 (l=8th).2. Families of dissonances operative in the work: D6 — all members; Dx+2

(D12+2, D6+2, D3+2); "G6/4."3. Recurring juxtapositions or superpositions: D6+2 and D2 + 1; D6+2 and

G6/4.4. Proportion of primarily consonant and primarily dissonant passages:

mostly dissonant with brief incursions of consonance, except in no. 4,where the opposite is true.

5. Amount of subliminal dissonance: much subliminal G674.6. Frequency of change of metrical state: frequent change in no. 1 (every

4—6 measures); less frequent in nos. 2—4; quite frequent in nos. 5 — 6(though not as frequent as in no. 1).

7. Basic metrical narrative: no single narrative, but many interesting subplots.D6+2 undergoes many adventures, sometimes in the company or G6/4 orD2+1. G6/4 is subjected to several diminutions. Ever closer associations be-

tween the two basic classes of dissonance culminate at striking passages atmm. 109 and 129 in the fifth intermezzo, and mm. 113-14 in the sixth.

If we look up the term "intermezzo" in any reputable musical dictionary,we find that "nineteenth-century piano piece" is the most recent of its variousmeanings. In the seventeenth century, an intermezzo (or intermedio) was a mu-sicodramatic entertainment involving masks and dancing that took place be-tween the acts of a larger production, and in the eighteenth century, intermezziwere comical plays. Whereas it is not certain that Schumann was familiar withthese early meanings of the term, his Intermezzi op. 4 have, with respect to met-rical structure, something of the atmosphere of a theatrical spectacle featuring acolorful array of metrical "characters." The main dramatis personae are intro-duced early in the cycle and subsequently undergo a variety of adventures,

alone or in interaction with of her characters.The metrical protagonist of the Intermezzi D6+2 (1 =8th); he appears more

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EXAMPLE 8.5. D6+2 in Robert Schumanns Intermezzo op. 4 no. 1

frequently than any of her player, in a wide variety of guises. In mm. 3—6 of the

first intermezzo (Example 8.5a), D6+2 introduces himself in the role of a

pedantic old schoolmaster, speaking in stentorian tones. He declaims in the

same vein in mm. 17—18, 37-40, and corresponding later measures. In mm.

14-15 (Example 8.5b), 43-48, and 57-60, he reveals a gentler aspect of his

character (the antimetrical layer is created by durational rather than dynamic

accents, and the "schoolmasterly" imitation is abandoned).Throughout this intermezzo, related characters cluster round D6+2 and at

times push him into the background. Among these are his little cousin D2+1

(mm. 12 — Example 8.6a, and 45-48 — Example 8.6b); his brothers D6+3 (inthe passage in Example 8.6b, D6+3 definitely overshadows D6+2) and D6+4

(mm. 24-26);6 and his loose relative D12+2 (mm. 27-32 and corresponding

later measures, where dynamic accents appear on second beats of alternate

measures). A mysterious, masked stranger also appears briefly, namely sublim-

inal G6/4 (in mm. 20—23 — Example 8.6c—the metrical layer is submerged and

dynamic accents occur on alternate beats, the latter accentuation resulting from

a stretto treatment of the motive first associated with D6+2, shown in Example

8.5a). The close juxtaposition of G6/4 and D6+2 in mm. 17—21 foreshadows

later even closer interactions of the two characters. A daughter of G6/4, namely

G3/2, makes a brief entrance with D6+2 (and D6+3) in mm. 45—48 (Example8.6b); the dynamic accents on the fourth eighth-note pulse result in a hint at a

3-layer and hence at G3/2. This passage presages a more intimate association ofD6+2 and G3/2 in a later intermezzo.

The second intermezzo provides a complete change of scene (a new meterand a faster tempo). Two new metrical characters replace those of the first in-

termezzo and romp around on the rearranged stage, namely D3+2 and his loose

cousin D6+5. The former is present in mm. 2-3 (Example 8.7), 18, etc. The hit-ter is generally a faithful companion of D3+2 but also makes some independent

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EXAMPLE 8.6. "Minor characters " in op. 4 no. I

EXAMPLES 8.7. D3+2 and D6+5 in op. 4no. 2

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appearances (in mm. 4-5, 9-12, etc.). These new characters are related tothose of the first piece; D6+5 is yet another sibling, and D3+2 a tight cousin ofthe protagonist D6+2.7 The characters abruptly disappear as the scene changes

(at the two-four section superscribed "Meine Ruh ist hin"). Here, D4+1 timidlyshows himself (created by density accents in mm. 64-67 and related measures),and his tight cousin D2+1, who had already appeared during the first inter-mezzo, makes a brief appearance as well (mm. 97-100). As the initial stage-setof this intermezzo is restored (Tempo I), D2+1 exits, and D6+5 and D3+2 bois-terously return at in. 105 and remain on stage almost constantly until they be-take themselves off just before the end.

In the third intermezzo Schumann brings back the initial metrical scene(three-four time). The characters of the first piece also return, and some of themare developed in interesting ways. The mysterious G6/4, for example, throws

off his mask and, now clearly recognizable, plays a major role within the A sec-tions, as in mm. 1-15 (see Example 8.8), 19-24, 27-34, and 49-56. The 4-layerfrequently arises from repetition of a rhythmic pattern, and at times from dy-namic accents (mm. 7-9) and slurring (mm. 13—15), whereas the metrical 6-layeris established by significant harmonic changes (for example, tonic-dominant al-

ternation in mm. 3—6). D12+8, a loose cousin of the protagonist D6+2, makes abrief appearance in this section (mm. 4—6), and D6+2 himself, revealing a newjovial side of his character, is on stage throughout mm. 11—48, where dynamicaccents frequently occur on second beats. As was mentioned, G6/4 is also pres-

ent in much of this section; these two characters, who had a brief encounternear the opening of the first intermezzo, now form a closer liaison. In mm. 35-

48, D12+4, a loose relative of D6+2's brother D6+4, heralds the latter charac-

ter's personal appearance within the "Alternative" (note the antimetrical slursand dynamic accents in mm. 57—64).

The metrical scene of the fourth intermezzo is very similar to that of thesecond (twelve-eight rather than six-eight meter). Its outer sections do notcarry the metrical drama forward; much of the intermezzo is a pastoral songthat stands outside the main metrical action.8 In the central section, however(mm. 8-10—Example 2.1), there appears D3+1.5, son of D6+3 (one of theminor characters of the first intermezzo), in the company of G1.5/1, grandson ofG6/4 (isolation of three-sixteenth-note groups within the aforementioned

Carnaval des analyses 195

EXAMPLE 8.8. G6M in op. 4no. 3

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196 Fantasy Pieces

EXAMPLE 8.9. Metrical dissonance in op. 4 no. 5

D3+1.5 results in a superposition of two- and three-sixteenth-note groups, and

hence in a double diminution of G6/4).The fifth intermezzo, reverting to the scene of the first and third inter-

mezzi, more significantly advances the metrical action, numerous familiar char-

acters being associated in new ways. D2 + 1, D6+2, and D6+4 engage in danceensembles in mm. 6-8 (Example 8.9a), 50-52, and 141-43, and D6+2 and

D2 + 1 each dance pas seules at various points— D6+2 in mm. 20-25, 65–66,9 andlater corresponding measures (Example 5.13); D2+1, with particular energy, in

mm. 37-40 (Example 8.9b) and the corresponding mm. 174-77.At mm. 109-12, there is another close encounter between the G and D

clans. The former clan is represented by G3/2, daughter of G6/4. This frolic-

some maiden dances vigorously across the stage in masked (subliminal) form inmm. 32-34, and coyly begins to remove her mask wi th in the "Alternative"

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Carnaval des analyses 197

EXAMPLE 8.10. D6+1 and other dissonances in op. 4 no. 5

melody (which includes a weakly stated 3-layer as well as a clear 2-layer — mm.

70—76). At in. 109 (Example 8.9c), she fully reveals her identity (the 3-layer is

clearly expressed in the dotted-quarter durations of the rising inner-voice

melody) and dances briefly with the protagonist D6+2 and his brother D6+5.

But when her father, G6/4, appears at mm. 116—18 (he is masked — the 4-layeris expressed by harmonic pattern repetition while the 6-layer is not articulated),

D6+2 and D6+5 scurry off and G3/2, too, demurely begins to retreat (G3/2 is

again weak in mm. 119—26).

Moments later, however, G3/2 reappears in the arms of another of D6+2's

brothers, namely D6+1. D6+1, the only member of the "D6" family who had not

appeared in the first four intermezzi, is first introduced in mm. 41—44 of thefifth (Example 8.10a) as a somewhat unstable individual; at mm. 43-44, he al-

most transforms himself into G6/5 (the five-eighth-note pitch succession C—Dl —

E — G — B t is reiterated to form a 5-layer, but the sforzando on the second eighthnote of in. 44 prevents D6+1 from disappearing entirely). This Protean char-

acter dances with G3/2 at mm. 129-31 (Example 8.10b); these measures fea-ture not only G3/2 but also D3+1 and D6+1 (the 3-layer, and the 6-layer em-

bedded in it, does not begin on a metrical downbeat, as in all of the earlierstatements of G3/2, but one eighth note thereafter). Once again, G3/2's father,

G6/4, appears and decisively puts an end to his flighty daughter's entanglement(mm. 133-34).

The sixth intermezzo draws a number of familiar characters together for asplendid finale. D6+2 plays a prominent role within the A sections, in whichmany second beats are dynamically and durationally accented (see Example

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198 fantasy Pieces

EXAMPLE 8.11. Metrical dissonance in op, 4 no. 6

8.11, and mm. 12—16, 39—41, and later corresponding measures). His brother

D6+4 appears in mm. 3-4, 39-40, 55-56, 59, 71, and 75. In the first two ofthese passages, the two brothers tread the measure together (although D6+2

diinces with greater energy), recalling the opening of the filth piece. D6+2's lit-

tle cousin D2+1, who already played a role within the first, second, and fifth in-termezzos, is prominent within the "Alternative" (especially at mm. 58—60 and

62 — 68 and later similar passages, with their offbeat density and durational ac-

cents) . G6/4 appears, masked, at various points, beginning with the first mea-sures (Example 8.11). The third beat of in. 1 is identical to the first; the incipi-

ent pattern repetition results in the initiation of a 4-layer. The tour duplet eighth

notes at the end of in. 2 create a third pulse of the 4-layer. The metrical 6-layer,

meanwhile, keeps a low profile until in. 3. At mm. 8b-10, a reiterated melodic

sigh creates a 4-layer, again in the absence of clear articulation of the metrical 6-

layer. In mm. 24—25, a repeated harmonic pattern reawakens the 4-layer, the 6-layer again becoming dormant. Further appearances of G6/4, mostly masked,

occur at the beginning of the "Alternative" and at mm. 76—85.We are granted only one tantalizing glimpse of the lovely G3/2 in the final in-

termezzo: in in. 72, a melody whose contour expresses a 3-layer (G5-A5-B5-E5-

FS5-G5) is superimposed on a continuing 2-layer. At mm. 5-6 (Example 8.11)

and 98—99, however, there appear new generations of descendants of G6/4; in theformer measures, one of these arises from the superposition of triplet and non-

triplet eighth notes, and in the latter measures, another emerges from the group-

ing of triplet eighth notes into twos by the repetition of a falling octave pattern.10

An interesting twist in the metrical drama takes place close to the end.Measures 113-14 are a varied repetition of mm. 20-21 and, as in those earlier

measures, G6/4 is present (albeit masked). In addition, however, Schumannplaces dynamic accents on the second members of alternate triplet groups, thus

creating a diminution of the protagonist D6+2, and therewith bringing the G

and D clans together once more.Schumann's Intermezzi op. 4 represent a major advance over his earlier

works in terms of the pervasive and cohesive use of metrical dissonance. Per-

haps it is in this context that we can understand the numerous quotations from

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Carnaval des analyses 199

his earlier works (mentioned by numerous earlier authors): aside from theaforementioned quotations of "Hirtenknabe," Schumann alludes to the PianoQuartet in C Minor (in the fourth intermezzo, mm. 1, 6, 7-10, and 15—18), andto the "Abegg" Variations (in the sixth intermezzo, mm. 43-45 and 127-31).Although both of those works constitute important stages in Schumann's met-rical odyssey, dissonance is there not nearly as pervasively and interestinglyemployed as in op. 4. Schumann appears to be taking stock of his progressas a composer and saying to himself and to his audience, "I've come a longway."

Eusebius covertly glanced at Florestan, who had shown signs of agitation atthe mention of the words "Meine Ruh ist hin." "Look, Florestan," he said sooth-ingly, "the next section discusses the music of Chopin." At the sound of thatname, Florestan repeatedly put his hand to his head and gazed worriedly aboutthe room. Eusebius gently asked, "What is the matter, Florestan?" Florestanmumbled, "Where is my hat? I need my hat." With some difficulty, Eusebiuspacified him, and read on:


Whereas metrical dissonance is not a hallmark of Chopin's style, his music con-tains numerous examples of metrical and hypermetrical dissonance.11 Chopin'sfiguration owes much of its sparkling charm to metrical conflict. I offer only afew examples, extracted from the scherzos and etudes. In the Second Scherzo,some of the ornamented arpeggio figures that cascade up and down the key-board are based on reiterated four-eighth-note segments, which create G6/4 inrelation to the metrical 6-layer (l=8th). This dissonance is already suggested inthe first arpeggiating figure in the work (mm. 49-52 — Example 8.12a); theeighth notes within the dramatic downward arpeggiation of the Dt major triadform groups of four (although there are not enough of these groups to establishG6/4 securely). The delicate arabesque outlining the dominant of C# minor inmm. 307-9 (Example 8.12b) more clearly exhibits the quadruple grouping andhence the dissonance G6/4, as do the ornamented E major arpeggiations of mm.358-64 (Example 8.12c) and the climactic descending arpeggiation of V of Btin mm. 540-43 (Example 8.12d). The diminution of G6/4, G3/2, is also featuredwithin some of the figuration, namely at the end of the Scherzo section (mm.118—29 —Example 8.12e). The contour of these figures establishes a 3-layer,conflicting with the 2-layer that reigned in the foregoing measures and that herecontinues to be conveyed by the left hand.

In the Third Scherzo, the shimmering descending eighth-note figureswithin the Trio involve hand shifts at four-eighth-note intervals, and the left-hand figure segments into four-eighth-note groups on the basis of pattern rep-etition, resulting, along with the metrical 6-layer, in G6/4. In the Fourth Scherzo,pattern repetition in the right hand of mm. 69-71 (DS-C#-A-E) results in four-

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200 Fantasy Pieces

EXAMPLE 8.12. G6/4 and G3/2 in Chopin's Scherzo op. 31

eighth-note groups that conflict with the established metrical 6-layer. The cli-

mactic cascade at mm. 122-27 similarly divides into four-eighth-note groups,this time on the basis of a repeated contour rather than a repeated pitch pattern,resulting, in interaction with the metrical 6-layer, in subliminal and indirect

G6/4 (l=8th).Some of Chopin's etudes explore intriguing low-level dissonant relation-

ships. At the opening of the second etude from op. 25, for instance (Example8.13), the 2-layer (l=triplet 8th) established by left-hand quarter-note triplets isdissonant against the 3-layer formed by the right hand's reiterations of C5. Fre-

quently, the 2-layer invades the right-hand part, so that it dominates the texture

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CarnavaI des analyses 201

EXAMPLE 8.13. Metrical dissonance in Chopin's Etude op. 25 no. 2

and G3/2 is submerged. In in. 3, for example, reiterations of E5, then Bt5 occuron alternate triplet pulses in the right hand, together with the left-hand quarter-note triplets. (The pianist can, of course, continue to articulate the 3-layer dur-ing such passages, so that the dissonance becomes perceptible to listeners.)

The fifth etude of op. 25 begins with displacement dissonance (Example8.14a), and the first part of the B section continues that dissonance (althoughthe displacement index grows from a sixteenth note to a triplet — Example8.14b). The second statement of the B material (mm. 81-97 —Example 8.14c),however, is based on a scintillating grouping dissonance. The right-hand arpeg-giations are composed of single notes and dyads, the dyads occurring on everythird sixteenth-note pulse. The 3-layer (l = 16th) created by these density ac-cents conflicts with the 4-layer established by the beautiful "tenor" melody. Theresulting dissonance (G4/3) casts a delightful sheen over the passage. At times,for example in mm. 82 and 84, the right hand's 3-layer encroaches on the left-hand melody; in these measures the final note of the melody (the resolution ofthe first-beat suspension) is surprisingly postponed, so that the measure endswith a three-sixteenth-note pulse (not aligned with the right hand's 3-layer) in-stead of the expected quarter-note pulse.

EXAMPLE 8.14. Metrical Dissonance in Chopin's Etude op. 25 no. 5

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202 Fantasy Pieces

EXAMPLE 8.15. G3/2 and its resolution in Chopin's Mazurka op. 17no. I

Chopin's metrical dissonances are by no means restricted to his figuration.

His dance pieces are rich in brief, yet striking examples that do not involve fig-

uration. The earliest mazurkas contain much displacement dissonance pro-duced by dynamic accentuation of metrically weak beats, sometimes D3+1

(l=quarter), as in op. 6 no. 2, mm. 1—4, sometimes D3+2 (for example, in op. 6no. 1, mm. 4-7), sometimes both in juxtaposition (op. 6 no. 4, mm. 1 — 8). Such

antimetrical accentuation is, of course, typical of the mazurka.

A particularly interesting example of grouping dissonance occurs in the Bsection of the Mazurka op. 17 no. 1 (Example 8.15). In mm. 41-50 and 53-58,

the left hand consists of an "oom-pah" pattern that forms a 2-layer dissonant

against the right-hand melody (in which a 3-layer is formed by varied repetition

of a rhythmic pattern). As the phrase ends approach (mm. 52 and 60), Chopin

expands the left hand's "oom-pah" pattern to "oom-pah-pah," thus creating the

potential for resolution into the primary consonance. At the first phrase ending,

however (mm. 51—52 — Example 8.15a), the right hand refuses to collaborate inthe resolution; instead of continuing its 3-layer, it lapses into repetition of therhythm "quarter-eighth-eighth," thus taking over the 2-layer previously articu-lated by the left hand. This "layer exchange" subverts metrical resolution at this

phrase ending. At the next phrase boundary, on the of her hand (mm. 59—60 —Example 8.15b), the right hand does maintain its 3-layer and joins the left handin a definitive metrical resolution. The earlier evasion of metrical resolutionmakes the resolution at the end of the B section all the more satisfying. In sum,

although Chopin employs metrical dissonance more sparingly than Schumann,

he does so with skill and subtlety.

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Carnaval des analyses 203

Eusebius noticed that Florestan had fallen asleep. He left him to his slumber

and continued reading silently:



1. Main recurring dissonances: D6+5 and D3+2 (l=8th) in the Scherzo,G3/2 and D2+1 in the Trio.

2. Families of dissonances operative in the movement: D6+5 and the tighterrelative D3+2.

3. Recurring juxtapositions or superpositions: aside from the trivial super-position of the above related displacement dissonances, none.

4. Proportion of primarily consonant and primarily dissonant passages:mostly dissonant.

5. Amount of subliminal dissonance: much subliminal dissonance in theScherzo sections, very little in the Trio.

6. Frequency of change of metrical state: very frequent in the Scherzo (forthe most part, every two or three measures), infrequent in the Trio (onlythree significant changes over 47 measures).

7. Basic metrical narrative: in the Scherzo section, a metrical and an anti-metrical placement of 6/3 consonance vie for supremacy, the formerplacement being victorious in the end. The Trio provides contrast byclearly articulating the metrical layer throughout and by presenting rel-atively weak dissonances. The narrative of the movement as a whole isthus a variant of "D-C-D"; the middle section is not fully consonant, butmuch more weakly dissonant than the outer sections.

Schumann composed his original version of the Piano Sonata op. 14, enti-tled Concert sans orchestre, in 1835-36. It was to be a five-movement work withtwo Scherzos. Apparently at the request of the publisher, he excised one of theScherzos, which Brahms published in 1866 along with the abandoned finale tothe Piano Sonata op. 22.12 The decision to excise the movement was probably awise one, for, as Anton Kuerti points out, it would have resulted in a potentiallytedious succession of three F-minor movements.13 In the revised sonata, onlytwo F-minor movements—the last two — occur in a row.

I imagine that Schumann excised the movement only reluctantly, for itwould have created interesting metrical relationships within the sonata. A vari-ant of its most prevalent dissonance, D3+2 (l=8th), for example, plays a signif-icant role in the remaining Scherzo, where the augmentation D6+4 appears atthe opening and at various of her points (for example, mm. 16-18 and 35—38).A diminution of one of the dissonances of the Trio of the excised movement,D2 + 1, underlies the third variation of the slow movement. Aside from thesecontributions to the unity of the sonata, however, the excised Scherzo is an ex-

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204 Fantasy Pieces

EXAMPLE 8.16. Indirect D3+2 and D6+5 in Robert Schmann's Scherzo in F minor

tremely interesting and beautiful piece, which Schumann could not have dis-

carded without much soul-searching.At the opening (Example 8.16), a 3-layer established by changes of har-

mony, and a 6-layer formed by density changes (imitative entries), together re-

sult in an aural impression of perfect consonance. This apparent consonance is

disrupted at in. 3, where a stammer — a reiterated diminished-seventh chord —

displaces the initial 3-layer by one eighth-note pulse. At in. 4, with a similar sen-sation of disruption or intrusion, the initial placement of the 3-layer (and the 6-

layer) returns, only to be dislodged again at in. 7. The listener is similarly tossed

back and forth between two rival consonances — rival meters, one might say —

throughout the Scherzo section. The effect is that of a highly animated, in fact,

maniacal dialogue; the points where the shifted 3-layer intrudes on the metri-

cally aligned passages, or where metrical layers are forcibly imposed on the an-

timetrical ones, sound like interruptions by an over-eager respondent.

Eusebius mused, "Florestan's notation, with its alternation of beams that contra-dict, and beams that support the primary consonance, strongly suggests that he

regarded the dialogue between meters as an essential aspect of the movement.

Were the pianist to articulate the notated meter by stresses throughout the

Scherzo section, the effect of a dialogue between meters would be much less pro-

nounced, and the movement would lose much of its dramatic impact. The pianist

should apply stresses to the metrical pulses only where Florestan requests them."

At times, the interlocutors even speak simultaneously, the nonaligned lay-

ers being superimposed rather than merely juxtaposed. At in. 10, for instance(Example 8.17a), changes of harmony strongly delineate the antimetrical 3-

layer, but the quarter-note attacks of the inner voice weakly affirm the metrical

3-layer. At mm. 31—38 (Example 8.17b), high and low points within the left-hand pattern and a repeated arpeggiatory pattern in the right hand maintain theantimetrical 3-layer, while the metrical 3-layer is again announced by umer-

voice melodic attacks. In addition, occasional dynamic accents support bothlayers (as in mm. 32 -33). In mm. 40--42, staccatos highlight the pulses of the

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Carnaval des analyses 205

EXAMPLE 8.17. Direct D3+2 and D6+5 in the Scherzo in F minor

metrical 3-layer, while the arpeggiating pattern of both hands articulates the

displaced 3-layer. At mm. 58-61 (Example 8.17c), finally, the left hand's dy-namic accents and arpeggiations and the right hand's registral accents (high

points) continue to articulate the shifted 3-layer, while right-hand dynamic ac-

cents clarify the metrical 3-layer in preparation for metrical as well as harmonicresolution at the final cadence of the Scherzo section.

In more technical terms, the Scherzo section contains much indirect dis-

placement dissonance (at each collision between the two "meters") and some di-rect dissonance of the same type. Furthermore, one of the apparent consonances

is actually a subliminal dissonance. Interestingly, Schumann treats the antimet-

ncal placement of 6/3 as if it were a dissonance; he frequently resolves it into themetrical consonance at phrase ends (mm. 3-4, 7-8, 18-19, etc.; see Figure 8.1).

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FIGURE 8.1. Metrical map of Schumann's Scherzo in F minor, mm. 1 — 111

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Carnaval des analyses 207

EXAMPLE 8.18. Metrical consonance and dissonance in the Trio of the Scherzo in F minor

Its dominance at significant formal junctures notwithstanding, the metricalconsonance is, within the Scherzo section, by far the weaker of the two metrical

interlocutors. Because it occupies much less time than the "antimetrical conso-

nance" and, unlike that consonance, is only rarely present in its full-fledgedform (i.e., its 3-layer is only rarely associated with a 6-layer), the metrical con-sonance gives the impression of a speaker desperately attempting to "get a wordin edgewise."

Within the Trio section, however, the metrical consonance succeeds in hav-

ing its say, uninterrupted by its rival. The metrical 6- and 3-layers remain in ef-fect throughout the Trio; the 6-layer is generally announced by dotted half-noteattacks in the left hand, and melodic lines moving primarily in dotted quartersprovide a consonant 3-layer (Example 8.18a).

The primary consonance does not, however, remain entirely uncontra-dicted in the Trio; a close listening reveals the presence of a number of subtleconflicts. The reiterated dyads within the right hand's accompaniment patternresult in a 2-layer, and the attacks of the right-hand doubling of the left-handmelody form a nonaligned layer of the same cardinality. The resulting disso-

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208 Fantasy Pieces

EXAMPLE 8.19. Return of the Scherzo section in the Scherzo in F minor

nances are D2 + 1 (within the right hand) and G3/2 (in interaction with the left

hand's melody). In mm. 80—84, the first portion of a restatement of the opening

of the Trio (Example 8.18b), D2 + 1 continues in the right hand in a slightly

more intense form (the attacks of the second 2-layer are now sustained duringthose of the first). The metrical 3-layer, after being stated with particular em-

phasis by dynamic stress in mm. 76–78, is not articulated in mm. 80–84, so that

G3/2 is submerged. A new, diminished version of the latter dissonance, how-ever, appears at this point (Gl .5/1); the left hand presents an eighth-note pulse

while the right hand continues in triplets. Sparks of the same diminution of

G3/2 occur in mm. 96, 98, and 100, where both triplet and duplet eighth notesare presented in the upper register. Near the end of the Trio (mm. 104 — 7 —

Example 8.18c), D2+1 is augmented (thus being treated in a manner diametri-

cally opposed to the of her motivic dissonance of the Trio, G3/2): D6+3 is

formed by dynamic accentuation of second beats. Thus, although the Trio is

substantially less intensely dissonant and expresses the nolated meter much

more clearly than the Scherzo, it does remain subtly conflicted.At in, 111, the antimetrical interlocutor of the Scherzo's metrical dialogue

brutally bursts in, as if unable to contain himself any longer (Example 8.19).

This intrusion has a "brutal" effect not only because of the indirect dissonanceresulting from juxtaposition of differently placed 6- and 3-layers, but also be-

cause after in. 111 we anticipate a return of the opening of the Trio, in analogy

to the corresponding in. 79.14

The second Scherzo section is, in metrical terms, much like the first; the

state of constant mutual interruption of metrical interlocutors is reestablished,

the antimetrical speaker apparently being unmoved by the reasoned appeal ofthe Trio. Near the end of the movement, the displaced layers contradict the

meter with unprecedented ferocity. Measures 163-68 (Example 8.20) corre-spond to an earlier passage in which both metrical and antimetrical levels arearticulated by dynamic accents (mm. 58—60 — Example 8.17c). In this altered

restatement, however, both hands express the antimetrical 3-layer by dynamic

accents, the metrical layer being articulated only weakly (in mm. 165-68) by

durational accents on the lower notes of the right hand.The antimetrical interlocutor, then, very nearly has the last word — but in

the final t h ree measures his metrical respondent (irmly quashes him. Schu-

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Carnaval des analyses 209

EXAMPLE 8.20. Conclusion of the Scherzo in F minor

mann's fermatas and sforzandos request the pianist to strive for an effect ofresolution into the notated meter. A broad and emphatic rendition of the final,metrically aligned measures should, in fact, be able to convey the impression

that the notated meter wins the argument that has raged throughout themovement

Eusebius glanced at the sleeping Florestan and thought, with a sigh, "The

metrical argument within this Scherzo reminds me very much of numerous re-cent occasions: me trying to bring Florestan into alignment with reality, he con-stantly interrupting with his ravings and not heeding me at all." He turned back

to the manuscript and started as he encountered the name "Chiarina" over thefollowing section of the manuscript. His eyes filled with tears and it was sometime before he was able to continue his reading.


Clara Schumann employed metrical dissonance sparingly, but effectively in hercompositions. The figuration in her early Piano Concerto, for instance, is occa-sionally seasoned with grouping dissonance. In the climactic triplet material inthe piano part at mm. 123-25 of the first movement, harmonic changes occuron the first triplet of each group, reinforcing the metrical 3-layer (1 =triplet 8th).In mm. 123 — 24, however, a recurring pattern — dyad followed by triad — over-

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210 Fantasy Pieces

EXAMPLE 8.21. Metrically dissonant figuration in the second movement of Clara Schumann's Piano

Concerto op. 7, mm, 58—40

lays the triplets with a duple layer. In in. 125, the 2-layer continues, now pro-duced by a repeated pitch pattern; the 3-layer is not articulated here.

The second section of the second movement of the concerto, in which asolo violoncello restates portions of the main theme to an elaborate piano ac-companiment, contains a similar dissonance (Example 8.21). From in. 38 on-ward, the left hand's quarter notes reinforce the metrical 3-layer, but the right-hand triplet figuration is generally grouped into twos by recurrence of a single

pitch (El in m. 38), or by repetition of a pattern (e.g., "single note, chord"). Themetrical state is further enriched by the superposition of the cello's dupleteighth notes on the piano's triplets, resulting in a diminution of the grouping

dissonance embedded in the piano part.In the finale of the concerto, Clara Schumann employs displacement disso-

nance in an interesting manner. The first utterance of the violins and violas is asyncopated reiteration of the dominant note (mm. 3—4), resulting in the disso-nance D2+1 (l=eighth) against the trumpet's metrical layer. This dissonance

flares up in accompanying voices at various points in the movement. Its mostdramatic reappearance, however, is at the very end of the movement, wherepiano and orchestra shout the tonic triad at each of her, the piano on the quarter-note beats, the orchestra on offbeat eighth notes (mm. 352-54). The movement

is thus effectively framed by D2 + 1.Further interesting usages of metrical dissonance occur in Clara Schu-

mann's songs, most strikingly in "Geheimes Fliistern" (op. 23 no. 3). In thepiano introduction, melodic attacks alternately suggest a 3-layer and a 2-layer(l = 16th). This indirect dissonance (G3/2) becomes direct as the voice enters inin. 8; the voice continues the 2-layer of mm. 2, 4, and 6, while the piano persistsin the 3-layer of mm. 1, 3, 5, and 7-8. The dissonance is obviously intended tomimic the "secret whispering" of forests and wellsprings.

Clara Schumann's most thoroughgoing usage of metrical dissonance occursin the Scherzo movement of her Piano Trio op. 17. A summary follows:

1. Alain recurring dissonances: D3+1 and G3/2 (l=quarter).2. Families of dissonances operative in the movement: none.

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EXAMPLE 8.22. Metrical dissonance in the Scherzo section of the second mvmt. of Clam Schumann's

Piano Trio op. 17. © AmadeiM Verlag, 1989. Utte'c) by permission of the publisher.

3. Recurring juxtapositions or superpositions: D3+1 and G3/2.

4. Proportion of primarily consonant and primarily dissonant passages: the

Scherzo is mostly consonant, the Trio mostly dissonant, so that in the

movement as a whole, the two basic states are fairly equally represented.

5. Amount of subliminal dissonance: brief passages of subliminal G3/2 in

the Trio, one of them being employed as a gesture of culmination near

the end of the final statement of the Trio material.

6. Frequency of change of metrical state: the Scherzo is somewhat more

volatile, alternating between consonance and weak dissonance every fewmeasures. The Trio alternates fairly strong dissonance with weaker dis-

sonance, changes occurring much less frequently than in the Scherzo(only at mm. 60, 75, 100, and 115).

7. Basic metrical narrative: in the Scherzo section, two dissonances are

weakly announced. They are gradually intensified in the Trio, then re-

stored to their original weak versions with the return of the Scherzo. The

Scherzo section contains a nesting of this narrative; dissonance is veryweak in the opening section, somewhat stronger after the double bar,then weaker again when the opening returns.

The Scherzo section contains some weak metrical dissonances, among them

allusions to D3+1 (l=quarter) in mm. 3 (Example 8.22a), 9, and 11-12 (Exam-ple 8.22b), and hints at G3/2 in mm. 9—17 (Example 8.22b shows the beginning

of this passage). It is in the Trio section, however, that metrical dissonance flour-

ishes; here, Clara Schumann develops at length both of the dissonances weaklybroached in the Scherzo section.15 In mm. 35-51 (Example 8.23a), she dwells

on G3/2; the dissonance is mainly subliminal through in. 46, the 2-layer reigning

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212 Fantasy Pieces

EXAMPLE 8.23. Metrical Dissonance in the Trio section of the second mvmt, of Clara Schumann's

Piano Trio op. 17. © Ama'deus Verlag, 1989. Used by permission of the publisher.

virtually without contradiction, but it surfaces in mm. 47—51, where harmonicchanges and durational accents reinforce the metrical 3-layer. In mm. 51—55

(Example 8.23b), the composer develops D3+1, articulating the displaced 3-

layer by second-beat dynamic accents and slurs in the violin (cf. in. 3, Example

8.22a). In mm. 55—58, she loosens the dissonance to D6+1, the loosening leading

nicely into the resolution at the end of the section (mm. 59-60a). The section fol-

lowing the double bar (mm. 60b-75) provides contrast to the pervasively disso-

nant preceding section, containing only brief allusions to the two motivic disso-

nances. These include the weak G3/2 in mm. 60b–61, created by melodic

new-event accents in the strings, and the hints at D3+1 in mm. 63 and 67, wherea shifted 3-layer is suggested by second-beat durational accents. At in. 75, Clara

Schumann begins the first of two restatements of the opening music of the Trio,

which departs from the initial version in pitch, but not in metrical structure. Asecond restatement of the opening material of the Trio (following another state-

ment, in mm. 100—115, of the weakly dissonant material of mm. 60—75) does de-

viate from the initial version in terms of meter; at mm. 119-22, a new passage ar-ticulates the 2-layer in an unprecedently strong manner (by chord changes)

while the metrical 3-layer is not explicitly stated.The movement illustrates not only subtle preparation of metrical disso-

nance to be enlarged upon later, but also the coordination of metrical progres-

sion and form. Most obvious, the Trio is set off from the Scherzo by its gener-ally more prominent dissonance. Formal boundaries within the two mainsections are also coordinated with changes in the metrical progression. In theScherzo section, the double bar is highlighted by the proliferation of dissonance

immediately after it. In the Trio, conversely, the double bar is followed by amarked decrease in degree of dissonance.

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Carnaval desanalyses 213

Eusebius found the title of the next section puzzling; with wrinkled brow heread:



1. Main recurring dissonances: D3+2 (l=quarter).

2. Families of dissonances operative in the movement: none.

3. Recurring juxtapositions or superpositions: none.

4. Proportion of primarily consonant and primarily dissonant passages: the

two states are present in approximately equal proportions.

5. Amount of subliminal dissonance: much subliminal D3+2.

6. Frequency of change of metrical state: change occurs with each new sec-

tion of the rondo form. There are very few fluctuations of metrical state

within sections.

7. Basic metrical narrative: alternation of consonance and dissonance, be-ginning with consonance and ending with last-minute reestablishment of


The first movement of the FtuchingMcbwank op. 26 contains some of Schu-

mann's most prolonged and powerful metrical dissonances, as well as some

dramatic hypermetrical conflicts.16 Metrical dissonance in the movement falls

almost exclusively into the category D3+2 (l=quarter). The antimetrical layerwithin each statement of the dissonance is produced either by durational ac-

cents (i.e. syncopation) or new-event harmonic accents on upbeats. Example

2.14 shows the first appearance of the syncopated version. This version re-

turns in the coda (at mm. 465-90 and 547-51). A different form of D3+2, still

involving syncopation, is found in mm. 409—40; here, one or more voices con-

vey the metrical layer by durational accents while others present the synco-pation, with the result that D3+2 lies on the surface. During mm. 86-126,

465—90 and 547-51, on the of her hand, the dissonance remains primarily

subliminal. The metrical layer is never articulated within mm. 465-90 and

547-51, where all downbeats are suppressed. In the latter section, very close

to the end of the movement, the dissonance is particularly intense, the anti-

metrical layer being emphasized by dynamic accents. Within the section en-

compassing mm. 86-126, Schumann does permit the metrical layer to appear

at a few phrase endings (mm. 102, 110, and 126 — in the latter case, after in-tensifying the dissonance with dynamic accents — Example 8.24a). These re-minders of the metrical layer on the one hand result in a sense of resolution

appropriate to phrase endings, but with respect to the larger context they cre-

ate indirect dissonance and, by aiding the listener in maintaining the metricallayer, contribute to the upholding of subliminal dissonance. The positioning of

both mm. 86-126 and 465-90 after statements of the A section also helps thelistener to maintain the metrical layer and hence a vivid impression of disso-

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214 Fantasy Pieces

EXAMPLE 8.24. D3+2 in first mvmt. of Robert Schumann's Faschingsschwank aus Wien op. 26

nance, for the A section contains much downbeat emphasis by dynamic, du-

rational and density accents.

Schumann dramatically anticipates the second version of D3+2 (where the

displaced layer is created by harmonic changes) in mm. 117—18 (Example

8.24b). Since this is a phrase ending, one might expect metrical resolution,

which did occur at the two preceding phrase ends. Instead, Schumann emphat-

ically initiates a harmony on the last beat of in. 117, and reiterates it softly

within in. 118, thus continuing the antimetrical layer rather than abandoning itat the cadence. In in. 340 (Example 8.24c), he again initiates harmonies on thirdbeats and restates them (now in a higher register) on the following downbeats.

Harmonic change thus delineates an antimetrical 3-layer (while durational ac-

cents on the downbeats convey the metrical 3-layer). The dissonance resolves inmm. 405—8, where significant harmonic changes are again coordinated with the

metrical layer.17

Some of the metrical conflict within the first movement of op. 26 takesplace at a higher level. The major part of the movement is based on four-bar hy-

permeasurcs; as in many of her works by Schumann, the four-bar hypermeter

arises at least in part from a generic root that is of obvious relevance to the

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Fasichingsschwank: from the Viennese waltz. The movement is a succession ofwaltzes, influenced by those of Franz Schubert.18

Whereas Schumann's Schubertian waltz models virtually never deviatefrom four-bar hypermeter, Schumann disrupts that hypermeter quite fre-quently, at times only in a subtle manner, at times very dramatically. In the firsttwo waltzes (mm. 1-24 and 24-62, respectively), he creates high-level dis-placement dissonances by dynamically accenting the metrically weak measuresof four-bar hypermeasures. The resulting dissonances are D12+3 and D12+9(l=quarter). In the second waltz (the B section), he disrupts the hypermetermore drastically. After in. 37, there is some ambiguity as to the placement ofhigh-level downbeats (hyperdownbeats). The restatement of mm. 37-38 a sixthhigher in mm. 39-40 results in the possibility of hearing the beginning of in. 39as a new hyperdownbeat (equivalent to the downbeat of in. 37), or alternativelyas the third beat of the hypermeasure initiated in in. 37. The result of this am-biguity is the hypermetrical dissonance D12+6 (see Example 8.25a). At the endof the B section there is hypermetrical irregularity of a different kind; Schu-mann expands the final hypermeasure from four to six measures by repeatingthe cadential measures (mm. 57—62), resulting in the indirect hypermetrical dis-sonance G18/12.

The disruptions of the initially regular four-bar hypermeter within the Bsection are of a mildness that one could describe as "Eusebian." A more violent"Florestanian" disruption is shown in Example 8.25b. The section from whichthe excerpt is taken (mm. 150—228—the D section, or fourth 'waltz) adheresslavishly, in fact monotonously, to four-bar hypermeter until in. 211. At thatpoint, Schumann suppresses an expected downbeat and hyperdownbeat, thenstates two dynamically accented dominant ninth chords. In retrospect, mm.211—12 are perceived not as initiating a new hypermeasure, but as concludingthe hypermeasure that began in in. 207, for the recapitulatory in. 213 definitelyinitiates a new hypermeasure. Thus, the intrusive ninth chords stretch the hy-permeasure beginning in in. 207 to six measures. Bringing together strong pitchdissonance, metrical dissonance (G3/2), and hypermetrical dissonance, mm.211—12 explode the placid waltz character of the preceding music.

Further examples of hypermetrical disturbance, both Eusebian and Flo-restanian, occur in the coda of the first movement. Amidst its many four-bar hy-permeasures, the coda contains one that is five, and one that is six measures inlength (mm. 504-8 and 478-83, respectively). These expansions beyond thenormal four-bar length result in indirect hypermetrical grouping dissonance.Stronger disruptions occur within the last few measures. At in. 549, Schumanndisplaces a downbeat and hyperdownbeat, creating the dissonances D3+2 andD12+2. Both the displacement and the succeeding repetition of the cadence ofin. 548 blur the hypermetrical boundary, making it possible to hear a greatly ex-panded hypermeasure spanning mm. 545-52. The resolution to tonic in in. 552not only completes a hypermeasure, but at the same time initiates one. Thiscompression of two potential hyperbeats into one is a fitting final gesture forthis conflict-ridden movement.19

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EXAMPLE 8.25. Hypermetrical 'dissonance in the first mvmt. of the Faschingsschwank aus Wien

The frequent and prominent metrical and hypermetrical dissonances in the

first movement of the Faschingsschwank may carry extramusical meaning. Inorder to uncover it, we must take a short excursion to Vienna, the city in whichmost of the work was composed.20 In early October of 1838, Robert Schumannmoved from Leipzig to Vienna. He did so with some reluctance, for he had beenhappy in Leipzig, and his journal, the Neue Faschingsschwank Miuik, was securely es-

tablished there. But once he had moved, he found many aspects of lite in Vienna

very pleasant. In his letters to Clara Wieck and in of her writings, he praised thescenic beauty of the environs, the "festive rushing" in the streets, the impressivesteeple of Saint Stephen's, the beautiful women, and the public opulence.21 Fur-

thermore, he appreciated certain aspects of cultural life in Vienna. He enjoyedmeeting the various prominent musicians who lived in or passed through Vi-

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Carnaval des analyses 217

enna, and was impressed with the high quality of some of the theatrical and mu-sical performances. Finally, he reveled in a sense of spiritual proximity to hisrevered Viennese predecessors, Beethoven and Schubert. He made a pilgrimageto their graves soon after his arrival in Vienna, where he picked flowers forClara and found a pen that he reverently reserved for special occasions. Fol-lowing an urge to become acquainted with someone who had been close toFranz Schubert, he visited the composer's brother, who gave him access to atreasure trove of Franz's manuscripts.22 Such experiences, especially the latter,were uplifting and life changing.

Schumann's positive reactions toward life in Vienna were, however, coun-terpointed by intensely negative ones. He observed a number of serious prob-lems in cultural and artistic circles. He wrote in the note Zeitdchrift, "In Vienna,they are afraid of anything new, anything that goes beyond the run-of the-mill[alten Schleridruin\; in music, too, one desires no revolution there."23 This resis-tance to the new and unfamiliar became ever more obvious to him during hisstay in Vienna. He complained of the xenophobic attitude of the Viennese: "TheViennese are, in general, extremely suspicious of foreign musical greats (except,perhaps, the Italian ones) ,"24 When he wrote this sentence, he had Mendelssohnin mind, whose music was generally not popular in Vienna at this time. He also,however, had some personal experience of Vienna's suspicion of foreign musi-cians. His own music was even less well received there than Mendelssohn's; ina letter written from Vienna in 1837, Clara Wieck had mentioned only one pro-ponent of his works and referred to all of her indigenous musicians as Schu-mann's enemies.25 Furthermore, Schumann was informed soon after his arrivalthat because he was a foreigner, he would not be permitted to let his name standas editor of his journal if it were published in Vienna.26

Schumann became aware that the Viennese narrow-mindedness arose inlarge part from the existence of certain powerful cliques. In a letter to his fam-ily of 10 October 1838, he wrote: "You would hardly believe what petty fac-tions, coteries, etc. exist here; to become well established, one must possess aserpentine character, of which, I believe, there is little within me."27 A particularclique to which he referred frequently in his writings was that controlled by To-bias Haslinger. He wrote to Clara on Easter Monday 1839, "Sedlnitzky [the di-rector of the Censorship Department] is angry with me; I had written about theperformance of St. Paul, and since I am leaving, I wrote for once according tothe facts and in my own fashion about the Haslinger clique, not, of course,roughly and inimically, but rather jovially and wittily."28 Schumann's remarkswere not as benevolent in tone as he would have had Clara believe: "There ex-ists here a clique, the descendant of that which once booed Don Giovanni and. theLeonore Overture ... a clique ... as impoverished, as ignorant, as incompetent interms of judgment and achievement as any in Flachsenfingen."29

Schumann also viewed with concern the censorship with which the Metter-nich regime sought to nip revolutionary tendencies in the bud. After a few monthsin Vienna, he fully recognized how difficult it was "to speak what one thought,"and began to fear that the journal would never prosper in such an atmosphere.30

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Schumann's letters indicate his planned courses of action in the face of

these negative aspects of political and cultural life in Vienna. As far as political

repression was concerned, his attitude seems to have been one of learning tolive with it rather than one of attempting to change it. He was "careful in his

speech and writing" so as not to annoy the censors and potentially embroil therecipients of his letters (especially Clara Wieck) in difficulties.31 He also took

steps to ensure that the journal would not offend the authorities. Soon after his

arrival in Vienna, he wrote to Oswald Lorenz, who was running the journal inLeipzig during his absence: "Be very careful not to accept anything that might

give the Viennese censors reasons for displeasure. You have no idea what power

they have; it reminds one of the time of the Vebrne'.32

Schumann's attitude toward the cultural problems was less passive; he was

eager to attempt to alter the state of affairs through his journal. As early as 25

October 1838, he wrote to Clara Wieck:

The petty coteries should be blasted apart, the various factions

brought closer together, but all of this in an open, honest manner. Viennahas means aplenty, as has probably no of her city, but a leader is lacking,

someone like Mendelssohn, who could fuse and rule over them. Also, they

are glad to let themselves be led here; they listen carefully when something

is expounded in the appropriate manner. Indeed, some of the finer individ-

uals actually hope for a Messiah to whom they would immediately offer

crown and scepter. Thus, there would surely be much for the journal to dohere."33

Reading between the lines, one gathers that, the reference to Mendelssohn not-

withstanding, Schumann himself hoped to become the Messiah who would save

Vienna.Schumann's determination to take action against the Viennese Philistines

seems to have reached a peak late in 1838. In an aggressive vein, he wrote to

Clara on 30 December 1838: "Later ... I would like to, and must, strike into the

midst of this pettiness in such a manner that their eyes shall be opened."34 A few

days thereafter (on 10 January 1839), he wrote to Karl Montag: "Later, when

the journal is fully established here, which will probably be accomplished by the

middle of the year, I shall strike into it all with a great sword."35

The inner and outer conflicts with tyranny and cultural demagoguery de-

tailed above seem to me to be reflected in the metrical structure of the first

movement of the Faschingsschwank. Musical meter with its regularly recurringdownbeats and bar lines is a logical metaphor for a rigid cultural or political

framework. The metrical scheme designated by the time signature and barlines — and no less by a clearly audible four-bar hypermeter —could symbolize arepressive, restrictive system. Overriding of those schemes would then suggest

rebellion against the system.As we have seen, the first movement of the Faschingsschwank contains many

passages in which the music is at odds with the metrical framework, some of

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these dissonances being relatively weak, some of them very powerful. Passageslike that shown in Example 8.25b, in which the dance-like four-bar hypermeterof the preceding measures is smashed, may be translations into music of the vi-olent, Florestanian language of some of Schumann's anti-Viennese remarks,particularly that referring to the symbolic sword with which he planned tostrike into the midst of Vienna's complacent clans and coteries.

Eusebius looked up from the manuscript and mused, "Was the first move-ment of the Faschingsschwank really a protest against the Viennese Philistines? Itmight have been! Our quotation of the Marseillause in mm. 293—300 certainlybears out the author's suggestion that the movement has a rebellious connotation.The author's linking of metrical dissonance and protest is supported by ErnstWagner's remark about the 'tyranny of meter,' which Florestan quoted when wewere in Euphonia; this remark had suggested to us the metaphorical associationbetween musical meter and repression on the one hand, and between the veilingof meter and freedom on the of her." With a sigh, he added, "I suppose that all ofFlorestan's violent metrical dissonances partake of a spirit of protest againstmindless constraints, of lashing out against complacent Philistinery—the spiritthat animated him when he was well."

The crackle of paper as he turned to the next page of the manuscript awak-ened the sleeping Florestan. Anxious to engage his attention before it focused onsomething that would provoke him, Eusebius said to him, "Listen to this analy-sis of one of the works of our friend Brahms—in fact, of the sonata movementthat we briefly discussed while we were walking through Euphonia with HectorBerlioz." Florestan sat up, and Eusebius read:


A number of composers seem to have learned to handle metrical dissonance bystudying Schumann's music. Stephen Heller is one obvious example. His adula-tion of Schumann is clearly evident from his letters to him, and his music providesfurther evidence of his reverence for Schumann's works.36 His Rondo-Scherzoop. 8, dedicated to "Florestan and Eusebius," contains numerous Schumannesquemetrical devices. In mm. 59-68, for example, Heller almost entirely abandonsthe triple meter on the surface; the passage is dominated by a clearly duplerhythmic figure. The Scherzo of Heller's Sonata op. 9, a work that Schumannreviewed positively, contains a great deal of metrical dissonance.37 Heller opensthe movement, for example, with displacement dissonance (D3+2), then brieflypresents G3/2; a repeated descending octave in the right hand forms a duplelayer while the left-hand chords continue to assert the metrical layer.

The first opus of another composer, Julius Schaeffer, is a set of Fantasiestucke

for piano, also dedicated to Robert Schumann. The influence of Schumann isevident not only from the title but also from extended metrically dissonant pas-

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220 Fantasy Pieces

sages. The middle section of the first piece, for example, is based on consistentD3+2 (l=8th). At times, dynamic accents keep the metrical layer alive, but in-ceptions of harmonies and melodic attacks always contradict the meter byfalling on the third eighth note of metrical groups of three. The fourth piece

contains not only long passages of D2 + 1 (1 = 16th), reminiscent of numerousSchumann pieces, but also some dramatic G12/8.38

The best-known younger composer who was influenced by Schumann'smetrical structures is Johannes Brahms. Brahms studied Schumann's musiccarefully during September 1853, and came into personal contact with him inthe following months.39 His works written before this time are, to be sure, notdevoid of metrical dissonance, suggesting that of her music might have influ-enced him earlier.40 The Scherzo of his Piano Sonata op. 1, for instance, is per-meated by a figure consisting of sequentially descending thirds in eighth notes(mm. 3, 11, 23, etc., and especially 78-80); the thirds create a 2-layer within the

prevailing six-eight meter. These allusions to a 2-layer neatly prepare the Trio,which is written in three-four meter. Walter Frisch mentions another relevantpassage from this sonata, namely the G-major episode in the Rondo finale,

where a 6-layer, and at times a 12-layer, are imposed on the nine-eight meter.41

In the first movement of the Sonata op. 2, there is an interesting instance ofG4/3 (l=triplet eighth). In mm. 40-41, 43-44, 46-47, 49-50, and correspond-

ing later measures, Brahms reiterates a pitch pattern consisting of four tripleteighths, which is dissonant against the three-triplet durations intermittently set

out by the right hand.Frisch observes, however, that metrical dissonance is relatively rare in

Brahms's early works and is employed systematically only in his works of the

1860s.42 It is likely that the upswing in metrical dissonance in Brahms's music of

the latter decade can be attributed to his newly acquired knowledge of Schu-mann's music. In the following paragraphs I briefly investigate the metricalstructure of the first movement of the Piano Sonata in F Minor op. 5 —a move-ment conceived during Brahms's stay with the Schumanns, and first performedfor Robert Schumann.43


1. Main recurring dissonances: G6/4, D6+2 (l=8th).2. Families of dissonances operative in the movement: "G6/4" (diminutions

appear frequently).3. Recurring juxtapositions or superpositions: G6/4 and D6+2.4. Proportion of primarily consonant and primarily dissonant passages:

mostly dissonant.5. Amount of subliminal dissonance: much subliminal G6/4, some sublimi-

nal D6+2.6. Frequency of change of metrical state: frequent throughout (for the most

part, every two to four measures).7. Basic metrical narrative: constant struggle between 6- and 4-layers.

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EXAMPLE 8.26. Metrical Dissonance in the exposition of the first mvmt. of Brahms's Piano Sonata

op. 5

The movement appears to begin with an unambiguous establishment of themetrical 6-layer (l=8th); the initial three statements of the dramatic openingmotive occupy six eighth-note pulses, or one measure, each (Example 8.26a).On the basis of harmonic change, however, a displaced 6-layer emerges as well;the third beat of the first measure introduces a new harmony, which is thenmaintained through the first two beats of the second measure. The same is trueof in. 2 beat 3 through in. 3 beat 3, and, possibly, of in. 3 beat 3 through in. Abeat 2. The interaction of these 6-layers results in subtle D6+4.

The situation from the end of in. 3 through in. A is, however, complicatedby the repetition of a contour pattern ("high chord — low note"), which resultsin a 4-layer and in a hint at G6/4. The durational accent at the beginning of in.5—the strongest such accent so far— temporarily brings the metrical layer tothe fore and resolves the dissonances.44

In the second phrase Brahms elaborates on the dissonance broached in in. A.

Beginning in in. 7, the bass simultaneously presents two 4-layers, one formed byits durational accents (quarter notes among triplet eighths), the of her by therepetition of the pattern "three triplets, quarter note." These layers result inD4+2, but also, more obviously, in G6/A. The right hand attempts to assert themetrical 6-layer against this pattern, and is at times successful (for example, inmm. 7-8, where the 6-layer is announced by dynamic accents and the repeatedpattern "quarter, eighth, eighth, quarter"). Already in in. 8, however, the righthand exhibits a tendency to join the left hand in articulating the 4-layer; its six-pulse repeated pattern is curtailed in mm. 8-9 to the four-pulse pattern "quar-ter, eighth, eighth," which aligns with the 4-layer formed by the left hand's du-rational accents. In mm. 12-13, while the inner voices reiterate the six-pulsepattern from mm. 7-8 (thus articulating the metrical 6-layer), the right hand'sdynamic accents and reiterations of D5 reinforce the same 4-layer.

Brahms continues to exploit G6/4 within the second theme area. The theme

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EXAMPLE 8.27. Metrical disonance in the development section of the first mvmt. of Brahms's Piano

Sonata op. 5

begins with metrical consonance, but in mm. 49—50, harmonic changes, melodicattacks, and dynamic accents strongly articulate a 4-layer in the absence of themetrical 6-layer, resulting in indirect and subliminal G6/4. In mm. 58 — 59 (Ex-ample 8.26b) and 64—65, again after several measures of consonance, the righthand asserts a 4-layer by a series of registral accents and by repetition of a two-quarter-pulse pattern of falling fifths; again, indirect and subliminal G6/4 isformed. A few consonant measures close the exposition.

The metrical narrative of the exposition clearly centers on the struggle of themetrical 6-layer to assert itself against the rival 4-layer. The development sectionbrings this narrative to a climax (Example 8.27a). It opens, interestingly enough,with two measures in common time (mm. 72 — 73). The 4-layer, now a metrical

layer in terms of surface structure, is clearly articulated by the imitation of a four-pulse-long motive (a motive first stated in in. 16), and by durational accents.

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EXAMPLE 8.28. Metrical dissonance in the coda of the first mvmt. of Brahms's Piano Sonata op. 5

Eusebius looked up and remarked, "Johannes must have glanced at our sketch-books when he visited us! This passage is strikingly similar in terms of motivicand metrical structure to my violin and piano sketch in the third sketchbook (Ex-ample 5.5a), which we later transformed into the second section of the fifth In-termezzo from op. 4 (Example 5.13)."

The triumph of the 4-layer is, however, short-lived; in. 74, a five-four bar, juxta-poses a four-pulse segment with one of six pulses (the segments being delineatedby harmonic change), and thus accomplishes a "modulation" back to the 6-layer.Not that the 4-layer is out of the picture after this point; it rears its head at intervalsthroughout the remainder of the movement. A large segment of the developmentsection is based on the version of G6/4 that originated in the second phrase of thefirst theme (cf. mm. 7—16 and mm. 78—87). A later climactic passage, at mm.119-22 (Example 8.27b), allows the 4-layer to dominate again; changes of har-mony project the 4-layer, while the metrical 6-layer is not clearly articulated. Thispassage is reminiscent of the first statement of G6/4 in the movement (mm. 3 –4).

During the recapitulation (beginning at in. 131), Brahms suppresses someof the exposition's instances of G6/4, either by altering or by omitting measures;he replaces the hemiolic mm. 3–4 with consonant measures (mm. 133—34), andomits the dissonant material of mm. 7—16. The subliminal G6/4 of mm. 49—50does reappear (in mm. 171-72), as does the falling fifth material shown in Ex-ample 8.26b (mm. 180—81 and 186—87). The coda contains one more flare-upof the 4-layer; in mm. 209-13 (Example 8.28), each chord occupies four eighth-note pulses, resulting in subliminal G6/4.

A secondary character within the metrical narrative of the movement is thedissonance D6+2. The first allusion to this dissonance occurs at mm. 9-10 (si-multaneously with continued development of G6/4); in in. 9, Brahms places adynamic and durational accent on the second beat, and in in. 10, a durationalaccent only. During the transition, where the material of mm. 9—10 is devel-oped, additional dynamic and durational accents on the second beat (mm. 27,

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28, and 35—38) result in more D6+2. The dissonance is associated with differentmusic in mm. 51-52 and 54-55, but reappears in its original guise during thedevelopment section (mm. 81 and 86). In the coda, Brahms dramatically bringsthis dissonance into association with G6/4— an association that he had alreadyforeshadowed in mm. 9 and 49—52. The Piu animato section at in. 205 (Example8.28) begins with several measures of subliminal D6+2 (the metrical 6-layerbeing suppressed). The succeeding subliminal G6/4 emerges naturally fromD6+2; the displaced half-note chord of in. 209, rather than being followed byanother chord in the same metrical position (so as to continue D6+2), is fol-lowed by a chord of the same duration, resulting in subliminal G6/4 instead.

Having neatly slid from D6+2 into G6/4, Brahms proceeds to resolve thelatter dissonance in a subtle manner. Measure 214 (intriguingly similar to theopening of the third movement of Brahms's Fourth Symphony!) is a finelysculpted "modulatory" measure. At the beginning of the bar, one is likely to heara duple grouping of quarter notes, and hence a continuation of the 4–layer ofmm. 209—13; the first significant harmonic change takes place on the thirdquarter note, the second triad being heard as an embellishment of the tonic. Ifone takes the whole measure into account, however, a triple grouping of thequarter notes probably makes more sense, for the second-most significant triadof the measure (V) tails on the fourth quarter. This important harmonic changedivides the six quarter notes of the measure into two groups of three, and thusreestablishes the metrical 6-layer. After this measure, one is prepared for theclear and uncontradicted final presentation of that layer in the form of repeateddotted half-note attacks. The metrical 6-layer, threatened until the end by the 4-layer as well as by an antimetrical 6-layer, is finally triumphant.

Florestan (whose nap had done him good) whispered, "Johannes is a finecomposer, and a good lad, too! So nice of him to look in on us here at Endenich!"Eusebius agreed, adding, "I am delighted to learn that he will write symphonies!It is a pity that we shall never hear them." He turned back to the manuscript andread aloud the following analysis of one of his most beautiful slow movements.



1. Main recurring dissonances: D3+2, D6+3 (l=8th).2. Families of dissonances operative in the movement: Dx+3, "G6/4" (G6A4

appears in the fourth variation, the high-level relative G24/16 at the endof the fifth).

3. Recurring juxtapositions or superpositions: none.4. Proportion of primarily consonant and primarily dissonant passages:

changes from section to section. The theme contains both states in equalproportion, the first variation is entirely and strongly dissonant, the sec-

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ond almost entirely consonant, the third mildly dissonant, the fourth

strongly dissonant, the fifth variation and the coda mostly consonant.

The sections are thus clearly distinguished by metrical state.5. Amount of subliminal dissonance: the D3+2 in the first variation is

mostly subliminal. The fifth variation, in common time, could be consid-

ered subliminally dissonant against the primary metrical consonance of

the movement. otherwise, dissonance is on the surface.

6. Frequency of change of metrical state: frequent in the theme, infrequent(only at section ends) in the first variation. In the second variation, the A

sections involve frequent change (approximately every two measures),

whereas the B section (mm. 41—44) adheres to one state (consonance)

throughout. Infrequent change characterizes the third and fourth varia-tions. In the fifth variation, alternation between consonance and D4+1 is

frequent (each measure). The coda involves only two changes of state —

from consonance to dissonance in in. 111, and back to consonance in the

final measure of the movement. To some extent, frequency of change of

metrical state helps to characterize the individual sections of the movement.

7. Basic metrical narrative: the movement begins with intensification of dis-sonance (D3+2) in the theme, culminating in the pervasive dissonance of

the first variation. Thereafter, the movement alternates between conso-

nant and dissonant areas. The theme returns with its intensificationprocess, but this time it is followed by the primarily consonant coda

(with flareups of motivic dissonances at the very end).

The second movement of Schumann's Second String Quartet is marked

"quasi Variazioni." "Quasi" is an appropriate designation: the various sections of

the movement do not exhibit the close harmonic correspondence to the themethat one expects from a true set of variations. The "first variation" (mm.

16—32), for example, preserves very few aspects of the "theme." Some melodic

fragments of the theme make an appearance (for example, the F4-BI3 descent

from the second violin part of in. 1—2 — compare the cello in mm. 17-18; and the

EI>-F neighbor motive of mm. 1, 6, 12-14, and 16 — see the second violin part inmm. 17—19). A few large-scale melodic and harmonic features are preserved as

well, such as the El octave coupling (compare the first violin part in in. 4 and

the cello part in mm. 22-24), and the motion to the mediant at the beginning of

the second part (flat mediant rather than diatonic mediant in Variation 1). The

differences between the theme and the variations, however, by far outweigh thesimilarities. The first variation's first half, for example, ends on the dominantrather than the tonic (compare mm. 8 and 24). The second, third, and fifth vari-ations (mm. 32-48, 48-64, and 76-89) are based on the first variation ratherthan the theme, and the fifth variation compresses the material of the first vari-

ation almost to the point of the unrecognizability. Nevertheless, the term "vari-ations" is appropriate, for the movement is, to a large extent, a set of variationson the metrical states of the theme.

The theme presents several dissonances. It begins with allusions to D12+3

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EXAMPLE 8.29. Metrical dissonance in the theme and beginning of Variation I in the second mvmt. of

Robert Schumann ',> String Quartet op. 41 no. 2

and D6+3 (l=8th). In in. 2, a registral and dynamic accent on the seconddotted-quarter beat hints at D12+3 (Example 8.29a). In mm. 3, 6, 7, and later

measures, registral and/or dynamic accents occur on both of the weak beats,

with the result that D12+3 is tightened to D6+3.Much more significant throughout the theme, however, is D3+2.

Eusebius looked up and said, "I recall making a revision to ensure that D3+2 wouldnot be overshadowed by D6+3. In my first draft, the melodic contour of in. 14 was

quite different; I approached the second and fourth beats by upward leaps of a sixth

in the first violin part, creating pronounced registral accents and therewith thedissonance D6+3. I subsequently eliminated those leaps and therewith the statement

of D6+3, thus allowing D3+2 to remain in the forefront of the metrical action."45

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D3+2 is very weakly present at the opening, where the metrical 3-layer, estab-

lished by the durational accents of the violins and the cello, is contradicted by the

attacks of the viola. The dissonance, initially almost inaudible, becomes more in-

tense later in the theme, where Schumann involves outer voices in the antimet-

rical layer, and increases the number of instruments participating in that layer.

The enlistment of outer voices begins in mm. 2 and 4, where the cello contributes

one antimetrical pulse. At the beginning of the second section (mm. 8 and 9), the

violin, which so far has staunchly adhered to the metrical 3-layer, joins the sec-

ond violin in presenting intrusive antimetrical attacks. Measure 11 is the culmi-

nation of the increasing outer-voice involvement; both cello and first violin par-

ticipate in the articulation of the antimetrical 3-layer (as do the inner voices).

Measure 11 is also the climax of the textural intensification process — of the

encroachment of the antimetrical layer on an increasing number of voices. In in.

4, Schumann expands the antimetrical ranks from the initial single participant

(the viola in in. 1) by adding the second violin and, briefly, the cello (see Ex-

ample 8.29a). In mm. 8-9 he gives the antimetrical layer to both violins, in

mm. 10—11 to the violins and the cello, and in in. 15 (the first measure of Ex-

ample 8.29b) to the three lower instruments. This process is reversed at the

very end of the theme, where only the cello adheres to the displacement.

As the first variation begins (see Example 8.29b), the cello persists in the

same displaced 3-layer, providing smooth continuity from the theme. D3+2 is

much more pervasive in this variation, both in a vertical and a horizontal sense.

Whereas in the theme at least one instrument articulated the metrical layer at all

times, in the first variation all sounding instruments are, except at a few signif-

icant points, engaged in the displaced layer — initially groups of three instru-

ments, then all four in mm. 22-24 (Example 8.30a). This takeover of the entire

texture by the displaced layer, which results in a total suppression of the metri-

cal layer and hence in the "submerging" of D3+2, is a continuation of the inten-

sification process initiated in the theme.

Schumann cleverly leaves vestigial remnants of the metrical layer in place

within the first variation, and thus occasionally brings D3+2 to the surface. He

does so not at arbitrary points but at important formal boundaries. The first such

event occurs at the end of the first half of the variation (in. 24), where the viola,

with a stammer, breaks out of the antimetrical 3-layer and asserts the metrical

one (Example 8.30a). This surfacing of G3/2 coincides with particularly pungent

pitch dissonance. The second violin resolves the leading-tone D4 to El4 at the

end of in. 23, and the viola, heading for the same resolution, trails behind the sec-

ond violin, stating C5 against the second violin's D4, and D5 against its Et4.

A more emphatic assertion of the metrical layer (and surfacing of G3/2) oc-

curs at the end of the third phrase, just before the return of the opening of the

variation (in. 28 —Example 8.30b). This time, a displaced harmony —the Et

triad—is sustained an eighth-note pulse longer than expected, and a corrective

accent on the final beat of in. 28 reestablishes the metrical layer. Schumann re-

tains the metrical layer during the first beat of in. 29, then again suppresses it in

all instruments until the end of the variation.


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EXAMPLE 8.30. Metrical Dissonance in Variation 1 of the second mvmt. of Robert Schumann's String

Quartet op. 41 no. 2

Eusebius remarked, "In my first draft, the displacement continued until the end

of in. 28, and restoration of the metrical consonance occurred only in in. 29.46

The revised resolution at the end of a measure is much more dramatic (because

more unexpected), and thus much more strongly highlights the return of the

opening material of the variation. The siorzando on the final dotted quarter of in.

28," he added, "also results in an allusion to the of her significant dissonance of themovement, D6+3."

The final cadence of the first variation, unlike the earlier cadences, is not

associated with assertion of the metrical layer; Schumann saves metrical resolu-

tion for the second variation (mm. 32—48), which, in contrast to the first, is pri-

marily consonant (Example 8.31). The attacks of the first violin consistently

and unambiguously express the metrical 3-layer, while the of her instrumentsgenerally articulate the eighth-note pulse. Only a few weak dissonances disturbthis Eusebian idyll. In mm. 33—36, for example, allusions to antimetrical 3-layers

in the second violin create intermittent weak D3+1 and D3+2 (Example 8.31).

In mm. 38-40, D3+1 and D3+2 occur in more expansive form, the former dis-sonance created by attacks of the second violin and viola, the latter by those of

the cello. This island of metrical dissonance effectively highlights the impending

phrase ending; the resolution to V harmony at the cadence of in. 40 is coordi-nated with metrical resolution.

In the third variation (beginning at in. 48), Schumann returns to the two

main dissonances established in the theme and first variation. He alludes to

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EXAMPLE 8.31. Metrical dissonance at the end of Variation 1 and beginning of Variation 2

D3+2 in mm. 49-52 (Example 8.32), 54 and 64, where registral accents withinthe sixteenth-note figuration, most frequently in the first violin, result in a sug-gestion of a displaced 3-layer. In mm. 55 and 63, the same dissonance is formedby durational as well as registral accentuation; the highest sixteenth notes aredotted — a striking departure from the otherwise unbroken flow of undotted six-teenth notes. Example 8.32 shows that D6+3 is also present in this variation. Inmm. 48—54 and 60—61, the metrical 6-layer is conveyed by significant harmonicresolutions (usually the tonics within surface-level V-I progressions). In the for-mer passage, Schumann creates an antimetrical 6-layer by regular alternationbetween instrumental groups containing the first violin (sometimes only that in-strument), and groups lacking the first violin. In mm. 60-61, the antimetrical 6-layer arises from an alternation between maximally thick and thin textures.

Metrical connections between the third variation and earlier portions of themovement, then, are manifold. Another dissonance that is weakly presented inthe third variation, on the of her hand, provides links to the following variation,namely Gl.5/1 (l=8th). The groups of six sixteenth notes in the violin parts oc-casionally divide on the basis of contour into subgroups of three sixteenths (forexample, on the first and third beats of in. 49), while the plucked eighth notes ofcello and viola maintain the expected two-sixteenth-note pulse.

The fourth variation (mm. 64-76) is dominated by G3/2, a relative ofGl.5/1 (Example 8.33); an alternation between embellished I and V harmonies

EXAMPLE 8.32. Metrical dissonance in Variation 3

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EXAMPLE 8.33. G3/2 in Variation 4

(over atonic pedal) delineates the metrical 3-layer, while the cello attacks andmelodic pattern repetitions in the upper instruments form a 2-layer. Aside fromthe connection with the G 1.5/1 of the preceding variation, there are two addi-tional subtle relationships between the fourth variation and the earlier sections.First, by various means — dynamic accents in the viola in in. 65 (the first mea-sure of Bxample 8.33), durational accents and tenutos in the first violin in mm.65—69, etc. — Schumann creates D6+3, which he already employed in the themeand third variation. In addition, the fourth variation includes allusions to D6+1,which is related to the D3+1 employed in the first variation; the hairpins in mm.

65 and 67 result in dynamic accentuation of the second pulses of three-eighth-note groups.

The metrical structure of the fourth variation, however, makes sense pri-marily in relation to the following music. The fifth variation, unlike all of theothers, is in duple meter. The fourth variation's G3/2 is thus a "passing disso-nance" between the triple consonance of earlier variations and the duple conso-

nance of the fifth (Example 8.34).The fifth variation is primarily consonant (4/2), with only a few allusions to

D4+1 (created by registral accents in mm. 77, 79, and similar measures) andD+3 (formed by dynamic accents in mm. 78 and 80), which are tightened toD2+1 at the end of the variation (in. 88). The statement of D2 + 1 coincides with

EXAMPLE 8.34. Resolution of G3/2 at the beginning of Variation 5

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EXAMPLE 8.35. Recall of motiviv dissonances at the end of the second mvmt. of Robert Schumann's

String Quartet op. 41 no. 2

an interesting hypermetrical dissonance. The latter half of in. 88 and the firsthalf of in. 89 constitute new material that expands the prototypical mm. 83—84.This expansion creates indirect G24/16 (three measures against two measures),an augmentation of the mid-level dissonance of the preceding variation (G3/2).The coincidence of G24/16 and D2+1 adds considerable tension to the finalmeasures of the variation.

The fifth variation is followed by a return of the theme. The return is virtu-ally identical to the opening statement, but there is an interesting addition in theform of the introductory El's in the viola. The function of these two attacks maybe to "modulate" from the duple meter of the fifth variation to the primary triplemeter, for the first El occupies two eighth-note pulses, the second, three. Thetwo attacks also immediately reintroduce the main metrical dissonance of themovement, D3+2, for the second Et is displaced.

The following coda beautifully summarizes the metrical dissonances of themovement. Since it is based primarily on the third variation, it is not surprisingthat it alludes to D6+3. That dissonance is, however, considerably weaker in thecoda, where its antimetrical layer is merely suggested by the slurring in the firstviolin and viola parts (mm. 105-10). Near the end, Schumann reminds us oncemore of the main dissonance of the movement; D3+2 makes a final appearancein the last two measures (Example 8.35), where dynamic accents appear on thethird eighth notes of groups of three. The sforzando on the third eighth note ofthe final measure, however, in conjunction with the tempo and articulationchange two eighth notes later, also suggests a duple partitioning of the eighth-note pulse and hence recalls G3/2, the dissonance of the fifth variation.

As Eusebius turned the page, Florestan remarked, "Your slow movement isindeed a beautiful one. It nicely leads into my third movement, too, in which Itake up the second movement's main dissonance, D3+2, at a faster tempo (in mm.5-6, 12-16, etc.)."

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The next section, they saw, dealt with the music of a composer namedCharles Ives, of whom they had never heard. As Eusebius leafed through thesection, they caught sight of the musical examples. Florestan, appalled by theharsh harmonies of Example 8.37, shouted, "Is this the music of the future?" Eu-

sebius attempted to soothe him by saying, "That example is indeed dreadful, butthe others do not displease me as much. Please listen to the analysis before youexcite yourself."


Even the early tonal songs of Charles Ives contain interesting metrical disso-nances. The Lenau setting "Weil auf mir" of 1902 is notated in six-eight time,and the 12- and 6-layers (1 = 16th) suggested by the time signature are clearlyarticulated in the piano part. The remaining layer that one would expect, how-ever— a 2-layer — is only latent; the six-sixteenth-note arpeggiating figure in theleft hand of the piano consistently divides into two groups of three on the basis

EXAMPLE 8.36. Metrical dissonance at the climax a) Charles Ives's "Weil auf mir" (mm. 27—30).

© 1955 by Peer International Corp. International Copyright Secured. Reprinted by permuuian.

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EXAMPLE 8.37. G6M and G4I3 in Ives's "West London, " mm. 13-14. From Thirty Four Songs.© 1933 Merion Music, Inc. Used by permission.

of contour, the 3-layer and the latent 2-layer resulting in subliminal G3/2. Du-plet quarter-note attacks in the voice and the piano's right hand frequently re-inforce the 3-layer. In the final, climactic phrase of the song, metrical dissonancebecomes most intense; Ives adds a displacement dissonance to the subliminalgrouping dissonance (Example 8.36). As voice and left hand continue the3-layer, the right hand states octaves that occupy six pulses each; the resulting6-layer is not, however, coordinated with the metrical 6-layer of the left hand.The displaced 6-layer, remote from the metrical context, suggests the "lonelyhovering" of the beloved over the poet's existence to which the final line of textrefers,

"You see, Florestan," remarked Eusebius, "this composer coordinates metricaldissonance with poetic meaning, just as we did." Florestan only grunted noncom-mittally, and Eusebius continued to read.

Even more adventurous dissonances are found in the radical later songs.In "West London," for example, the vocal line, derived from the hymn tune"Fountain," usually articulates the common time and hence the 4-layer (l=8th)of that tune by means of durational accents, occasionally by of her means suchas pitch recurrence and new-event or registral accentuation.47 In the first sec-tion of the song, Ives superimposes various ostinatos on the vocal allusions tothe tune, the pattern repetitions of each ostinato creating a variety of layers.The resulting metrical states are G6/4 (mm. 1-7), consonance (mm. 9-11), andG6/4/3 (mm. 11-14 —Example 8.37). The remainder of the song is virtuallyconsonant; Ives brings the piano into alignment with the voice and in the end,when the hymn tune is fully unveiled, even allows the piano to double the voice.The metrical progression is clearly tied to the form and content of the text. Ivesassigns a different state to each couplet of Matthew Arnold's sonnet through theend of the octet, and sets the sestet apart from the octet by consistent conso-nance. The underlying metrical narrative of the song — the progress toward con-

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sonance — suggests progress from a time out of joint toward the "better time"mentioned in the final line.

Florestan admitted grudgingly, "I suppose the man does know what he is doing."Eusebius smiled and read on:

The lovely little song "Two Little Flowers," from the same period as "WestLondon," is less adventurous in pitch structure, but no less interesting in termsof meter. A summary follows:

1. Main recurring dissonances: G8/7/4 (l=8th).

2. Families of dissonances operative in the movement: none.3. Recurring juxtapositions or superpositions: none, aside from the obvious

G8/7 and G7/4.

4. Proportion of primarily consonant and primarily dissonant passages:mostly dissonant.

5. Amount of subliminal dissonance: none. All dissonance is on the surface.

6. Frequency of change of metrical state: infrequent (change at mm. 9, 13,23 only).

7. Basic metrical narrative: struggle between the 7-layer and the metrical8/4 consonance; eventual resolution to 8/4.

The text, with its almost consistent iambs, suggests duple meter, and Ives

roots the vocal melody securely in common time. He not only sets the text insuch a way that metrical accents (on beats one and three) and textual accentscoincide, but generally reinforces the metrical accents with registral and dura-tional accents. In mm. 3, 6, 8, 19, 21, 23, 24, and 25, for instance, registral ac-cents occur on downbeats, and in mm. 4, 6, 7, 9, 13, and 15, there are durationalaccents on first and/or third beats. Because of the placement of textual and mu-

sical accents, the metrical 8-layer and the subsidiary 4-layer (1 =8th) are veryclear in the voice. This is not to say that Ives allows the vocal line to conveythese levels consistently; some of the fascinating weeds within the voice's met-

rical flowerbed are mentioned below.The piano accompaniment, evoking the strumming of a guitar or the pluck-

ing of strings (the uppermost pitches in fact correspond to three of the openstrings of a violin), begins with a pretense of setting up the metrical 8- and 4-

levels; the registral accent on E5 appears at first to bisect a metrical group ofeight eighth-note pulses (Example 8.38a). One might expect Ives to proceed byrepeating the pattern encompassed by the opening measure, but this expecta-tion is promptly defeated; the final eighth note of in. 1 instead acts as the begin-ning of a second group of seven eighth notes, and further repetition of theseven-note pattern results in a 7-layer, strongly dissonant against the metrical 8-and 4-layers.

The dissonance G8/7/4 is uprooted at several points within the song, thedisruptions occurring within the voice, the piano, or both. The vocal line firstdeviates from its plodding 8/4 consonance at the end of the first stanza (mm.

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EXAMPLE 8.38. Metrical dissonance in Ives's "Two Little Flowers. "From Nineteen Songs. © 1935

Merion Music, Inc. Used by permission.

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9—10 — see Example 8.38b), where durational accents and recurrence of D4 re-

sult in durations of five and nine eighth notes. Significantly, five plus nine equals

fourteen (two times seven); Ives seems to be sowing the seeds of a rapproche-

ment between the metrical strata of voice and piano. This strategy comes to

fruition in mm. 13 and 14, where the voice's reiteration of the notes B4-G4-A4

suggests two pulses of a 7-layer, aligned with that of the piano. Some sensation

of metrical dissonance, however, lingers in mm. 13-14; the durational accents of

the voice part, falling on the A4's, result in a different 7-layer that is not aligned

with that of the piano.

The disruptions of G8/7/4 in the piano part are more frequent and regular;

beginning at in. 10 (Example 8.38b), they occur every four measures, in coor-

dination with the four points of harmonic change that precede the harmonically

more active final phrase, and also in coordination with the ends of couplets

(mm. 14, 18, 22). From in. 14 onward, the disruptions result, like those already

discussed, in a metrical rapprochement between piano and voice; tendrils from

the vocal layers creep into the piano at each of these points, the prevailing 7-

groups being curtailed to groups of four. The effect of these curtailments of the

piano's 7~layer is the alignment of voice and piano at the first accented syllable

of three successive couplets (marigold, violet, lovliness [sic]). Temporary resolu-

tion of dissonance thus articulates the form of the poem.

The incursions of the 4-layer into the piano part and the resulting tempo-

rary resolutions herald the subsequent definitive resolution of G8/7/4 into the

primary consonance 8/4: in mm. 23—27 — the final vocal measures, encompass-

ing the "punch line" of the poem — piano and voice are perfectly in accord, both

conveying the metrical layers (Example 8.38c). The postlude quickly reviews

the song's basic metrical progression by briefly bringing back the 7-layer (indi-

rectly dissonant against the immediately preceding consonance 8/4), then re-

verting to 8- and 4-layers (albeit displaced) in the final two measures.

There is an intriguing extramusical explanation for the prevalence of the

7-layer in the song: one of Ives's "little flowers," his adopted daughter Edith,

was seven years old in 1921, the year in which the poem and the song were


Eusebius pointed out, "Here is another link between this composer and us:

he hides biographical details within his music, as we so often did in our youth.

He looked ahead to the next section and said, "Ah, Florestan, here comes an

analysis of one of your finest recent movements," and began to read.



1. Main recurring dissonances: G6/4, D6+4 (l=8th).

2. Families of dissonances operative in the movement: "G6/4" (the diminu-

tion G3/2 and the augmentation G36/24 appear frequently).

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3. Recurring juxtapositions or superpositions: the two main dissonances,

G6/4 and D6+4.A. Proportion of primarily consonant and primarily dissonant passages:

about equal.5. Amount of subliminal dissonance: much subliminal G6/4.

6. Frequency of change of metrical state: varies from section to section

(e.g., increasingly frequent during the first theme, infrequent during the

second theme).7. Basic metrical narrative: constant struggle between 6- and 4-layers, the

former, and metrical consonance, ultimately being victorious. Subplot:

intensification of D6+4.

To superficial listeners, the first movement of Schumann's Third Symphony

(chronologically, his fourth and final symphony) will appear to begin with two

juxtaposed metrical consonances (see Example 2.5). The first six measures ap-

parently establish the consonance 12/4/2 (l=8th). The 12-layer is created by a

slow rising arpeggiation of the tonic harmony in the first violins and flutes (El>5-

G5-Bl>5), the 4-layer by new-event melodic accents and durational accents in the

first violin, cello, and double bass, and the 2-layer by new-event accents in the

second violin and viola (not shown in Example 2.5). This apparent duple meter

collides in the second phrase segment (mm. 7-13) with a different surface-level

consonance, 12/6/2. The 12-layer is here formed by the attacks of a descending

line in the melody (At-G-F-El>), and the new 6-layer arises from harmonic

changes and from durational accents in first violins and flutes.

More sophisticated listeners will not perceive this opening as being fully

consonant. They will note that the collision of 6- and 4-layers at the intersectionof these two surface-level consonances results in indirect G6/4. They might also

observe that the initial 4-layer conflicts with the conductor's beats, which

•would, at the movement's quick tempo, express the metrical 6-layer. They would,furthermore, perceive in. 7 as the point of resolution of this conflict. Even with-

out watching the conductor, I believe, the attentive listener would gain from in.

7 an impression of resolution, or at least relaxation, as a result of the broadeningfrom a governing 4-layer to a 6-layer.

The score, of course, makes perfectly clear that the movement begins withsubliminal G6/-4, resolved at in. 7 into the primary consonance (with indirect

G6/4 lingering during the first few beats of the consonance). At mm. 11—14,

Schumann brings G6/4 to the surface; the 4- and 6-levels are presented simul-taneously for the first time, the 4-layer being articulated by the attacks of thecello, bass, bassoons, and brasses, the 6-layer by durational accents in the re-

maining instruments. In mm. 13-18, the dissonance is again submerged; Schu-mann repeatedly juxtaposes 4- and 6-layers, but no longer superimposes them.The juxtaposition here occurs at much closer intervals than at the opening; the4-layer is active in mm. 13-14, the 6-layer in mm. 15-16, and the 4-layer once

again in mm. 17—18. Because of: the increasing frequency of metrical change,mm. 1-20 give the impression of increasing instability.

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238 Fantasy Pieces

This first section of the movement introduces two metrical dissonances

aside from G6/4 that are significant later on: the displacement dissonance D6+4and the hypermetrical dissonance G36/24. The former dissonance appears at

the end of the section. Measure 19 reinstates the metrical 6-layer (by durational

accents in the melody) while also alluding to the 4-layer (cello and bass). As thelast quarter note in the bass of in. 19, however, is tied to a halt note instead of a

quarter, G6/4 fails to materialize, and a hint of D6+4 emerges instead.

G36/24, an augmentation of G6/4, arises from juxtaposition or superposi-tion of four- and six-bar hypermeasures. It is possible to hear mm. 1-20 in four-

bar segments, most of them marked off by prominent new harmonies: the domi-

nant in in. 5, a tonic substitute in in. 9, an actual tonic in in. 13, another dominantin in. 17, and the tonic in in. 21. There is, however, some conflict against this

four-square hypermeter. The initial motion from music dominated by the 4-layer

to music dominated by the 6-layer, and the resolution of the initial subliminal dis-sonance, occurs in in. 7, so that one gains a strong impression of a hypermetrical

boundary at that point. The beginning of another six-bar hypermeasure could be

heard at in. 15, because of the confluence of the initiation of a prominent newharmony (V of V), of the first dynamic accent in the movement, of a registral ac-

cent in the high strings and woodwinds (created by a leap of a ninth!), and of a

shift from 4- to 6~layer domination. The hypermetrical dissonance is weak at thispoint, but is worth noting because of its later importance.

The remainder of the exposition continues to dwell on the same metrical

material, and begins to develop it. During the second section (the second part ofthe first theme area — mm. 21 — 56), Schumann continues the alternation be-

tween two surface-level consonances (or between subliminal dissonance and

consonance). The alternation no longer proceeds at regular time intervals, sothat the aforementioned sense of instability becomes somewhat more pronounced

in this section. Like the first section, the second ends with a decrease in the du-

rations occupied by individual metrical states (four measures of 12/4/2, then sixmeasures of 12/6/2, then four measures of 12/4/2, eight of 12/6/2, four of 12/4/2,

two of 12/6/2, four of 12/4/2, and four of 12/6/2).Although the section brings no striking metrical innovations, some of the

thematic metrical states come into sharper focus. The two rival surface conso-

nances (and hence the primary consonance and subliminal dissonance) collide

more sharply than ever before at mm. 47-52, where each state is associatedwith one of a pair of repeated segments. At the half-cadence at mm. 47-49 (Ex-ample 8.39a), Schumann makes use of the primary metrical consonance 12/6/2,

whereas during the immediately following varied repetition he reshapes the ca-dence into a form governed by f2/4/2 (and, subliminally, G6/4—mm. 51—52).

The hypermetrical dissonance suggested within the first section also becomes

more prominent during mm. 21-56. Whereas four-bar hypermeter reigns be-tween mm. 31 and 51, change of metrical state results in hypermetrical down-beats at mm. 25, 31, 51, and 57. These boundaries, in turn, result in the juxta-

position of four-bar and six-bar hypermeasures in mm. 21 — 31 and 47—56, and

hence in indirect G36/24.

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Carnaval des analyses 239

EXAMPLE 8.39. Metrical dissonance in the exposition of the first mvmt. of Schumann's Symphony

no. 3

At the very end of the first theme area (mm. 53-56), Schumann introducesindirect G3/2, a diminution of G6/4; the reiterated rhythm of the cellos and

basses suggests a 3-layer, which conflicts with the 2-layer of the surrounding

measures. This distinctive dissonance was already broached by allusions to a 3-layer at mm. 25, 27, and 29. Its clearer emergence at mm. 53—56 sets the bound-ary between first theme and transition into relief.

The transition (mm. 57-94), largely modeled on the first theme, continuesto alternate 12/6/2 and 12/4/2, and to present some indirect hypermetrical dis-

sonance by juxtaposing four-bar and six-bar hypermeasures. Measures 73—76,

for instance, constitute a four-bar dominant prolongation, mm. 77-82, a six-barsequential passage, and mm. 83-86 represent the first of several four-bar hy-

permeasures delineated by melodic and harmonic recurrences. The latter por-tion of the transition entrenches itself ever more firmly into the primary conso-nance 12/6/2. One of the portions of the first theme that was dominated by

12/4/2 (mm. 21-24) is omitted from the transitional restatement; mm. 77-82,instead of restating mm. 21-24, go on to the material of in. 25, which is basedon 12/6/2. The final measures of the transition (mm. 83-94) are virtually con-

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240 Fantasy Pieces

sonant. Only a hypermetrical displacement dissonance, D24+6, slightly rufflesthe metrical surface; the displaced layer is produced by dynamic accents on thesecond downbeats of the four-bar hypermeasures at mm. 83-86 and 87-90.

The almost total elimination of metrical conflict at the end of the transitionprepares the second theme area, which begins with the primary consonance(mm. 95—111) . The initial bars of the second theme are, however, touched byhypermetrical dissonance. The melody of the second theme divides clearly intofour-bar hypermeasures, but at in. 97 the local tonic of G unexpectedly appearsin the cellos and basses under the dominant-prolonging winds. The adherenceto the bass-note G for six measures results in conflict against the four-bar hy-permeasures of the melody, and thus in an allusion to direct G36/24.

At in. 1 l l , the long-absent 12/4/2, creating the usual indirect and sublimi-nal G6/4, breaks out with a vengeance and remains in effect for no less thantwelve measures (Example 8.39b). A four-bar prolongation of V of V of Gminor (mm. 123—26), reverting to the primary consonance, ends with a brief al-lusion to D6+4, created by syncopation in first violins and high winds. At mm.

127—38, the second theme material reappears. This material, formerly conso-nant (except for a brief hypermetrical conflict), now absorbs the preceding dis-

sonance D6+4, which is formed by added syncopation in the second violins andhigh winds (mm. 135—38). D6+4, then, thus far of peripheral significance, be-gins to gain ground. The following precadential section articulates first theprimary consonance (mm. 139 — 52), then 12/4/2 (mm. 153 — 62). In the latterpassage, the 4-layer is announced with unprecedented emphasis by dynamic ac-centuation in the brasses in mm. 157—58, and in all instruments in in. 159. Thecadence at mm. 163 — 65 reverts to the primary consonance.

The rate of metrical change in the second theme is much slower than in thepreceding sections; individual metrical states last much longer than before. Thisincreased metrical stability lends most of the section an Eusebian quality, in

strong contrast to the Florestanian character of the surrounding music.The closing theme begins with a reappearance of D6+4 (mm. 165 — 72 — Ex-

ample 8.39c), which is resolved into the primary consonance at the end of eachof two four-bar hypermeasures. The following reiterations of the authentic ca-dence remain metrically consonant. In order to prevent tin effect of completemetrical resolution at the conclusion of the exposition, Schumann brings back

12/4/2 and its attendant indirect and subliminal G6/4 dissonances in mm.177-80.

To summarize, the most pervasive dissonance of the exposition is G6/4. It isintroduced in subliminal and indirect form, then surfaces at several points andis ultimately intensified by the use of dynamic accents. A hypermetrical aug-mentation of this dissonance appears intermittently. The displacement disso-nance D6+4 is introduced very gradually, beginning with momentary allusionsand culminating at a rather extensive statement within the closing theme.

Rather than analyzing the remainder of this long movement in comparable

detail, 1 restrict the following discussion to a tracing of the further careers of themetrical states established within the first twenty measures.

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Carnaval des analyses 241

G6/4, the key metrical player of the exposition, recedes into the back-

ground during much of the development section; Schumann, knowing that the

recapitulation will of necessity feature this dissonance, avoids it during most ofthe development section. It does appear indirectly and subliminally duringthose portions of the development that allude to the first theme material (mm.273-93 and 311-27). Furthermore, it is represented by relatives—by aug-mentations and diminutions already found in the exposition. The developmentsection begins with intermittent G3/2. Allusions to this diminution alreadyoccurred during the exposition, as was mentioned, but in mm. 187—88 and 195—96 the 3-layer that creates the dissonance is articulated with unprecedentedclarity by triad arpeggiations in bass instruments. The augmentation G36/24appears frequently, for example at mm. 209-20 and the related mm. 247-72.Both points involve not only indirect but also direct hypermetrical dissonance.At in. 209, a series of six-bar hypermeasures intrudes into a context in whichfour-bar segments prevailed, resulting in indirect, then direct G36/24. The di-rect portion of the dissonance is shown in Example 8.40a. The six-bar units

(shown in the example as 36-pulses) are delineated by large-scale harmonicchanges (D major to G major), the four-bar segments (24-pulses) by surfaceharmonic patterns (D major to G minor in mm. 215—18 and D major to G

major in mm. 219-22). This music is subsequently transposed (mm. 247-72),resulting in a similar progression from indirect to direct G36/24. The process ofrendering an indirect dissonance direct, applied to G6/4 within the first section

of the movement, is here extended to the augmentation of that dissonance aswell.

The development of D6+4 is even more interesting. This dissonance, of sec-ondary though increasing importance in the exposition, moves into the limelightearly in the development section. The material comprising the parallel sectionsin mm. 215-22 (Example 8.40a) and 259-72 begins with D6+4, which is sub-

sequently loosened to D12 + 10 at mm. 217 and 261, where ties appear only onalternate upbeats. Between the two parallel passages, at mm. 253-57, lies an-other prominent statement of D6+4, created by a 7-6 suspension chain. (This

chain reappears at mm. 351-55.) D6+4 not only becomes more pervasive in thedevelopment section, but is also intensified by the frequent addition of dynamicand registral accents to the durational accents that previously created the anti-metrical 6-layer (at mm. 299-301, 307-9, and 333-35).

Whereas I have discussed the development of the motivic grouping anddisplacement dissonances separately, the two types actually intersect at timeswithin the development section. Schumann applies a typical developmentalstrategy—the bringing together of materials earlier stated separately—to themetrical dissonances. One such encounter between dissonances of differenttypes occurs during the second of the two 7-6 chains mentioned above; at mm.351—54, D6+4 is counterpointed by G3/2, the 3-layer resulting from new-eventmelodic accents in the second violin and viola. A dramatic juxtaposition of G6/4and D6+4 occurs in the retransition (Example 8.40b). That section begins witha magical moment; against a static background of tremolos and sustained notes,

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242 Fantasy Pieces

EXAMPLE 8.40. Metrical Dissonance in the development section of the first mvmt. of Schumann's

Symphony no. 3

the horns portentously present a metrically consonant version of the openingtheme (mm. 367—70). From this form, there emerges the usual subliminally dis-

sonant "duple" version of the theme, which now sounds like a distortion of the

consonant form (mm. 371—73). Immediately thereafter Schumann launches into

a suspension chain whose upbeat preparations are emphasized by dynamic ac-

cents (resulting in strong D6+4). Thus Schumann reminds us at a significant

formal boundary of the primary metrical consonance and of the two mam ways

in which it is contradicted during the movement.

Another juxtaposition of D6+4 and G6/4 concludes the development sec-

tion. The former dissonance appears in mm. 399—402, the displaced layer an-nounced by cellos, double basses, trumpets and tympani. Subliminal G6/4 im-

mediately follows, heralding the triumphant recapitulation.

A few words about the recapitulation and coda must suffice. The recapitu-

lation is much like the exposition in terms of metrical structure. In terms of hy-

permeter, however, it differs significantly; several passages of the expositionthat involved hypermetrical dissonance are not recapitulated (mm. 25—30,

51-56, and 77-87), so that the recapitulation contains less hypermetrical dis-

turbance than the exposition. The recapitulation thus paves the way for the

coda, which, not surprisingly, performs a resolving function.The coda contains many statements of the motivic dissonances, followed by

emphatic resolutions. The resolution of the indirect and subliminal G6/4 at mm.531-33 is particularly interesting. Most G6/4's in the movement resolve at the

end of a cycle; that is, the 4-laycr continues until a pulse of the metrical 6-laycr

(i.e., a bar line) is reached. Schumann could easily have resolved the G6/4 at

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Carnaval des analyses 243

EXAMPLE 8.41. Hypothetical and actual resolution of metrical Dissonance in the coda of the first

mvmt. of Schumann's Symphony no. 3

mm. 531—33 in the same manner, as is shown in Example 8.41a. Instead, he ex-tends the chord of in. 533 to a six-pulse duration and follows it with a two-pulseduration (Example 8.41b). The displaced six-pulse duration results in an allu-sion to D6+4, and hence in another intersection of the two motivic dissonances.

D6+4 returns more explicitly at mm. 543-45, where its antimetrical layerresults from durational and dynamic accents. The succeeding passage, in whichthe downbeats are emphasized by corrective durational and dynamic accents,firmly resolves the dissonance. At mm. 563-68, subliminal and indirect G6/4appears for the last time, and is then resolved just as firmly as was D6+4; fromin. 569 onward, the metrical 6-layer is conveyed without contradiction by dura-tional, and often by dynamic, accents. Aside from a brief allusion to the high-level dissonance D12+6 in mm. 571-75 (in the form of passionate appoggiaturasin weak hypermeasures), Schumann maintains a state of metrical consonanceuntil the end of the movement. V

They sat awhile in silence, reveling in these ecstatic final measures, and en-tirely ignoring Dr. Richarz, who had entered the room with a cheerful "Goodday, Herr Doktor Schumann" as Eusebius was finishing the section. The doctornoticed the empty tray near the open window, looked out, and shook his headwhen he saw what had happened to its contents. He wrote in his notebook, "Hemoves his lips as if talking to himself, seems to be suffering from aural hallucina-tions again, and has eaten nothing,"49 then took his farewell. Eusebius turned tothe final section of the manuscript and read:

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244 Fantasy Pieces


In his essay "Brahms the Progressive," Arnold Schoenberg cites in. 49 from thefinale of Mozart's String Quartet in D minor, K. 421, as an example of "poly-

rhythmic construction."50 In order to highlight this aspect of the excerpt, he

renotates the various voices in different meters. The dynamic, registral and du-

rational accents in the first violin line suggest to him a quadruple grouping of the

twelve sixteenth-note pulses of Mozart's six-eight measures; thus he rewrites this

line in three-four time. Mozart's dynamic accents on the fourth and tenth sixteenth-

note pulses in the second violin part strongly imply a triple grouping of thetwelve sixteenths; Schoenberg therefore notates this line in twelve-sixteen meter.

In the viola part, Schoenberg adheres to Mozart's notated meter; the dotted-

quarter beats of six-eight time are indeed reinforced by dynamic accents and by

the repetition of a triadic pattern. While the cello attacks actually suggest six-

eight time as well, Schoenberg renotates the cello part in two-four time, appar-

ently carried away by his desire to demonstrate "polyrhythmic construction." Ina second Mozart excerpt cited in the same essay, from the Minuet of the C-major

Quartet, Schoenberg draws attention to a 5-layer (l=quarter) in the first violin

line, created by the immediate repetition of a melodic segment. Schoenberg doesnot comment on the passage in detail, but it is apparent that he is again intent on

illustrating "polyrhythmic construction"; the 5-layer is superimposed on a 3-layerin the lower voices, determined by the repetition of: the rhythmic pattern "quar-

ter note, quarter rest, quarter note."Schoenberg's interest in metrical dissonance, already evident from the above

analyses of Mozart excerpts, is even more amply demonstrated by his own music.

I discuss only one example here: the "Valse de Chopin" from Pierrot lunaire.51


1. Mam recurring dissonance: G6/4 (l=8th).

2. Families of dissonances operative in the movement: "G6/4."

3. Recurring juxtapositions or superpositions: none.

4. Proportion of primarily consonant and primarily dissonant passages:

mostly consonant (17 dissonant measures out of 44).5. Amount of subliminal dissonance: very little (in. 17 only).

6. Frequency of change of metrical state: fairly infrequent (changes at mm.

14, 18, 27, 32, and 41 only).7. Basic metrical narrative: C-D-C-D-C-D; struggle between 6- and 4-layers

appears to end with victory of the metrical 6-layer, but the 4-layer taints

the ending.

The movement is based throughout upon the interaction of the metrical 6-

layer and a 4-layer (l=8th). Initially, Schoenberg imposes a 12-layer on theeighth-note pulse, that interpretive layer being created by durational accents in

the bracketed (most prominent) voices on the downbeats of mm. 2, 4, 6, and 8.

luisa balaguer

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Carnaval des analyses 245

EXAMPLE 8.42. Layers of motion in Schoenberg'd "Valde 'de Chopin" from Pierrot lunaire, mm.

9-16. Used by permission of Belmont MusicPublishers, Pacific Palisades, CA 90272. © 1914 by

Universal Edition. Copyright renewed. All rights reserved. Used in the territory of the world excluding

the United Stated by permission of European American Music Distributors) Corporation, sole Cana-

dian agent for Universal Edition.

The metrical 6-layer is suggested by the successive durational accents on the

downbeats of mm. 6 and 7 (in piano and voice, respectively), then clarified bydurational accents and rhythmic pattern repetitions in mm. 9—16. The various

repeated rhythms, as well as the durational accents on downbeats in the latter

passage, are shown in Example 8.42.In mm. 12—16, Schoenberg superimposes a 4-layer on the 6-layer, creating

G6/4. The antimetrical layer is at first produced by the repetition of the dactylicpattern "2-1-1" (l=8th) in the piano (mm. 12—13), then by the repetition of "3-

1" in piano and voice (mm. 14—17 — Example 8.43). In in. 17, the 4-layer tem-

porarily ousts the metrical 6-layer, rendering G6/4 subliminal. In mm. 18—19,

however, the 6-layer conquers and in fact engulfs the 4-layer. In in. 18, Schoen-berg adds a quarter note to the "3-1" pattern and reiterates the resulting rhythm

("3-1-2") in the voice part of in. 19. The pattern that created the 4-layer (3-1)thus becomes a component of a larger pattern that forms a 6-layer.

In mm. 19 — 20, the reiterated rhythm "4-2" in the piano reinforces and con-

tinues the 6-layer, and in mm. 21—22, while no layer larger than a 2-layer clearly

interprets the eighth-note pulse, the dynamic accent in the flute briefly refers to

the 6-layer. That layer is strongly reinforced in mm. 23—26 by the suggestion of

a three-quarter-note "oom-pah-pah" accompaniment in the piano part and by

the repetition of "3-1-2" in the clarinet (mm. 24-25).

In mm. 27—29, the climactic measures of the movement (Example 8.44),

G6/4 reappears. The 4-layer arises, as in mm. 14—18, from the reiteration of a "3-

1" pattern. The 6-layer is delineated by changes of rhythmic pattern rather than

by repetition of pattern; in mm. 27-29, six-eighth-note durations (measures) are

respectively occupied by steady sixteenth-note motion, then eighth-note motion,

then sixteenth-note motion again (in the flute — not shown in the example).After the climax, Schoenberg allows the 4-layer and the dissonance G6/4 to

peter out. He abandons the 4-layer briefly at the beginning of in. 30, brings it

back (now displaced in comparison to the climactic measures) for two morepulses as the voice reiterates the "3-1" rhythm, then eliminates it entirely forsome time (see the last beat of Example 8.44). The 6-layer is, throughout mm.

30-41, created by various repeated patterns.52 It is noteworthy that in mm.30-41 pattern repetitions occur in pairs of measures, resulting in a 12-layer inaddition to the 6-layer; this 12-layer is clearly evident in the piano part in mm.

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246 Fantasy Pieces

EXAMPLE 8.43. Schoenberg, "Valse de Chopin," mm. 14-19, piano and voice parti. Used by

permission Belmont Music Publishers, Pacific Palisades, CA 90272. © 1914 by Universal

Edition. Copyright renewed. All rights reserved. Used in the territory of the world excluding the

United States by permission of European American Music Distributors Corporation, sole

Canadian agent for Universal Edition.

30-31, 32-33, 34-35, 38-39, and 40-41. Mm. 36 and 37 have the same resul-

tant rhythm and thus also contribute to the delineation of the 12-layer. Since the

12-layer is so clearly articulated in mm. 32-41, these measures recall the met-rical consonance of the opening of the movement (12/6/2).

Schoenberg could easily have ended the movement as consonantly as he

began it. Instead, he hints once more at G6/4; he alters the pattern of mm.40-41 by the elimination of a quarter rest, resulting in the reiteration of a four-

eighth-note pattern and hence in the suggestion of a 4-layer. The final two A#'s

also occupy four eighth-note pulses each (although the resulting 4-layer is notaligned with the earlier one). Thus the dissonance G6/4 faintly colors the ending

— like a pale drop of blood on the lips of an invalid (Example 8.45).

Florestan had become increasingly restless as he had looked over the musical

examples for this section. As Euscbius looked on helplessly, he now sprang upand shrieked, "On these tones rests a destruction-seeking drive. These are chordsof wild lust that disturb icy dreams of despair. Hotly jubilating, sweetly Ian-

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EXAMPLE 8.44. Schoenberg, "Valse de Chopin, " mm. 27-31, piano and voice parts. Used by per-

mission of Belmont Music Publishers, Pacific Palisades, CA 90272. © 1914 by Universal Edition.

Copyright renewed. AIl rights reserved. Used in the territory of the world excluding the United Stated

by permission of European American Music Distributors Corporation, sole Canadian agent for

Universal Edition.

EXAMPLE 8.45. Schoenberg, "Vase de Chopin," mm. 40— 44, piano part. Used by permission of

Belmont Music Publisher.), Pacific Palisades, CA 90272. © 1914 by Universal Edition. Copyright

renewed. All rights reserved. Used in the territory of the world excluding the United States by

permission of European American Music Distributors Corporation, sole Canadian agent for

Universal Edition.

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248 Fantasy Pieces

guishmg, melancholy somber waltz, you shall haunt me forevermore!" As his in-creasingly incoherent shouts merged into a prolonged scream, he seized the man-uscript and attempted to tear it in half, but desisted abruptly and fell silent as abird landed on the window sill and gazed at him reproachfully. Florestan shrankback and whispered, "It is a vulture, waiting for my carcass." Their avian visitorsnorted, "A vulture, forsooth! Do you not remember me? I am the Prophet Bird,and I beg you not to damage that manuscript, for I must return it unharmed to itsauthor. In fact, since you appear to be finished with it, I had better collect it now.I trust you have enjoyed most, if not all, of it." As Eusebius looked on, Florestanwalked slowly to the window and held the manuscript out to the Prophet Bird,who took it in his beak and, flapping his wings vigorously, departed through thewindow.

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'Epilogue: Morning Song

This epilogue is an attempt to recreate an effect of "metrical dissonance" in wordsby superimposing "noncongruent" layers of discourse. My aim is to suggest bysuch superposition the mental and emotional state of Robert Schumann in theasylum at Endenich in June of 1856. In one of the three strands, that which Ihave labeled "R" (for "Robert"), Schumann reminisces quite rationally about hisrecent past. I have counterpointed with this strand two others, occupied primar-ily by trains of thoughts that I imagine were, consciously or subconsciously, al-most constantly active within Schumann at Endenich: one expressing a longingfor Clara, the of her, a longing for death. The former train of thought is here as-signed to Eusebius ("E."), the latter to Florestan ("F"). The three brief utterancesof the caretaker ("C.") make no impression on the main interlocutors; Schumannhas withdrawn so completely into himself that no words from outside are able toreach him.

The superposition of these three strands is an obvious "surface-level" disso-nance within the epilogue. The epilogue is also, however, characterized by a"subliminal" dissonance in the form of a superposition of three disparate func-tions and meanings. It can be read not only in the manner mentioned above butalso as an appendix to the sixth chapter — as a list of passages from Schumann'ssongs in which emotional states are highlighted or musically represented by met-rical dissonance. All of the utterances of Florestan and Eusebius are drawn fromtexts (in my translations) that Schumann set in a metrically dissonant manner.Interested readers may consult the footnotes for the location of the passages. Ihave not provided measure numbers, as very few editions of Schumann's songsinclude them; the passages can most easily be found by searching for the givenGerman text excerpts.


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250 Epilogue

Finally, the epilogue can be read as a metrical map of the third of the Gesange

der Friibe, op. 133; hence its title. Not every aspect of my dialogue relates to op.

133 no. 3; for example, the repetitions within the Florestan and Eusebius strandsdo not correspond to musical repetitions. The numbers above the "Robert"strand, however, are the measure numbers of that work, and each strand of the

dialogue represents one of the layers of motion in the piece. The "Robert" strandstands for the metrical 9-layer (l=8th), which is active without interruption inthe piece. The beginnings of most measures are strongly accented, either dura-tionally (as in the pervasive dotted "crowing" motive), dynamically, or by signif-icant harmonic change.1 Even during the few brief passages \vhere the accentsdelineating the metrical layer are relatively weak (as in mm. 20—22), the listener

can easily maintain that layer. The "Florestan" strand represents a 9-layer shiftedforward by three eighth-note pulses. This displaced layer originates in in. 9,where the durational accent within the bass's version of the "crowing" motivefalls not on the downbeat (as it did in mm. 1—2 and 6 — 7) but on the second beat.The shifted 9-layer is later articulated by dynamic accents (in mm. 37, 42, 47, 49,and, very near the end of the piece, in mm. 60—61). The last chord, which regis-

trally accentuates the second beat, constitutes a final allusion to the antimetrical9-layer.

The "Eusebius" strand denotes a 3-layer, shifted by two eighth-note pulses.

Hints at this layer appear in the bass of mm. 1—2 and the treble of in. 3. In mm.4 — 6 it becomes virtually continuous, then fizzles out in in. 7. The same cycleoccurs within each recurrence of: the opening material (cf. mm. 23 — 29 and43-46). Within the intervening developmental passages, there are additionalinstances of the shifted 3-layer (mm. 13-14 and 31-40). Since the shifted3-layer disappears after in. 46, Eusebius ceases to speak at that point of the

dialogue.The caretaker's strand represents a more rarely appearing 6-layer, created in

mm. 4 — 5, 16-17, 26—27, and 54 — 55 by pattern repetition; at the former three

points, the right hand reiterates a contracted version of the "crowing" rhythm,and in mm. 54 — 55 the progression I—IV is repeated within three successive six-

eighth-note segments.Simultaneous utterances within the dialogue represent particular metrical

dissonances; simultaneous "Robert" and "Florestan" lines represent the disso-nance D9+3, coincidence of the lines of Robert and Eusebius represents D3+2,and coincidence of Robert's and the caretaker's lines stands for G9/6. The in-tersections of three interlocutors represent compound dissonances. The "Robert"

strand on its own represents metrical consonance.This Gesang der Friihe is, like most of Schumann's very late music, quite spar-

ing and conservative in its use of metrical dissonance. Nevertheless, metrical dis-sonance is an important and pervasive feature.

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Epilogue 251

1 2 3R.The rooster heralds another day at Endenich. So I am still here. It seems like a long time since I

F.E. In the morning In the morning I arise,

4 5 6R. was taken here. I know that if I must live, I must live in a place like this, and as such placesF.E. I arise and ask, "Is my darling coming today?"2 Thy blessed wondrousC. Good morning, Herr Doktor! Here's your breakfast!

7 8 9R. go, this is not a bad place. But why must I live at all? They should have left me in the river,F. When, when willE. image

10 11 12R. ah, cool, dark, endlessly flowing Rhine! I knew it was time to go. In my youth I sometimesF. the morning come that will free

13 14 15R. felt that I was a cog meshing tidily with of her cogs in the machine of society. I felt like aE.dwells in the depths of my heart.3 Lift me, lift me up to Heaven, my radiant star!4

16 17 18R.driving force, making things happen with my journal and with my music. My marriage and ourF. my life from these bonds?5 Where is [my] joy?6

C. Have some of your nice food, Herr Doktor!

19 20 21R. family ran quite smoothly, too, with only occasional and minor frictions. But three years ago I

22 23 24R. began to realize that I was moving out of alignment with the world. My conducting job

25 26 27R. brought that home to me. What a nightmare to stand in front of that orchestra, the playersE. When the world tries to push me into the abyssC. Please eat your food, Herr Doktor Schumann!

28 29 30R. expecting words of wisdom from me, and I having nothing to say to them! I felt that they hadE. of pain, I fly to thee, I fly to thee, I fly to thee.7

31 32 33R. nothing to do with me; I felt like a cog whirling aimlessly on its own, independent of the restE. The mist in me. The mist in me, The mist,



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252 Epilogue

34 35 36

R. of the machine. Within me, too, everything was going awry. I had suffered long ago from

E. The mist in me, the mist in me —transfigure it, my radiant star, into

37 38 39

R. premonitions of such a breakdown. Now I knew that it was beginning to happen. I knew that IF. Madness gnaws at mv soul.8

E. light, into light.9 The mist in me,

40 41 42

R. must be put away. I asked her to have me put away. She would not do it until in desperation I

F. If only I could finally see that hour, finally see that hour,E.transfigure it.

43 44 45

R. tried to put myself away. Now I am here, a displaced person, a defective cog that had to be

E. Nobody Nobody Nobody

46 47 48

R. discarded before it damaged its neighbors. I am alone. She cannot come to see me. They are

F. If only I could finally see that hour, finally see that hour

K. Nobody remembers me there.10

49 50 51

R. afraid that I would injure even her. But I could not harm my Clara, my light, my star! PleaseF. in which I would cease to see!11

52 53 54R. come, dear one, and hold me close. I need to feel that I am in accord at least with thee. In thy

C. All right, Herr Doktor,

55 56 57

R. arms I shall enjoy a blessed sensation of release. Thou shalt look into my eyes and thou

F. When I am buried,

C. I'll take that tray now.

58 59 60R. shalt say, "Thou sad, pale man!"12 And thou shalt smile at me as I blissfully slip out of

F. When I am buried, When I am buried, When I am buried,

61 62 63R. this world. Ah, come to me, dear one, come to me, Chiarma, and grant me Auflosung. . . ,13

F. then the tale shall be ended, ended.14

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Throughout the glossary, "consonance" refers to metrical consonance and "dis-sonance" to metrical dissonance.

Antimetrical layer: an interpretive layer that conflicts with at least one metricallayer

Augmentation: the progression from a relatively low-level to a higher-level ver-sion of a particular dissonance

Cardinality: an integer n denoting the constant number of pulse-layer attackssubsumed by each pulse of an interpretive layer. Each interpretive layer canbe characterized by this integer (i.e., as an n-layer).

Compound dissonance: dissonance produced by the combination of more thantwo conflicting interpretive layers

Contextual intensity: intensity determined by the manner of presentation of agiven dissonance in context

Cycle: a segment of a grouping dissonance demarcated by its periodic points ofalignment

Deintensification: the process of weakening a specific strong dissonance, or ofweakening dissonance in general across a given musical passage

Diminution: the progression from a relatively high-level to a lower-level versionof a given dissonance

Direct dissonance: dissonance resulting from superposition of layers of motionDisplacement dissonance: the association of layers of equivalent cardinality (i.e.,

congruent layers) in a nonaligned manner; labeled with a "D" followed bythe cardinality of the layers, a plus or minus sign (denoting displacement),and the displacement index


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254 G/ossary

Displacement index: the constant number of pulse-layer attacks that separatesthe metrical and antimetrical layers of a displacement dissonance

Grouping dissonance: the association of at least two interpretive layers whosecardinalities are not multiples/factors of each of her; labeled with a "G" fol-lowed by a ratio of the cardinalities involved

High-level (or hypermetrical) dissonance: dissonance formed by the interactionof large-scale (hypermetrical) layers of motion

Indirect dissonance: dissonance resulting from the juxtaposition rather than su-perposition of layers of motion

Inherent intensity: intensity of dissonance determined by the characteristics ofthe given dissonance type

Intensification: the process of rendering a particular dissonance more clearlyperceptible, or of rendering dissonance in general more clearly perceptibleacross a given musical passage

Interpretive layer: a layer of motion that moves more slowly than the pulse layerand allows the listener to "interpret" the raw data of the pulse layer by orga-nizing its pulses into larger units

Layer of motion: a series of approximately equally spaced pulsesLoose [displacement] dissonance: a displacement dissonance in which a rela-

tively small number of metrical pulses is contradictedLoosening: progression from a tight displacement dissonance to a looser relative;

accomplished by multiplication of the cardinality by an integral factor, withpreservation of the displacement index

Low-level dissonance: dissonance formed by the interaction of micropulsesMetrical consonance: a state of maximal alignment of layers of motion, existing

when all pulses of all interpretive layers coincide with pulses on all faster-moving layers; labeled by a ratio composed of the cardinalities of the inter-pretive layers involved

Metrical dissonance: nonalignment of layers of motionMetrical layer: one of the layers that form the primary metrical consonance of a

workMetrical map: diagram of the metrical progression of a work or movementMetrical progression: the succession of consonances and dissonances within a

given work or movementMicropulse: an intermittently appearing layer of motion moving more quickly

than the pulse layerMid-level dissonance: dissonance at levels between the two extremes of micro-

pulse and hypermeter; formed by the interaction of metrical and antimetricallayers

Preparation: allusion within primarily consonant passages to dissonances thatwill be fully established later

Primary consonance: the consonance created by the primary metrical layer in in-teraction with the pulse layer

Primary metrical layer: the most prominent metrical layer in a work, generally

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Glossary 255

(but not always) the layer designated by the upper integer of the time signa-ture and rendered visually apparent by the bar lines

Pulse layer: the most quickly moving pervasive series of pulses in a given work orsection

Resolution: progression from dissonance to consonanceResultant rhythm: the rhythm formed by the summation of the pulses of a collec-

tion of superimposed interpretive layersSimple dissonance: a dissonance composed of the minimum number of layers (a

pulse layer and two conflicting interpretive layers)Strong dissonance: clearly perceptible dissonanceSubliminal dissonance: dissonance formed by the interaction of at least one ex-

plicitly stated interpretive layer and at least one conflicting layer that is onlyimplied (by the context and by the notation). The implied interpretive layerwithin such dissonances is generally the primary metrical layer.

Submerging: the process of rendering a surface-level dissonance subliminal; thedissonance begins in a form involving explicit articulation of all constituentlayers but then, by the elimination from the musical surface of the con-stituent metrical layer, becomes subliminal

Surface-level dissonance: dissonance formed by at least two explicitly stated in-terpretive layers

Surfacing: the process of rendering explicit a subliminal dissonance; the disso-nance begins in a subliminal form (without articulation of the constituentmetrical layer) but then, by the addition of an explicitly articulated metricallayer, becomes obvious on the musical surface

Tight [displacement] dissonance: a displacement dissonance in which a relativelylarge number of metrical pulses is contradicted (as opposed to loose disso-nance)

Tightening: progression from a loose displacement dissonance to a tighter rela-tive; accomplished by division of the cardinality by an integral factor, withpreservation of the displacement index

Weak dissonance: subtle, not immediately obvious dissonance

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1. Euphoma is a fictitious town in the Harz Mountains in Germany, devoted en-

tirely to musical pursuits. It was invented by Hector Berlioz, who in the Gazette Mui-

cale for April 28, 1844 described the activities in that town during the twenty-fourth

century. Berlioz's description is translated and reprinted in Barzun, Berlioz and the Ro-

manti£ Century, 2:330 — 55. I am assuming that the musical activities in the town in 1854

were much the same as they were to be in the twenty-fourth century. (The Rhythmic

Quarter is my contribution to Berlioz's fantasy, suggested by his fairly extensive dis-

cussion of rhythmic matters in the aforementioned essay.) Florestan and Eusebius are

fictitious personae invented by Schumann, reflecting, respectively, the extroverted and

passionate, and the introverted and gentle sides of his own personality. They make fre-

quent appearances in his early critical writings and in his early music, sometimes in

published works (for example, in Camaval), even more often in the autographs. (Schu-

mann originally ascribed the individual pieces of the Davidsbundlertanze, for example, ei-

ther to Florestan or to Eusebius.) Throughout the first section of this chapter, actual

quotations from the written works of the various speakers are italicized. Translations

are mine unless otherwise indicated.

2. Barzun, Berlioz and the Romantic Century, 331.

3. The excerpt shown in Example 1.1 is found, along with the commentary para-phrased here, in Robert Schumann, "Phantasien, Capricen u[sw.] fur Pianotorte," Gesam-

melte Schriften, 3:97 (1838). It appears to be Bergson's intention that the seven-eight mea-

sure displace the remainder of the bass line by one eighth note.4. Barzun, Berlioz and the Romantic Century, 33 1.

5. Hauptmann, The Nature of Harmony and Metre, 344.

6. Robert Schumann, "Das Komische in der Musik," (Gesammelte Scbriflen, 1:184 — 86




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Notes to pages 7-l2 257

7. Robert Schumann, "Die dritte Symphonie von C. J. Miiller," Gesammelte Schrif-

ten, 1:115 (1835). Schumann's example lacks the natural before the E.8. Schumann mentions a negative remark of Fetis's about Berlioz's music in Gejam-

melte Schriften, 1:127. For further information on Fetis's ambivalent view of Berlioz, seeBarzun, Berlioz and the Ronwntic Century, 1:92, 105, 151, and 2:70.

9. Fetis, "Du developpement future de la musique." Mary Arlin's paper "MetricMutation and Modulation: The Nineteenth-Century Speculations of F-J. Fetis" (deliv-ered at the meeting of the Society for Music Theory in Tallahassee on 1 Nov. 1994)brought Fetis's articles and some of Berlioz's related remarks to my attention.

10. Fetis, "Du developpement future de la musique," 326. William Caplin pointedout to me that Fetis's example is derived from the last movement of Beethoven's PianoConcerto op. 19 (compare mm. 1-4 and mm. 261-65).

11. Ibid., 300.12. Ibid., 326.13. Ibid., 327.14. Berlioz, "Feuilleton du Journal des Debate, November 10, 1837," reprinted as

"Berlioz on the Future of Rhythm" in Barzun, Berlioz and the Romantic Century, 2:336—39.15. Mary Evans Johnson mentions this passage as an example of "metrical reposi-

tioning" in "Characteristic Metrical Anomalies." Her term encompasses both of Fetis'smutation types.

16. Young Riemann's argument comes, for the most part, from his later work System

der Musikalischen Rhythmik and Metrik, 203-5. The Beethoven passage is treated in thesame manner by the French theorist Mathis Lussy. See his Traite'de l'exexpression mu^icate,

26—27, and Edmond Monod's summary of Lussy's views on renotation (including a cita-tion of Beethoven's op. 27 no. 1) in Mathis Lussy et le Rythme Musical, 78.

17. Riemann, System, 101—11.18. Ibid., 110.19. Example 1.9b and the commentary are drawn from ibid., 89—90.20. Hauptmann's reference to syncopation as a conflict between two nonaligned

layers is found in The Nature of Harmony and Metre, 341.21. For Riemann's discussion of these conflict types, see System, 111—21.22. See Riemann, System, 118: ". . . it would be wrong, if during such configurations

one were to cancel the meter and instead were simply to observe the rhythmic organiza-tion marked by the motivic lengths. Just as the changing significance of these immedi-ately repeating figures is determined only by the unswerving adherence to the metricalorganization, so does their contradiction of the harmony endow them with additionalnew meanings."

23. Ibid., 121.24. Robert Schumann, Geoammelte Schriften, 2:64 (1836).25. Ibid., 3:101 (1839).26. For the references to Kittl's Scherziand Miller's Etudes, see ibid., 4:37 (1841): "A

frequent unclarity of the phrase rhythm such that there appears to us to be somewhat toomuch or too little especially at the cadences of some sections." See also ibid., 1:80 (1835):"I have various complaints about [Miller's] cadences, at which I almost consistently findthat there is something extra or something missing."

27. Robert Schumann, "Phantasien, Capricen u[sw.] fur Pianotorte," Ge^ammeLte

Schriften, 3:101 (1839): "To be sure, we sometimes encounter apparently disturbed phraserhythms in the masterworks, which, however, immediately resolve themselves" ("die sichaber zur Secunde wieder ausgleichen").

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258 Notes to Pages 12-18

28. Robert Schumann, "Symphonie von H. Berlioz," Gesammelte Schriften, 1:125(1834).

29. "Berlioz on the Future of Rhythm," in Barzun, Berlioz arid the Romantic Century,2:338.

30. Cooper and Meyer, Rhythmic Structure of Music, 81, 90, 106-15, 165.31. Berry, Structural Functions, 318-19, 325-26, 359.32. Ibid., 324—26, 365 — 71. Berry also uses of her terms such as "metrical incon-

gruity" and "polymeter" to describe metrical conflict.33. Their analysis of the opening of the finale of Haydn's Quartet op. 76 no. 6 is a

good example; Lerdahl and Jackendoff, Generative Theory of Tonal Music, 90-96.34. An example of conflicted grouping structure is their Example 3.23, in connec-

tion with which they state that a grouping into fours is preferable on the basis of slurring,but they do not deny the presence of a grouping into threes on the basis of motivic par-allelism (repetition of a pitch pattern).

35. Lester, Rhythms of Tonal Music, 48, 77-126.36. See especially Schachter, "Rhythm and Linear Analysis: Aspects of Meter,"

1-60.37. Ibid., 26-28, 50-51, 36, respectively.38. Schachter's discussions of these displaced passages are found in ibid., 33—35

and 53—58, respectively. For a more recent discussion of processes involving hypermet-rical displacement, see William Rothstem, "Beethoven with and without 'Kunstgeprang,'"especially 186-93.

39. Cowell, New Musical Resources, 50.40. Cowell elsewhere discusses both types of metrical conflict addressed in this vol-

ume, but does not apply consonance-dissonance terminology to them; ibid., 64—65, 70—71.41. Seeger, "On Dissonant Counterpoint," 25—31.42. Schillinger, System of Musical Composition (New York: Carl Fischer, 1941).43. Schillinger, Encyclopedia of Rhythms (New York, 1966).44. The following excerpt illustrates the imprecision of Colin's analogy: "The vari-

ous resultants (3:2 or 4:3) correspond to the acoustical ratios of the harmonic overtoneseries. This means that the rhythmic resultant of 4:3 is slightly more dissonant than therhythmic resultant of 3:2. The former corresponds to the perfect 4th and the latter to theperfect 5th." Ibid., I.

45. Yeston, The Stratification of Musical Rhythm (New Haven: Yale University Press,1976).

46. Ibid., 39-54.47. Ibid., 79-102.48. Ibid., 102-12.49. Wallace Berry, Structural Functions, 362.50. Krebs, "Some Extensions of the Concepts of Metrical Consonance and Disso-

nance," Journal of Music Theory 31/1 (1987): 99-120.51. Hlawicka, "Die rhythmische Verwechslung," and "Musikalischer Rhythmus und

Metrum."52. Cohn, "Metric and Hypermetric Dissonance," and his "Dramatization of Hy-

permetric Conflicts."53. Imbrie, "'Extra' Measures"; Epstein, Beyont) Orpheus, 131—32; Rothstem, "Bee-

thoven with and without 'Kunstgeprang'"; Krebs, "Rhythmische Konsonanx und Dis-sonanz," 29 — 32.

o4. Among studies dealing with Brahms's metrical conflicts are Frisch, "The

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noted to Paged 18-22 259

Shifting Bar Line"; Frisch, Brahnu and the Principle of Developing Variation, 57-58, 93-95,112, 115-16, 138, etc.; and Agmon, "Rhythmic Displacement in the Fugue of Brahms'sHandel Variations." Another relevant study of the music of Brahms is David Lewin's"On Harmony and Meter in Brahms's Op. 76, No. 8." In the course of his analysis,Lewin not only analyzes metrical structure but also brilliantly develops pitch/meteranalogies, assigning "tonic," "subdominant," and "dominant" qualities to particular hyper-meters, and showing how a modulatory pitch passage is also modulatory in metrical terms.

55. For relevant analyses of works by Wagner and Debussy, see Krebs, "DramaticFunctions of Metrical Consonance and Dissonance in Das Rheingold" and "RhythmischeKonsonanz und Dissonanz," 33-36, respectively.

56. August Reissman, Schumann (Berlin, 1865), 152; Dahms, Robert Schumann , 268;Gertler, Robert Schumann in seinen friihen Klavienverken, 74—78; Daniel Mason, "RobertSchumann," in Oscar Thompson, The International Cyclopedia o/Miutic and Mudicianj (NewYork, 1946), 1683.

57. Knayer, "Robert Schumann als Meister der rhythmischen Verschiebungen,"177-79, 201-3, 231-33.

58. Kohlhase, Die Kamnurnuuik Robert Schumaniu, 2:30, 35, 50, 66, 105, 125.59. Appel, "Robert Schumanns Humoreske fur Klavier Op. 20," 289-305.60. Edler, Robert Schumann und steine Zeit. In his discussion of the incomplete Ju-

geno'jinfonie in G minor, he points out various metrical idiosyncrasies that anticipate thecomposer's mature style (118). Within an analysis of the Fantasy op. 17, he refers severaltimes to the significance of syncopation, which "sometimes remains in effect over suchlong stretches that the perception of the measures is in danger of being lost" (144). Hementions the metrical and hypermetrical complications in the second movement of theFirst Symphony (152), the finale of the Piano Concerto (161), the first movements of theString Quartets (166), the Scherzo of the Second String Quartet (168), and the secondTrio of the Piano Quartet (172), among others.

61. Gerhard Dietel, 'Eine neue poetidche Zeit', 267.62. Schnebel, "Riickungen—Ver-riickungen,"Musik-Konzepte, Sonderband Robert Schu-

mann I (1981), 4-89.

63. Rosen, The Romantic Generation, 655, 684, 688.64. Honsa, "Synkope, Hemiola und Taktwechsel in den Instrumentalwerken Schu-

manns"; Mary Evans Johnson, "Characteristic Metrical Anomalies."65. Kaminsky, "Aspects of Harmony, Rhythm and Form," 34—35, 39, 157—58.


1. In earlier writings, I employed the term "level of motion" rather than "layer."Here, I require the term "level" for of her purposes and thus replace it with "layer" (whichrecalls Yeston's term "stratum").

2. See chapter 1, notes 12, 19, and 20.3. Roeder, who employs the model in the discussion of nontonal music in "Interact-

ing Pulse Streams," uses the term "pulse stream" for individual layers. This term suggestsan emphasis on the horizontal continuity of the phenomena in question, whereas "layer"suggests an emphasis on the vertical dimension —on the metrical states that result fromcombined streams. For the of her sources cited here, see chapter 1, notes 33, 45, and 52.Not all twentieth-century theorists subscribe to a "layer" model. Christopher Hasty, forinstance, attempting to "rescue" meter from its historical role of inexpressive "grid" in

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260 Notes to Pages 22-32

Meter tu Rhythm, rejects stratification (see, for example, pp. 154 and 201). As 1 hope toshow, the stratification model of meter does not necessarily preclude expressiveness.

4. Lerdahl and Jackendoff Generative Theory of Tonal Music, 17.5. My categories of phenomenal accent are drawn primarily from Joel Lester's

Rhythnu of Tonal MUM, 18-40.6. In the examples, pulses that are relatively weakly articulated are shown by inte-

gers in parentheses. (Time signatures in parentheses indicate that the time signature isnot actually present within the cited excerpt.) When a pulse is not articulated at all, Idraw a stroke through the corresponding integer. In simplified examples, some numbersfor pulses that appear to be absent may lack strokes; this situation indicates that the pulseis articulated in the full score.

7. In some editions, even more of the accents are missing, namely the first and thirdin the second measure of (he example (in. 9). These, however, are present in the Stichvor-

lage housed at the Staatsbibliothek zu Berlin — Preufiischer Kulturbesitz (Musikabteilungmit Mendelssohn-Archiv), Mus. ins. autogr. R. Schumann 29.

8. Yeston gives many examples of layers arising from subsurface melodic change inchapter 3 of Stratification of Musical Rhythm, 55 — 76.

9. For a detailed discussion of such grouping devices, see Lerdahl and Jackendoff,Generative Theory of Tonal MIMIC, 36—39.

f 0. Maury Yeston draws attention to layers formed by various types of pattern rep-etition (Stratification of Musical Rhythm, 50—54). My article "Some Extensions" deals al-most exclusively with layers formed by pattern repetition. Several authors have pointedout that the separation between accentuation and grouping is not necessarily a sharp one;Yeston states that "the beginnings of repetitions of patterns become points of accent" (p.85), and Joel Lester similarly observes that initiation points of patterns carry an accent(Rhythms of Tonal Music, 37).

11. Lester makes this point in Rhythms of Tonal Music, 40.12. The special significance of harmony in forming metrical layers has been noted

by many earlier writers, including Lerdahl and Jackendoff (see their Metrical Prefer-ence Rule 5f Generative Theory of Tonal Music, 84) and William Rothstein (see "Beethovenwith and without 'Kunstgeprang,'" 173). Albert S. Bregman discusses the tendency ofdynamic accents ("loud sounds") to group together (i.e., to form layers) in Auditory Scene

Analysis, 648.13. I do not include the possibility of aligned presentation of interpretive layers of

identical cardinality because I consider such a situation as a single interpretive layer cre-ated by the collaboration of a number of musical means. Albert S. Bregman discusses thesignificance of such "collaboration" in the formation of auditory streams in Auditory Scene

Analysis, 651-52.14. Lester, Rhythms of Tonal Music, 50. Lester uses the term "level" rather than

"layer."15. This definition, again, excludes the possibility of associations of layers of identi-

cal cardinality (which could, of course, never produce dissonance).16. Kaminsky, "Aspects of Harmony, Rhythm and Form," 27. note that the term

"grouping" is here employed with a meaning different from that used in the earlier dis-

cussion of layer formation.17. The coffee-bean diagrams in this chapter are modeled on the dot diagrams in

Lerdahl and Jackendoff, Generative Theory of Tamil Music.

18. Yeston, Stratification of Muscal Rhythm, 140; Horlacher, "The Rhythms of Reit-

eration," 174.

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19. Kaminsky, "Aspects of Harmony, Rhythm and Form," 27.20. Where there is no metrical framework, the layer initiated earlier usually func-

tions as the referential layer.21. Bo Alphonce makes the distinction between forward and backward displace-

ment in "Dissonance and Schumann's Reckless Counterpoint," par. 4-6 and 10-11.22. note that Dx-a and Dx+b, the sum of a and b being x (the cardinality), are the

respective "backward" and "forward" labels for a given displacement dissonance. Thus,D3+2 and D3-1, D4+3 and D4-1, etc., where the displacement indices of each pair addto the cardinality, are alternate designations for the same displacement dissonance.

23. I have adopted the term "resultant" from Yeston, Stratification of Musical Rhythm,


24. There are of her types of families of grouping dissonances. Pairs of the typeGx/y, G(x+y)/y, for instance, are closely related; the resultant of the dissonance with thehigher numerator is similar, but reiterates y. Thus, the resultant of G5/3 is "3 2 1 3 1 2 3,"while that of G8/3 is "3 3 2 1 3 3 1 2 3 3." Yeston constructs families of grouping disso-nances on the basis of inclusion relations, modeled on Allen Forte's pitch-class set com-plexes (ibid., 143—47). I do not dwell on these families here since they do not seem to besignificant in Schumann's music.

25. I coined the term "indirect dissonance" in "Some Extensions," 103. A number ofwriters had, however, previously acknowledged the possibility of metrical conflict in thehorizontal dimension. Fetis's discussion of five-four meter as a horizontal association oftriple and duple meter, and his extrapolation to of her juxtapositions of meters in regularalternation, hints at the idea of indirect metrical conflict ("Du developpement future dela musique," 353). Charles Seeger considers the possibility of horizontal as well as verti-cal dissonance, describing the latter as much more strongly dissonant ("On DissonantCounterpoint," 27). \Vallace Berry refers to horizontal as well as vertical "noncongruity,"giving an example of juxtaposition of three- and four-quarter-note groups at the opening

362-65).26. Yeston refers to this tendency in Stratification of Musical Rhythm, 31, 96.27. See, for example, Charles Rosen, Romantic Generation, 684—85.28. This analysis differs slightly from that in Kaminsky's Example l.5b, in which the

3-layer is continued through in. 68 ("Aspects of Harmony, Rhythm and Form," 34-35).29. "Grille" means "whim" or "quirk."30. If the pulse unit were determined by the underlying pulse of the lowest-level

dissonances in the given work, the numbers associated with higher-level dissonanceswithin the same work would be cumbersomely large. I therefore admit fractional valuesinto the labels of low-level dissonances.

31. The term "hypermeter" is derived from Edward T. Cone's term "hypermeasure,"designating a metrical unit of greater length than a notated measure; see his Musical Form

and Musical Performance, 79. For more recent developments in hypermetrical theory, seeRothstein, Phrase Rhythm in Tonal Music; and Kramer, The Time of Music, esp. 83—107.Some rhythmic theorists have questioned the existence of hypermeter, or meter at highlevels (for instance, Lester, Rhythms of Tonal Music, 158-69), and would thus question theexistence of hypermetrical dissonance as well. others, for example, Richard Cohn (in"Dramatization of Hypermetric Conflicts," 188-206), have convincingly demonstratedthat dissonance at high levels not only exists but can have great dramatic impact.

32. John Daverio draws attention to some of the subtleties of hypermeter in thispassage in Robert Schumann, 14 — 15.

Notes to Pages 33- 55 261

o f t h e s e c o n d m o v e m e n t B e e t h o v e n ' s S y m p h o n y ( S t r u c t u r a l F u n c t i o n s i n M u s i c

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262 Notes to Pages 56-71

33. William Rothstein notes that the conclusion of an exposition with a three-bargroup was a "generic norm by Beethoven's time"; see "Beethoven with and without'Kunstgeprang,'" 175n. Even if this particular hypermetrical irregularity was a norm,Schumann employs it here in an unusually interesting manner.

34. In the autograph of the first edition of this symphony, held at the Archive of theGesellschalt der Musikfreunde in Wien (A289), in. 84, there notated as two measures oftwo-four time, is deleted. Its deletion, revoked in the second edition, would have re-moved the hypermetrical dissonance.

35. Charles Colin suggests this point in his introduction to Encyclopedia of Rbythnu

(New York, 1966. Rpt. New York: Da Capo Press, 1976), p. L: "You will notice as therhythms become more dissonant, their total durations are longer."

36. This principle is also operative in the domain of pitch; the intervals of a majorseventh or minor second are, in tonal contexts, very strongly dissonant because they soclosely approach the most stable intervals, the unison and the octave.

37. Richard Cohn demonstrates this aspect of grouping dissonance intensity in"Metric and Hypcrmctric Dissonance," 13.

38. Albert S. Bregman's observation, in Auditory Scene Analysis, 649, that "continu-ous sounds hold together better as a single stream than discontinuous ones do," suggestsanother possible way in which sustention affects contextual intensity. A succession ofsustained sounds will be more clearly perceived as a stream than one containing gaps;therefore, dissonances whose layers consist of sustained sounds will be more clearly per-ceived and hence more intense than those \vhose layers are "gapped."

39. The above statements do not apply if dynamic or harmonic new-event accentsare involved; I regard those as creating intense dissonance no matter where and how theyarise.

40. Not all combinations of three or more layers of dif ferent cardinality result incompound grouping dissonance, for when any two of the cardinalities are multiples/factors of each of her, they result in consonant relationships. Thus, the superposition of a2-layer, a 3-layer, and a 6-layer does not result in compound dissonance, but only in acombination of G3/2 and the two consonances 6/3 and 6/2.


1. See Daverio, Robert Schumann, 22.2. Macdonald, "Schumann's Earliest Compositions and Performances," 259-83;

and Daverio, Robert Schumann, 22, 29, 47, 68.3. Daverio, Robert Schumann, 47.4. Schumann's comment on Hummers Method is found in his Gesammelte Schriften

uber Musik and Musiker, 1:15 (1834).5. Schumann saw a painting similar to this vision while he was transcribing Pa-

ganini's G-minor Caprice, and was subsequently haunted by that painting; Robert Schu-

mann, Tagebucher, 1:404.6. Discussions of the influence of Paganini on Schumann are found in Daverio,

Robert Schumann, 63, and Boetticher, Robert Schamanns Klavierwerke, Teil II, 56.7. See Daverio, Robert Schumann, 71. Evidence of Schumann's familiarity with Bach's

Partitas is to be found in (Gesaammelle Schri/len iiber Musik and Musiker, 2:36-41. Schumannlists a number of movements from this collection as studies in particular technical d i f f i -


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Notes to Pages 72- 82 263

8. Schumann mentions finding the pen in Guaimnelte Schriften uber Musik and Musiker,

3:203 (1840).9. Mary Evans Johnson refers to the influence of Beethoven's rhythmic style on

Schumann in "Characteristic Metrical Anomalies," 250. Arnfried Edler believes thatSchumann consciously adopted "humoristic" metrical dissonance from the Scherzomovements of Beethoven; see Robert Schumann and deine Zeit, 144. Schubert's influence onSchumann has been studied in detail by Marie-Luise Maintz in her "Studien zur Schu-bert-Rezeption Robert Schumanns."

10. John Daverio discusses the influence of Schubert's chamber music on Schu-mann in Robert Schumann, 49—52.

11. Robert Schumann, Gesammelte Schriften iiber Music and Musiker, 2:11—13.Maintz, in "Studien zur Schubert-Rezeption Robert Schumanns," 282, mentions thesimilarity between "Arlequin" from Carnaval and Schubert's op. 33 no. 2 (although, asshe points out, Schumann displaces Schubert's rhythm by a quarter note), and betweenthe rhythmic pattern of Papillan no. 6, mm. 7—14, and Schubert's op. 33 nos. 4, 6, and 9(the similarity is especially close in Schubert's sixth dance). I cite additional Schubertwaltz quotations, not mentioned by Maintz, in connection with my analysis of the firstmovement of Schumann's Faschinqsschwank aus Wien in chapter 8. A further item of evi-dence of Schumann's interest in Schubert's waltzes is his fragmentary set of variationson Schubert's Sehnduchtdwalzer (op. 9 no. 2), which Schumann absorbed in part into hisown op. 9, the Carnaval.

12. Mary Evans Johnson discusses Schumann's fondness for the inherent duple/triple conflict in the waltz in "Characteristic Metrical Anomalies," 38—39, 302.

13. Hemrich Schenker briefly discusses the metrical structure of the passage fromop. 110 in Beethoven, die: letzten Sonaten, Somite A) Dur op. 110: Kritucbe Eitiftihrung and Er-

Ldiderung, ed. Oswald Jonas (Vienna: Universal Edition, 1972), 58.14. See chapter 1, note 7.15. For the dating of the Concerto sketches, see Boetticher, Robert Scbumamu

KLavierwerke, TeiI, 28, and Ted II, 10. These sketches occupy a large part of the first andthird of the six sketchbooks housed at the Universitats-und Landesbibliothek (ULB) atBonn.

16. Boetticher, Robert Schumanns Klavierwerke, Teil I, 99-104. Schumann's Forewordand preparatory exercises are found in Robert Schumann, Studien op. 3 and Konzertetiiden

op. 10 nach Capricen von Paganini, ed. Hans Joachim Kohler (Leipzig: Edition Peters,1981), 4-12.

17. The Piano Quartet remained unpublished during Schumann's lifetime and wasissued only in 1979 by Heinrichshoten's Verlag, Wilhelmshaven (ed. Wolfgang Boet-ticher). One of the ideas from the Trio of the second movement seemed to Schumann toembody romanticism, and he quoted it in several of his later works. For one such quota-tion, see Example 2.1. Boetticher lists of her examples in the introduction to his edition ofthe Quartet (p. vii).

18. Schumann associated the ending of this Caprice with the described image of Pa-ganini; Robert Schumann, Tagebiicber, 1:404.


1. Clara was playing the Emperor Concerto in January of 1854. She performed it on21 January in Hanover; see Knechtges-Obrecht, "Clara Schumann in Diisseldorf," 215.

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264 Notes to Pages 83-117

2. Kirnberger, Art of Strict Musical Composition, 235-36.3. The idea that metrical anomalies are embellishments of the normative meter is

broached by Mary Evans Johnson in "Characteristic Metrical Anomalies," 249.4. I suggested at the end of "Some Extensions" that such reduction might be a

worthwhile pursuit. I have since come to a different conclusion.5. Some of these processes have been touched upon by earlier authors. Cooper and

Meyer show an intensification process in Dufay's Muua Sancti Jacobi (Rhythmic Structure

of Music, 113—15), and Walter Frish discusses intensification of a different type in "Met-rical Displacement in Brahms," 154. Peter Kaminsky's analyses indicate his awareness ofseveral metrical processes. For example, in his analysis of the Trio of Schumann's Davids-

biindlertanz op. 6 no. 6 in "Aspects of Harmony, Rhythm and Form," he mentions the in-tensification of dissonance by addition of dynamic accents nine measures into the Trio (p.57). He also analyzes the offbeat accents in the tenth and eleventh measures of the Trioas a development of those in mm. 2 and 4 — a hint at a process which I shall discuss lateras "tightening" (p. 57). In his analysis of op. 6 no. 1, he refers to an augmentation of asimple syncopation (p. 67).

6. The accents on the right-hand El> and At in mm. 12 and 13, respectively, aremissing in the Clara Schumann edition but are present in the Henle edition.

7. I have already applied the term "resolution" to metrical events at several points of

this volume. Several earlier authors have also applied the term in this metaphorical sense,notably Cooper and Meyer in Rhythmic Structure of Music, 111, 115, 165, and WallaceBerry in Structural Functions in Music, 359.

8. Peter Kaminsky points out that the end of the Preambule docs not completely re-solve the D2+1 dissonance; "Aspects of Harmony, Rhythm and Form," 39.

9. One might argue that the new bass line introduces a new interpretive layer: du-rational accents on the second beat result in a displaced 3-layer and in the dissonance

D3 + 1. Especially after in. 70, however, this layer is barely audible; the low-point registralaccents in the bass on the downbeats of mm. 71 — 74 render the metrical 3~laycr much

more perceptible than the displaced layer.10. This is the basic argument of Christopher Hasty's book Meier as Rhythm; his ap-

proach to the "rehabilitation" of meter is, to be sure, very different from mine.


1. Schumann preserved his sketches and of her autographs very carefully. It ispartly for this reason that a large number of them have survived. The most significantcollections are located at the Manuscripts Division of the Universitats- und Landes-bibliothek (ULB) in Bonn, the Deutsche Staatsbibliothek zu Berlin — PreufiischerKulturbesitz (Musikabteilung mil Mendelssohn-Archiv), the Schumann-Haus inZwickau, the Heinrich-Heine-Institut in Diisseldorf, the Archive of the Gesellschaftder Musikfreunde in Wien, the Bibliotheque Nationale in Paris, and the Pierpont Mor-gan Library in New York (Robert Owen Lehman Collection). The extant documentsinclude some sketches (for example, six sketchbooks housed at the ULB in Bonn, andsketches for the String Quartets op. 41 housed at the Deutsche Staatsbibliothek zuBerlin), and numerous fair copies and Stichvorlaaen. Although they have not receivednearly as much attention as Beethoven's, these sources have been studied by a numberof authors. The first author to write extensively abovit them was Wolfgang Gertlcr, whoin his Robert Schumann in jeinen friihen made some perceptive comments

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notes to Pagu 117-20 265

about the sketches for the PapiLLoiu. Wolfgang Boetticher discussed many of the auto-graphs in Robert Schumann, Einfiihrung in Perjonlichkeit and Werk and, more recently, inhis studies Robert Schumanns Klavierwerke, Teill: Opiu 1-6 and Robert Schumann*) Kiavier-

wcrke, Teil II: Opiu 7-13. Linda Correll Roesner, in her dissertation "Studies in Schu-mann Manuscripts: With Particular Reference to Sources Transmitting InstrumentalWorks in the Large Forms," investigated many of the technical aspects of Schumann'scompositional process (ink colors, correction techniques, etc.) and also demonstratednumerous large-scale consequences of Schumann's revisions. Jon Finson, Akio Mayeda,Claudia Macdonald, and Rufus Hallmark have also done exemplary source-basedwork on particular bodies of Schumann's output. A transcription of the sketchbookshoused in Bonn, by Reinhold Dusella, Matthias Wendt, Reiner Leister, and others, is inprogress, and will appear as a supplement to the Neue Robert-Schumann-Gejamtaujgabe,

beginning in 1998.2. The Osterreichische Nationalbibliothek in Vienna holds a photograph of the ear-

liest manuscript of the discarded finale of op. 22 (PhA 1519); the autograph itself is in aprivate collection. The fair copy is housed in the Archive of the Gesellschaft der Musik-freunde in Wien (A288). The inserts for the fair copy are not contained in theGesellschaft autograph; that for in. 99, labeled "a" in red crayon (just as is the point of in-sertion in the Gesellschaft copy), is at the Deutsche Staatsblbliothek zu Berlin — Preufii-scher Kulturbesitz (Muslkabteilung mit Mendelssohn-Archiv), Mus. ms. autogr. R. Schu-mann 36 no. 6 (verso), brace 2. The manuscript of the complete sonata, still with theoriginal finale, is also at the Deutsche Staatsblbliothek (Mus. ms. autogr. R. Schumann38). "Brace" will henceforth be abbreviated "br." The abbreviation "st." (for "staff") willbe used when a manuscript page contains both braces of staves and single staves (inwhich case single staves will be counted rather than braces).

3. Linda Correll Roesner discusses this revision in "Brahms's Editions of Schu-mann," 252—60. She points out that Brahms, when preparing the movement for publica-tion in November 1866, preserved two statements of the dissonant material—those be-ginning at mm. 337 and 367 —that Schumann had decided to excise; the penciled "gilt"(stet) beside those two deleted passages is in Brahms's, not Schumann's, hand.

4. Deutsche Staatsbibliothek zu Berlin —Preufiischer Kulturbesitz (Musikabteilungmit Mendelssohn-Archiv), Mus. ms. autogr. R. Schumann 19, p. 33, br. 1, mm. 6—7. Thepagination of this manuscript is confusing; there are numbers in light pencil at the topright-hand corners of each recto page, and different numbers in dark pencil below. Sincethe latter numbers are continuous throughout the manuscript, I cite only them.

5. The second of the six sketchbooks held at the ULB Bonn is a collection of shortdated sketches relating to Schumann's early works. The term "musical diary" seems ap-propriate for this sketchbook. The passage mentioned here is transcribed in Krebs,"Schumann's Metrical Revisions," A1.

6. Deutsche Staatsbibliothek zu Berlin, Mus. ms. autogr. R. Schumann 19, p. 18,br. 2, in. 5 to br. 3, in. 2.

7. The fair copy is housed at the Heine-Institut in Dusseldorf (no. 78.5025). The re-vision discussed here is found on p. 3.

8. The three versions are found in ULB Bonn, Schumann 8, p. A, br. 1-2; p. 6, st.1-3; and p. 6, br. 4-6. The latter draft is very similar to the final version, although onlyouter voices are notated.

9. Bibliotheque Nationale, Paris, ms. 320, p. 8, br. 1, in. 3 to br. 2, in. 3.10. The crossed-out anticipatory third F/D at the end of in. 5 foreshadows the dis-

placed figuration of the final version.

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266 Notes to Pages 120-25

11. The sketch on p. 38 of Schumann 15 shows an F as the uppermost note on thedownbeat of in. A. The F should, of course, be a D, tied from the preceding bar (as shownin my transcription).

12. The sketches for the Abegg Variation,!, op. 1, contain an example of change of dis-sonance type. In an early sketch of mm. 45-48 (ULB Bonn, Schumann 13, p. 55), Schu-mann featured the dissonances G4/3 and G3/2. In later sketches of the passage (ULBBonn, Schumann 13, pp. 6 and 17), he began to weed out the 3-layer, then added a

shifted 4-layer, thus replacing the original grouping dissonances with the displacementdissonance D4+1. For transcriptions of the relevant sketches, see Krebs, "Schumann'sMetrical Revisions," 40. An additional example of a revision that altered the tvpe of dis-sonance is found in the third Davu)<ibil>, mm. 43-44. In the autograph (Archive ofthe Gesellschaft der Musikfreunde in Wien, A281, p. 5, br. 4, mm. 4 — 6), Schumannplaced sforzandos on the third beats, creating the dissonance D3+2 (l=quarter). In the

first edition of the work, he moved the sforzandos to the second beats, so that the disso-nance changed to D3+1. This dissonance was anticipated in the autograph version of in.42, where the sforaando was already on the second beat.

13. A more substantial example of the addition of layers to an existing dissonancecomes from the slow movement of the Piano Quintet op. 44. Pages 25—27 of the fair copy(ULB Bonn, Schumann 5) correspond to the present mm. 132 — 64. The accompaniment

pattern of the passage, however, was originally different from the present one: all instru-ments were to play a quarter-note triplet pattern, the triplets being grouped into twos bypattern repetition. The passage was thus permeated by weak G3/2. Schumann crossed outthis material and wrote the present version as an appendix at the back of the manuscript.

He preserved the duply grouped quarter-note triplets in the piano and gave eighth notesto the strings, thus adding low-level three-against-four dissonance to the existing G3/2.

14. At times, Schumann intensified existing dissonance by adding accents of her

than dynamic stresses. For example, in the first draft of the first movement of the StringQuartet op. 41 no. 1 (mm. 52—55), he originally notated only the first violin part and afew notes of the second violin part (Deutsche Staatsbibhothek zu Berlin, Mus. ms. au-togr. R. Schumann 19, p. 5, st. 5, mm. 3 — 6). The second violin part contained'one tieacross the bar, and thus hinted at the displacement dissonance D6+3 (1 =8th). In the finalversion (Example 4.15b), Schumann gave the antimetrical durational accents to the cello,

and stated three of them rather than one. Both the relocation of syncopation in a moreprominent voice and its reiteration intensified the dissonance.

15. The sketch page (Schumann- Haus, Zwickau, 4648-A1, recto) begins with mm.103—23 of the twelfth and final piece of the first edition, and mm. 101—21 of the tenthand final of the second (br. 1, in. 1 to br. 4, in. 1). The material on the remainder of therecto through br. 2, in. 3 of the verso corresponds quite closely to the tenth piece of thefirst version and the ninth piece of the second (although the note values are twice as large

and the measures half as long as those of the editions).16. Bibliotheque Nationale, ms. 329, p. 12v, br. 3, mm. 1-5.17. This revision is found in the fair copy housed at the Heinnch-Heme-Institut,

Diisseldorf, ms. 78.5025, p. 18. The page is reproduced in facsimile in Krebs, "Schu-

mann's Metrical Revisions," 47.18. ULB Bonn, Schumann 14, p. 5, br. 4.19. Schumann apparently considered using the material shown in Example 5.11 as

the opening theme of the finale. In the manuscript of op. 14 held at the British Library(Additional ms. 37056, p. 17), the passage appears in 6/16 meter, marked prestissimo. It iscrossed out and followed on p. 18 by the present (male.

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Notes to Page 126-32 267

20. Archive of the Gesellschaft der Musikfreunde in Wien, A281, p. 17, br. 4, in. 11to br. 5, in. 6.

21. The revised ending, on p. 52 of the third sketchbook, continues from the thirdmeasure (marked with an x) on the last line of p. 90. The displacement dissonance in thefinal version, incidentally, sounds more like D3+1 rather than D3+2. The reiteration ofchords on second and third beats results in strong accents of harmonic change on the sec-ond beats, which overshadow the still active durational accents on the third beats.

22. This revision is reproduced in facsimile in Krebs, "Schumann's Metrical Revi-sions," 49. The autograph of the Davidsbiindlertanze op. 6 and the pencil revisions in Schu-mann's copy of the first edition contain additional examples of deintensification of disso-nance by removal of dynamic accents. In mm. 17—21 of the autograph of no. 13 (Archiveof the Gesellschaft der Musikfreunde in Wien, A281, p. 17, br. 2), there are dynamic ac-cents on the second beats. In the editions, Schumann retained these accents only in mm.19-21, so that the dissonance D2+1 (l=quarter) lasts less long and the section as a wholeis less dissonant. In the autograph (Archive of the Gesellschaft der Musikfreunde inWien, A281, p. 18, br. 4), Schumann also placed dynamic accents on the second beats ofmm. 113, 115, and 117, resulting, along with the ties from these beats to the followingdownbeats, in strong D4+2 (an augmentation of the earlier D2+1). In the editions, he ex-cised the accents so that the dissonance becomes considerably weaker.

23. Wolfgang Boetticher refers to "this harmonically unacceptable rhythmic dis-placement" in Robert Schumanns Klavienwerke, Teil l, 68.

24. The passages from op. 6 no. 6 are in the Archive of the Gesellschaft der Musik-freunde in Wien, A281, p. 16, br. 3, mm. 3—4, and br. 3, mm. 7—8 to br. 4, mm. 1—4. Thosefrom op. 6 no. 13 are in A281, p. 18, br. 4, mm. 4-12.

25. The fact that the passage is headed "Papillon" suggests that it was intended asa beginning.

26. Schumann's construction of pieces and movements by juxtaposing fragmentsoriginally composed independently, a process clearly evident from his autographs, hasbeen discussed by a number of authors who have studied those documents, for example,by Gerhard Dietel in "Eine neue poetische Zeit," 55, 57, and by Linda Correll Roesner in"Schumann's Revisions," 102, 107—9.

27. The opening theme was already worked out when Schumann sketched the in.46 passage; the staff above the in. 46 sketch in ms. A285 at the Archive of the Gesell-schaft der Musikfreunde in Wien corresponds to the first four measures of the finale (no-tated in 6/16 time). Most of the present weak-sixteenth accents in the theme are alreadypresent; only those on the present second beat of in. 1, and on the present second beats ofmm. 3 and 4, are missing.

28. Heine-lnstitut, ms. 78.5025, p. 1.29. In November 1853, the committee in charge of the Diisseldorf Musikverein had

designated Julius Tausch as primary music director; Schumann was to conduct only hisown works. Clara Schumann 'was infuriated by this decision. See Knechtges-Obrecht,"Clara Schumann in Diisseldorf," 212—13.

30. Revision of the discussion of metrical revision in op. 2 no. 1 (with dissonantlayers removed): "Another instance of small-scale process achieved by a series of revi-sions is that in the first Papillon (see Example 4.5). The intermediate stages of theprocesses of intensification and demtensification were not present in our first two ver-sions of the piece. In both, the inner-voice durational accents of mm. 4-6 were absent.In the first version, moreover, the second beats of mm. 9 — 12 were all dynamically ac-cented. The gradual additions and deletions of accents that render the metrical process

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268 Notes to Pages 132-43

in the final version so elegant were not fully worked out until our fair copy of the work."The early versions are in ULB Bonn, Schumann 15, pp. 93, 119. It is obvious thatthe version on p. 93 is later because it is labeled with a Roman numeral "I" (suggestingthat its ultimate context had been determined), whereas the version on p. 119 is called"Walter 6." In the fair copy (Bibliotheque Nationale, ms. 315), the passage appears onp. 3, br. 3.

31. The draft, probably dating from 1832, is housed at the Archive of the Gesell-schaft der Musikfreunde in Wien (A283). The pages discussed here are reproduced infacsimile in Boetticher, Robert Schumaniu Klavienverke, Teil II, plates 6 and 19, and in myarticle "Schumann's Metrical Revisions," 52. Wolfgang Boetticher addresses the dating ofthe Fandango draft in Robert Schunuiniu Klavierwerke, TeilII, 147.

32. The drafting of the future op. 11 movement continues on the first two braces ofa third page, with material anticipating the present mm. 175—90 (the opening of the de-velopment section), though with some gaps, arid not yet in the final keys. The third braceon the final page of A283 begins with a blank measure, then contains material reminis-cent of mm. 76—85 from the first movement of the Piano Sonata op. 14! The fourth braceappears to be intended as a continuation but does not correspond to any measures in ei-ther of the two versions of op. 14. The final two used braces on the page contain ideas forthe introduction of the first movement of op. 11 —the first phrase of the opening melodyin the treble with a sixteenth-note bass accompaniment, then the second phrase in thebass, with treble accompaniment, all in A minor. The latter pctssage corresponds closelyto mm. 14—19 of the present introduction.

33. It is not immediately obvious from the labels that D16+10 is a loose relative ofD4+2. The relationship becomes clear if one inserts the "missing step" D8+2. D8+2 is anobvious loose relative of D4+2, and the similar relationship between D16+10 and D8+2 isevident from the equivalence of the differences between the respective cardinalities anddisplacement indices (the constant difference is 8).

34. The manuscript of the "Exercice" is in the Robert Owen Lehman Collection, ondeposit in the Pierpont Morgan Library in New York. For information on the dating ofthis version, see Boetticher, Robert Schumanns Klavitrwerke, Teil II, 10.

35. All but the first page of the "Exercice" manuscript retain this original notation(predominantly eighth notes rather than sixteenths). On the first page, Schumanncrossed out the original alla breve time signature, replaced it with the present two-four sig-nature, and added a second beam to all four-eighth-note groups.

36. Wolfgang Boetticher mentions many of the differences, including "new synco-pated accents," in Robert Schumanns Klaviertverke, Teil II, 26—31, as does John Daverio inRobert Schumann, 64. Neither author discusses the metrical revisions in detail.

37. ULB Bonn, Schumann 14, p. 9, sk. no. 92; reproduced in Boetticher, Robert

Schumann,! Klavierwerke, Teil II, 38. This sketch must postdate the "Exercice" draft, as it isnolated in sixteenth notes.


1. Peter Kaminsky notes that "metrical dissonance may be a significant factor in thearticulation of form," and gives some supporting examples from the piano music of Schu-mann in "Aspects of Harmony, Rhythm and Form," 34. of her writers who have com-mented on the relation between form and particular interactions of layers or pulsestreams are Richard Colin in "The Dramali/ation of I lypermetric Conflicts," 200 — 205;

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noted to Pages 143-60 269

and John Roeder in "Interacting Pulse Streams in Schoenberg's Atonal Polyphony,"Mimic Theory Spectrum 16/2 (Fall 1994): 231-49.

2. Deutsche Staatsbibliothek zu Berlin —Preufiischer Kulturbesitz, Mus. ms. au-togr. R. Schumann 19, p. 12, br. 5 and 7, and p. 14, br. 1 and 3.

3. The passage from the Second Quartet is shown in Example 5.2. For the passagefrom the First Quartet, see Deutsche Staatsbibliothek zu Berlin, Mus. ms. autogr. R.Schumann 19, p. 5, st. 14-15.

4. The first sketch is in the ULB Bonn, Schumann 15, p. 81, br. 3, mm. 3-5. Thefair copy is housed at the Bibliotheque Nationale (ms. 315); the passage discussed here ison p. 5, br. 4—5.

5. Bo Alphonce discusses the "reckless counterpoint" of the latter passage in "Dis-sonance and Schumann's Reckless Counterpoint," Music Theory Online 0/7 (1994): par.13-14.

6. See Krebs, "Alternatives to Monotonality in the Early Nineteenth Century," and"Some Early Examples of Tonal Pairing: Schubert's 'Meeres Stille' and 'Der Wanderer,'"in Kinderman and Krebs, The Second Practice of Nineteenth-Century Tonality, 17-33. WilliamKinderman, Kevin Korsyn, and Deborah Stein have also discussed tonal conflict in early-nineteenth-century compositions. See Kinderman, "Directional Tonality in Chopin," inSamson, Chopin Studies, 59—75; Korsyn, "Directional Tonality and Intertextuality: Brahms'sQuintet op. 88 and Chopin's Ballade op. 38," in The Second Practice of Nineteenth-Century

Tonality, 43—83; and Stein, "When Pieces Begin and End in Different Keys."7. Deborah Stein discussed the significance of such enharmonically equivalent

dyads in tonally duahstic music in the paper cited in the preceding note. For further dis-cussion of such "enharmonic puns," see Stem and Spillman, Poetry into Song, 124—25 and155-57.

8. Peter Kaminsky, in "Aspects of Harmony, Rhythm and Form," 53—63, givessome examples of the highlighting of important points within the pitch structure bymeans of metrical dissonance; he shows, for example, how the onset and resolution ofmetrical dissonance in Schumann's Davuljbiindlertanz op. 6 no. 6 correspond to the riseand fall of arpeggiations.

9. I thank John Roeder for drawing my attention to the pitch component of thedual process.

10. For information on Schumann's activities as choral conductor, see Daverio,Robert Schumann, 397.

11. The original vocal line of this passage may have consisted of undisplaced halfnotes. The autograph at the Deutsche Staatsbibliothek zu Berlin — Preufiischer Kul-turbesitz, Mus. ms. autogr. R. Schumann 16/1, p. 78, br. 2, in. 7, shows that the quarterrest at the beginning of the measure was messily squeezed in. Furthermore, the quarternoteheads are unusually large, suggesting that they are filled-in half notes.

12. The autograph (Deutsche Staatsbibliothek zu Berlin, Mus. ms. autogr. R. Schu-mann 16/1, p. 130, br. 2 in. 9) shows that Schumann intended the piano part at "Philoso-phic" to be exactly as it is at the corresponding in. 9 (where there was no accent); he doesnot write out the latter measure but leaves it empty and labels it with an alphabeticallabel referring to the earlier corresponding measure — his usual practice when passageswere to be restated without change. The accent is present in the later copyist's manu-script held at the Bibliotheque Nationale in Paris (ms. 326, pp. 5-8).

13. The autograph (Deutsche Staatsbibliothek zu Berlin, Mus. ms. autogr. R. Schu-mann 16/1, p. 110, br. 2) shows deletion of ties from the third beats in the introduction,and their replacement with ties from the second beats.

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270 Notes to Pages 161-73

}4. The autograph (Deutsche Staatsbibliothek zu Berlin, Mus. ms. autogr. R. Schu-mann 16/1, p. 74, br. 3, mm. 3 — 5) suggests that the displacement dissonance during theword "Wahnsinn" was an afterthought. The first right-hand note, F#5, seems originally tohave been an E; its notehead appears to have been enlarged so as to extend over the Ftline. The second right-hand note, Ii5, was clearly added later, as is evident from its smallersize and from the fact that its stem, unlike those of the of her notes, crosses over the eighth-note beam. Before these changes were made, the right hand \vould have played the un~

syncopatcd eighth notes E5~Dt5-Ct5-B4-At4-Gx4, which would have sounded togetherwith the left-hand eighth notes. It appears that the word "Wahnsinn" triggered Schu-mann's recasting of the right-hand part into a syncopated form.

15. Deutsche Staatsbibliothek zu Berlin, Mus. ms. autogr. R. Schumann 16/1, p.118, br. 1.

16. The displacement was not present in the autograph of the tenth song (DeutscheStaatsbibhothek zu Berlin, Mus. ms. autogr. R. Schumann 16/2, p. 50); the high right-

hand notes coincided with the bass notes. In the autograph of the eleventh song (p. 51),the displacement dissonance was considerably weaker; although antimetrical durationalaccents already suggested the displacement dissonance, the dynamic accents were lack-ing.

17. The text comes from Eichcndorff's ViclLiinnen um mchts; it is sung within thatnovel by a recently married woman who longs for her childhood home. See HerwigKnaus, Miulkspracbe tint) Werkjlruktur, 19.

18. Herwig Knaus refers to the representation of unrest by a syncopated accompa-niment at of her points within op. 39 in A4u(nksprache und WerksLruktiLi', 67. His book con-tains an excellent facsimile of the Berlin autograph of op. 39.

19. In the third volume of the Peters edition of Schumann's songs, the text is mis-takenly given as "Ritter der Wildnis" ("knight of the wilderness").

20. Dietrich Fischer-Dicskau, Robert Schumann, 133, 140.21. Thorough discussions of these conflicts tire found in Dieter Schnebcl, "Riick-

urigcn — Ver-ruckungen," 4—89; Arnfned Edlcr, Robert Schumann and seine Zeit, and JohnDavcrio, Robert Schumann. Schnebel refers to numerous events in Schumann's life, in-cluding the conflicts surrounding his courtship, that negatively influenced his mentalhealth, and suggests that these events and Schumann's reactions to them find their ex-pression in his use of displacement in concurrent works. He cites a letter from Schumannto his former theory teacher, Heinrich Dorn, in which he states that the Piano Sonata op.14 (a work filled with displacement) is to be regarded as the artistic expression of theemotional strains arising from his courtship of Clara ("Riickungen — Ver-riickungcn,"43). John Daverio argues that Schumann resolved the "musician/poet" dualism by ad-

hering throughout his career to the "notion that music should be imbued with the sameintellectual substance as literature" (p. 19), and also by engaging in music-critical writing(p. 130). Daverio (pp. 392-415) and Edler (p. 277) address the "bohemian/bourgeois"dualism. For discussion of the "subjective/objective" dualism, see Daverio, p. 13. He citesthe following significant diary entry from 8 June 1831: "It sometimes seems to me as ifmy objective self wanted to separate itself completely from my subjective self."

22. Daverio, Robert Schumann, 394-95.

23. Schnebel, "Riickungen — Ver-riickungen," 16.24. Schnebel makes this point in ibid., 46—47.25. Bernhard Appel remarks on the comical aspect of certain metrical dissonances

in the Hitnwreskc op. 20 in "Robert Schumaniu Humoreske fur Klavte.r op. 20" 326.26. The dreaml ike , hovering na ture of some of Schumann's metrical dissonances is

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noted to Paged 173- 95 271

mentioned in Christian Knayer's "Robert Schumann als Meister der Verschiebungen,"129, and in Dieter Conrad, "Schumanns Liedkomposition—von Schubert her gesehen,"

155.27. Dieter Schnebel links Schumann's displacement dissonances with insanity in

"Ruckungen —Ver-ruckungen," 24-25, 37. On the latter page he employs the term"schizophrenic music" with reference to the pervasively displaced 'Paganini' from Car-



1. Martha von Sabinin had studied with Clara in Diisseldorf from November 1850to March 1851, and had then taken up the position of Hotpianuttin at Weimar. The twowomen remained close friends. Knechtges-Obrecht, "Clara Schumann in Diisseldorf,"200.

2. Wallace Berry discusses the "bringing out" of the meter and lists ways of doing soin metrically ambiguous situations in Structural Functions uiMudic, 335—36.

3. For a similar argument, see Epstein, "Brahms and the Mechanisms of Motion,"204.

4. The view expressed here diverges from that of Mary Evans Johnson, who feelsthat solo performers must make a choice between metrical or antimetrical inflection. See"Characteristic Metrical Anomalies," 297.

5. See Daverio, Robert Schumann, 246.6. I thank William Rothstein for his penetrating remarks on Schumann's "Im-

promptu," which brought the distinctive string-quartet texture of the piece, and themeans of articulating its various metrical layers, into focus for me.


1. The reader is urged to consult scores of the works analyzed here. It was not pos-sible to include all excerpts mentioned, and some excerpts are presented only in simpli-fied form.

2. Schumann's remarks on Berlioz's irregular phrase rhythms are quoted in chapter1 (see n. 28). Jacques Barzun gives some examples of Berlioz's use of metrical disso-nance in Berlioz and the Romantu; Century, 1:468n, 486.

3. Robert Schumann, Gedammelte Schriften fiber Musik und Musiker, 1:151.4. At in. 322 the 4-layer is shifted by one eighth note, resulting in D4+2 in addition

to G6/4.5. D6+4, brought about by dynamic accents in the horns, is much stronger than

D6+2 in these passages. D6+4 also appears at of her points of the movement, for example,in the statements of the See fixe at mm. 123-25 and 304-7, and at the climactic passageat mm. 327-29.

6. In the Berlin manuscript of the Intermezzi, there is a dynamic accent on the finalbeat of in. 26 as well as mm. 24-25 (Deutsche Staatsbibliothek zu Berlin, Mus. ms. au-togr. R. Schumann 29). There is also an accent on the second beat of in. 27, initiating thedissonance D12+2. These accents are missing in the Clara Schumann edition.

7. The latter relationships are admittedly hardly audible, for the eighth-note unit in-creases in speed in the second intermezzo.

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272 Notes to Pages 195-217

8. Measures 2-5 and 11-14 of the intermezzo are literally lifted from one of Schu-mann's early songs, entitled "Hirtenknabc" (Shepherd Boy); see Daverio, Robert Schu-

mann, 33.

9. In the Berlin manuscript (Deutsche Staatsbibliothek zu Berlin, Mus. ms. autogr.R. Schumann 29), the second beats of mm. 65 — 66 are dynamically accented. These ac-cents are missing in the Clara Schumann edition.

10. These dissonances could be named (rather cumbersomely) Gl/.67and G2/1.33(l=8th).

11. Discussions of these features in Chopin's music are found in Rothstein, Phnue

Rhythm in Tonal Mtuif, 221-24 and 239-45; and Cinnamon, "New Observations."

12. Linda Correll Roesncr provides information on Brahms's publications of thesemovements in "Brahms's Editions of Schumann," 251 — 60.

13. Anton Kuerti, liner notes for his recording of the work (Ace of Diamonds, SDD2154, 1967), par. 7.

14. The dynamic accent on the second eighth note of a triple group in in. 109 fore-

shadows the return of displacement of the 3-layer, although the index of displacement is1 rather than the 2 characteristic of the scherzo section.

15. Janma Klassen notes the metrical relationship between the sections beginningat in. 11 and in. 35, as well as of her rhythmic relationships between Scherzo and Trio inClara Wieck-Schumaim, 238-39.

16. I do not agree entirely with Daverio's assessment, in Robert Schumann, 137, ofthe work as "less idiosyncratic" in style than the earlier piano music; this remark is, at

least, not true of the first movement.17. The passage in mm. 340—404 is a near-quotation of the Trio of the Menuetto

movement of Beethoven's Piano Sonata op. 31 no. 3. Schumann no doubt quotesBeethoven because he is writing a "Viennese" piece. R. Larry Todd mentions this quota-

tion in "On Quotation in Schumann's Music," 81, as does Olivier Alain in "Schumannund die franzosische Musik," 58. It is interesting to compare the two passages. Bee-thoven's new-event harmonic and the durational accents coincide with the downbeats, sothat the metrical dissonance is much weaker than in Schumann's passage. As Frank

Samarotto pointed out to me, there is jom-e dissonance in the Beethoven excerpt; the lowbass notes on upbeats result in antunetrical accents.

18. The first movement contains several quotations from Schubert's op. 33 (a workthat Schumann, interestingly enough, described as "an entire Faschmg" within his fa-mous review of the work; Gesammelte Scbriften iibcr Musik und Musiker, 2:12). Schumann'smm. 253—56 are rhythmically and harmonically reminiscent of mm. 1—5 of Schubert'sop. 33 no. 6. The dotted rhythm of Schumann's mm. 269-92 recalls the seventh waltz inSchubert's set, especially mm. 9—11. Schumann's mm. 340—48, finally, recall not only theaforementioned passage by Beethoven, but also the opening of the eighth waltz oi Schu-bert's op. 33. Again, the quoting of Schubert is appropriate for a piece "aus Wien."

19. William Rothstein describes this phenomenon in Phrase Rhythm in Tonal Miufif,

52-56, using the term "metrical rcinterpretation." I thank him for pointing out the metri-cal reinterpretation at the end of the first movement of Faschingsschwank.

20. The first, second, and third movements were completed in Vienna, probably inMarch 1839; see Robert Schumann, Tagebiicher, 2:88-90. The finale was written after

Schumann's return to Leipzig.21. Robert Schumann, (n'.iaminellc Schri/tcn fiber Miuik uiid Miuiker, 3:195, 199

(1840). Translations are my own.22. Ibid., 195-96.

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Notes to Pages 217-43 273

23. Ibid., 1:51 (1838).24. Ibid., 3:76 (1839).25. Clara and Robert Schumann, Briefwechjel, 1:55.26. Ibid., 259.27. Robert Schumannd Briefs: Neue Folge, ed. F. Gustav Jansen (Leipzig: Breitkopf

undHartel, 1886), 119.28. Clara and Robert Schumann, Briefwecluel, 2:463.29. Robert Schumann, Ge,tammelte Schriften und/Witiik und Miuiker, 3:76-77. "Flach-

senfingen" seems to be a coined name suggesting a small-town cultural backwater.30. Robert Schumann 'ti Briefe, 151.31. Clara and Robert Schumann, Briefivechtiel, 1:337.32. Robert Schumann '<> Briefe, 142. The "Vehme" was a secret court active in West-

phalia until 1808.33. Clara and Robert Schumann, Briefwechdel, 1:273.34. Ibid., 337.35. Robert Schumann's Briefe, 146.36. Stephen Heller, Briefe an Robert Schumann, ed. Ursula Kersten, Europaische

Hochschulschriften, Vol. 37 (Frankfurt: Peter Lang, 1988).37. Robert Schumann, GedainmeLte Schriften iiber Miuik und Mudiker, 3:186—89

(1839).38. I thank Dr. Gerd Nauhaus of the Schumann-Haus in Zwickau for granting me

access to Schumann's copies of the Heller and Schaeffer works.39. Bozarth, "Brahms's Liederohne Worte," 370-71.40. For discussion of of her relevant influences, notably Beethoven, Haydn, and

early music, see Frisch, "The Shifting Bar Line," 149 — 52, and Virginia Hanco*ck,Brabiru'd Choral Composition*!, 159.

41. Frisch, "The Shifting Bar Line," 139-63.42. Ibid., 142-43.43. Max Kalbeck, Johannes Brabms, 1:126.44. It might be argued that one could, on the basis of apparent prolongation of C

major harmony, combine the last beat of in. 5 with the first of in. 6 to form another duplegroup. I do not hear the passage in this manner. The C major harmony on beat three ofin. 5 sounds like a passing chord 3within a typical fifth-species suspension resolution, notlike the actual resolution of the preceding six-four chord; only on the first beat of in. 6 isthe resolving C major harmony actually established.

45. Deutsche Staatsbibliothek zu Berlin — Preufuscher Kulturbesitz, Mus. ms. au-togr. R. Schumann 19, p. 20, br. 6, in. 3.

46. Deutsche Staatsbibliothek zu Berlin, Mus. ms. autogr. R. Schumann 19, p. 21,br. 2-3.

47. The hymn is reproduced in Clayton W. Henderson, The Charles Ives Tunebook

(Warren, Michigan: Harmonie Park Press, 1990), 29.48. Edith's dates are given in Charier E. Ives: Memos, ed. John Kirkpatrick (New

York: W. W. Norton, 1972), 22. Information about Susanna, Edith's playmate, is foundon p. 279. Her dates are not mentioned, but she was very likely of approximately thesame age as Edith—perhaps eight, which could account for Ives's inclusion of an 8-layer.

49. This is an excerpt from Dr. Franz Richarz's entry for April 19, 1854 in his case-book on Robert Schumann, transcribed in Robert Scbunanus letzte Lebensjabre: Prolokoll einer

Krankbeit (Berlin: Stiflung Archiv der Akademie der Kunste, 1994), 17. I thank BrigitteBercnbruch for the use of her copy of this publication (which is not widely available).

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274 notes to Pages 244-52

50. Arnold Schoenberg, "Brahms the Progressive," Style and Idea, ed. Leonard Steinand trans. Leo Black (Berkeley and Los Angeles: University of California Press, 1984),437-38.

51. I discuss hemiola in the various versions of the fourteenth of the George-Lieder

op. 15 in "Three Versions of Schoenberg's Op. 15 No. 14: Obvious Differences and Hid-

den Similarities," Journal of the Arnol'd Schoenberq Institute 8/2 (November 1984): 131-40.John Roeder studies interactions of pulse streams akin to metrical consonance and dis-sonance in two movements from Pierrot in "Interacting Pulse Streams in Schoenberg'sAtonal Polyphony."

52. When he temporarily abandons G6/4 at in. 30, Schoenberg creates its diminu-tion by superimposing triplet and duplet eighths.


1. The dotted motive at the beginning of op. 133 no. 3 conjures up the word "Kik-eriki" — the sound that a German rooster makes.

2. "Morgens steh' ich auf und frage: kommt fein's Liebchen heut?" From op. 24 no.1 (Heine).

3. "Dein Bildnis wunderselig hab' ich im Herzensgrund." From op. 39 no. 2 (Eichen-

dorff).4. "Heb' auf zum Himmel mich, mein schoner Stern." From op. 101 no. 4 (Ruckert).5. "Wann, wann erscheint der Morgen, der mein Leben lost aus diesen Banden?"

From op. 74 no. 6 (Geibel).6. "Wo sind deine Freuden hin?" From op. 142 no. 3 (poet unknown).7. "Wenn mich in Jammerschlucht die Welt zu drangen sucht, nehm' ich zu dir die

Flucht." From op. 101 no. 6 (Ruckert).8. Wahnsinn wuhlt in ineinen Sinnen." From op. 24 no. 5 (Heine).9. "Den Dampf in mir zu Licht, mem schoner Stern, verklaren hilf." From op. 101

no. 4 (Ruckert).10. "Es kennt mich dort keiner mehr." From op. 39 no. 1 (Eichendorlf)-11. "Wenn es endlich doch geschahe, dass ich sah' die Stunde, wo ich nimmer

sahe!" From op. 74 no. 6 (Geibel).12. "Du trauriger, blasser Mann!" From op. 48 no. 12 (Heine).13. "Auflosung" means both dissolution (death) and resolution.14. "Wenn ich begraben werde, dann ist das Marchen aus." From op. 127 no. 3


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List of Cited Works by Robert Schumann

Page numbers in italics indicate that a musical example appears on the given page. Page

numbers in boldface indicate substantial analytical discussions with numerous musicalexamples.


Piano Quartet in C Minor (1828), 199first mvmt., 78—79

second mvmt., 79—80

third mvmt., 78-79fourth mvmt., 7, 9, 78-79

Piano Quintet in tib Major, op. 44first mvmt., 57-38, 128-29, 130second mvmt., 37-38, 46, 130, 266third mvmt, 37-38, 51, 180fourth mvmt., 38, 53, 102

Piano Trio in F Major, op. 80

String Quartet in A Minor, op. 41 no. 1first mvmt., 105-6, 110, 111, 123, 132,

148, 266fourth mvmt., 105, 145 – 46

String Quartet in F Major, op. 41 no. 2first mvmt., 105, 118-19, 148second mvmt., 224–31third mvmt., 51, 123-24 180, 231fourth mvmt., 117—18

String Quartet in A Major, op. 41 no. 3first mvmt., 112-13, 148, 155 -56

second mvmt., 24, 26-31, 35, 105,110-11


Albumblatler op. 124no. 3 ("Scherxino"), 147-48no. 7 ("Landler"), 104-5, 152no. 9 (Impromptu"), 172-73, 183-84,

185no. 15 ("Walzer"), 152-53, 180

Biinte Blatter op. 99"Abendmusik," 98-99

Carnaval op. 9"Chiarina," 36—37

"Estrella," 58, 85-86"Eusebius," 53, 143"Florestan," 96"Marche des Davidsbtindler," 21"Paganini," 36, 271"Pierrot," 109"Preambule," 7-8, 9, 21, 33, 60, 87-88,

89, 109, 118, 131"Valsc allemande," 85 — 86


first mvmt., 54, 91, 118-19, 129, 144-45

Schumann Metrical Dissonance - [PDF Document] (298)

Cited Works 283

Davidsbilnilertdnze op. 6no. 1, 15, 24-25, 27, 28, 31, 35, 58no. 2, 24-25, 26, 27, 31, 33, 46, 59,

110no. 3, 266no. 4, 150no. 6, 130no. 10, 59no. 13, 126, 130, 131, 267

"Exercice," 136—37. See also Toccata op. 7Exercises, 77—78

"Fandango," 133— 34. See also Piano Sonatain F# Minor, op. 11, first mvmt.

Fantasy op. 17, 53Faschingsschwank aus Wien op. 26

first mvmt., 47, 151-52, 180-81, 182,213-19

fifth mvmt., 52, 56Gesang der Friibc op. 133 no. 3, 250-52Humoreske op. 20, 19Impromptus iiber ein Thema von Clara Wieck

op. 5, 125, 266no. 1, 150no. 9, 722

Intermezzi op. 4, 191-99no. 2, 98no. 4, 23, 24, 25-26, 31, 35, 60, 110no. 5, 120-27, 126-27, 149, 153-54,

156, 223Kintierscenen op. 15

no. 6 ("Wichtige Begebenheit"), 148Kreisleriana op. 16

no. 1, 144, 148, 150, 179no. 2, 150-57, 155

Nachhttiicke op. 23no. 3, 49-50

Novellettes op. 21no. 4, 77no. 5, 89-90no. 6, 57, 92-93, 94, 105, 149

Papillons op. 2, 72, 147no. 1, 91-92, 132, 149no. 4, 131no. 5, 149no. 6, 131no. 8, 722, 129-30, 131no. 10, 55, 127-28, 129, 130, 131, 150no. 11, 87-88, 146, 152no. 12, 126, 130, 267

Pbantasiestiicke op. 12no. 4 ("Grillen"), 49, 98, 110, 144, 148,

155Piano Sonata in F Minor, op. 14, 203

first mvmt., 100, 150, 268second mvmt., 51third mvmt., 125-26fourth mvmt., 119-20, 131, 150, 172,

179, 185, 186Piano Sonata in F# Minor, op. 11

first mvmt., 134-35, 268see also "Fandango"

third mvmt., 7-8, 60, 94-96,

111-12, 117, 119, 122, 131, 178, 180fourth mvmt., 48, 50, 124-25, 145,

180Piano Sonata in G Minor, op. 22, original

finale. See Presto in G minor

Presto in G minor, 27-28, 33, 97, 117, 130,178, 180, 203

Scherzo, Gigue, Romanze and Fugbette op. 32,60

Scherzo in F Minor (originally included inthe Piano Sonata op. 14), 172, 178,180, 182, 203-9

Seeks Concert--Etuden compoiurt nacb Capri-

cen von Paganini op. 10no. 2, 100-7, 102, 142-43, 149, 156

Studien fiir das Pianotorte nacb Capricen von

Paganini, op. 3, 77no. 4, 52

Toccata op. 7, 137-41see also "Exercice"

Variationen uber den Namen Abegg op. 1, 199,266

Waldscenen op. 82no. 1 ("Eintritt"), 55no. 5 ("Freundliche Landschaft"), 46no. 7 ("Vogel als Prophet"), 94-95, 149,



Piano Concerto in A Minor, op. 54, 47,91, 172

Piano Concerto in F Major (sketches),77-78

Symphony no. 1 in Bb Major, op. 38first mvmt., 60, 102-3,

Schumann Metrical Dissonance - [PDF Document] (299)

284 Cited Works

Symphony no. 1 in Bb Major, op. 38(continued)

second mvmt., 38, 53third mvmt., 89, 91fourth mvmt., 105—7

Symphony no. 2 in C Major, op. 61first mvmt., 38second mvmt., 103third mvmt., 103-4

Symphony no. 3 in lib Major, op. 97first mvmt., 26, 27, 148, 236-43second mvmt., 38—39

fifth mvmt., 51, 97, 123Symphony no. 4 in D Minor, op. 120

first mvmt., 146-47

third mvmt., 38fourth mvmt., 38, .56-57, 107-8


Dichterliebe op. 48, 163no. 3 ("Die Rose, die Lilie"), 16]no. 10 ("Hor' ich das Liecichen klm-

gen"), 162-63, 270no. 11 ("Ein Jungling liebt ein Mad-

chen"), 162-63, 270no. 16 ("Die alten, bosen Lieder"),

162-63Drei Gesange op. 31

no. 1 ("Die Lowenbraut") 157-58, 171Genoveva, 160, 161Funf Lieder und Grange op. 127

no. 3 ("Es leuchtet meine Liebe"),165-71, 173

"Hirtenknabe," 199Liederaibum fiir die Jugend op. 79

no. 17 ("Die wandelnde Glocke"),158

Liederkreis op. 24no. 2 ("Es treibt mich hin, es treibt

mich her"), 161no. 5 ("Schone Wiege memer Leiden"),

53, 161-62, 270no. 6 ("Warte, warte, wilder Schiffs-

mann"), 158

Liederkreis op. 39no. 1 ("In der Fremde"), 163no. 3 ("Waldesgesprach"), 159-60,

161no. 5 ("Mondnacht"), 162no. 10 ("Zwielicht"), 160

Lieder und Gesange op. 77no. 4 ("Stiller Vorwurf"), 165-64

Myrtben op. 25no. 16 ("Rathsel"), 159, 269

Sechs Gedichte op. 90no. 1 ("Lied ernes Schmiedes"), 158no. 2 ("Meine Rose"), 165no. 6 ("Der schwere Abend"),

163-65Vom Paqen and der Konigstochter op. 140,

158Zwolf Gedichte op. 35

no. 1 ("Lust der Sturmnacht"), 161

of her

Fugue subject (unpublished), 147

Schumann Metrical Dissonance - [PDF Document] (300)


Page numbers in italics indicate that a musical example appears on the given page. Page num-bers in boldface indicate substantial analytical discussions with numerous musical examples.

accent, 10and the formation of layers of motion,

23-28phenomenal, 23

density, 23durational (agogic), 23, 58dynamic, 23, 29, 58new-event, 10, 29, 58of ornamentation, 23, 93registral, 23

See also corrective accentantimetrical layer. See layers of motionAppel, Bernhard, 19augmentation. See metrical process

Bach, Johann Sebastian, 80English Suite no. 1 in A Major, Courante

II,71English Suite no. 2 in A Minor, Courante,

71Sarabande, 71

English Suite no. 3 in G Minor, Gigue, 71French Suite no. 2 in C Minor, Courante,


Partita no. 5 in G Major, Tempo di mm-uetta, 71-72

Beethoven, Ludwig van, 14, 15, 18, 72,80

Leonore Overture, 217Piano Concerto in El Major, op. 73, 82,

84Piano Sonatas, 73, 77, 272Piano Sonata in E! Major, op. 27 no. 1,

first mvmt., 8-10, 12String Quintet in C Major, op. 29, 5Symphony no. 3 in El> Major, op. 55, first

mvmt., 5, 73, 74 - 77Symphony no. 7 in A Major, op. 92, third

mvmt., 5, 73Bergson, Michael, Vier Mazurken, op. 1, 4Berlioz, Hector, 3-14, 79, 187, 191, 219

on metrical conflict, 7, 12, 13and the origin of the metrical dissonance

metaphor, 13Symphonic fantastique, 12, 187—91

"Scene aux champs," 187—88"Unbal,"188-91

Berry, Wallaceideas of metrical conflict, 14–15, 17

Brahms, Johannes, 14, 18, 203Piano Sonata in C Major, op. 1, 220Piano Sonata in Fit Minor, op. 2, 220


Schumann Metrical Dissonance - [PDF Document] (301)

286 Index

Piano Sonata in F Minor, op. 5first mvmt., 8, 219-24

Symphony no,4 in E Minor, op. 98, 224

cardinality, 23, 30, 31, 33, 34, 104-5, 132,207

Chopin, Frederic, 199Ballade no. 3, op. 47, 10

Etude op. 25 no. 2, 200-1Etude op. 25 no. 5, 201

Mazurka op. 16 no. 1, 202Mazurka op. 16 no. 2, 202Mazurka op. 17 no. 1, 202

Scherzo no. 2, op. 31, 199-200

Scherzo no. 3, op. 39, 199Scherzo no. 4, op. 54, 199-200

dementi, MuzioGradus ad Parnassum, 68

Cohn, Richardon layers of: motion, 22on metrical dissonance, 18

Colin, Charles, 17compound dissonance. See metrical disso-

nanceConcert sana orchestre. See Piano Sonata in F

Minor, op. 14Cooper, Grosvenor and Leonard Meyer, 14,


corrective accent, 1 1 0, 227, 243Cowell, Henry, 16-17Cramer, Johann Baptist, 65cycle. See grouping dissonance

Dahms, Walter, 19dcmtensilication. See metrical processDietel, Gerhard, 19diminution. See metrical processdirect dissonance. See metrical dissonancedisplacement dissonance, 33–39, 42-45

compound, 60, 119-20, 141, 193-95, 196,198

definition of 33high-level, 56, 105, 134, 215, 240-42indirect, 45, 205labeling of, 35-36, 41, 44loose, 44, 45, 66, 67, 72, 104-7low-level, 53, 54, 102, 103, 140-41, 161,

162-63, 201, 207-8, 220subliminal, 48, 51, 56, 98, 205, 213, 224tight, 44, 45, 57, 105See also metrical process (loosening, tight-

ening), syncopation

displacement index, 34, 53, 57, 104Dufay, Gmllaume, 14Diisseldorf, 21, 132

Edler, Arnfried, 19Endenich, 177, 187, 224, 249Epstein, David, 18Euphonia, 3, 4, 8, 12, 14, 33, 36, 61, 79, 117,

119, 191, 219, 256

Fetis, Francois-Joseph, 257and layers of motion, 22on metrical mutation, 6-8, 13, 22

Fischer-Dieskau, Dietrich, 171form,

and metrical revision, 130—31and metrical structure, 79, 94, 137-39,

142-49, 156, 205metrical structure contributing to con-

trast between sections, 130–31, 146,211-12, 225, 240

metrical structure creating relationshipsbetween sections, 66, 72, 131, 148-49

metrical structure highlighting formalboundaries, 130, 139, 143-45, 205,211-12, 213, 227, 228, 239

Gertler, Wolfgang, 19grouping dissonance

compound, 59, 233, 234-3636cycles in, 32, 57, 242-43definition of, 31high-level, 56, 71, 215, 231, 238-42indirect, 46, 52, 53, 54, 56-57, 69, 79, 151,

215, 222, 231labeling of, 31. 41low-level, 53, 54, 100-1, 190, 195-96,

198, 200-1, 208, 209-10, 220, 229periodic alignment of pulses in, 31-32subliminal, 48, 50-51, 52, 56, 71, 79, 97,

98, 151, 189-90, 193, 196, 222-23,233, 237-43, 245

grouping structure, 26, 58

Haslinger, Tobias, 217Hauptmann, Montz, 173

and layers of motion, 22and metrical conflict, 4, 10, 22

Heine, Heinrich, 167I Idler, Stephen

Piano Sonata op. 9, 219Rondo-Scherzo op. 8, 219

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Index 287

hemiola, 20, 71, 91, 223See also grouping dissonance

Hiller, FerdinandTwenty-four Etudes op. 15, 12, 257

Hlawicka, Karl, 18Honsa, Melitta, 20Horlacker, Gretcken, 32Hummel, Johann Nepomuk, 65, 77, 80

Piano Concerto in A Minor, op. 85, 67-69

Pianotorte Method, 68

hyperdownbeat, 215hypermeasure, 106, 214–15, 238-43, 261hypermeter, 18, 30, 54-57, 214-16, 218,

238-41, 261hypermetrical dissonance. See metrical disso-


Imbne, Andrew, 18incommensurable levels, synonym for group-

ing dissonance, 15indirect dissonance. See metrical dissonanceintensity. See metrical dissonanceintensification. See metrical processIves, Charles

"Two Little Flowers," 234-36"Weil auf mir," 232–33"West London," 233–34

Ives, Edith, 236

Johnson, Mary Evans, 20

Kalkbrenner, Friedrich, 65Kaminsky, Peter, 18, 20-21, 33Karlsbad, 65Kirnberger, Johann Phihpp, 83Kittl, Johann Friedrich

DreiSckerziop. 6, 12, 257Sectu Idyllen op. 1, 12, 257

Knayer, Christian, 19Kohlhase, Hans, 19Krebs, Harald, 17-18

large triplet, 10-11layers of motion, 17, 178

accentuation and the creation of, 23—28,58

antimetrical layer, 31, 33, 34, 46, 58-59,66-67, 172, 227, 229, 245, 250

cardinality of, 23, 85, 104grouping structure and the creation of,

26-27implicit in nineteenth-century theories, 22

interpretive layer, 23, 28, 29, 30, 31, 111in twentieth-century theory, 22metrical layer, 30, 31, 33, 34, 48, 96, 97,

110, 112, 172, 227, 245, 250pattern repetition in the creation of, 26, 28perceptibility of, 28-29, 58pitch repetition and the creation of, 26, 28primary metrical layer, 46, 47, 50, 151pulse layer, 22, 23, 30, 31, 34

Leipzig, 216, 218Lerdahl, Fred and Raymond Jackendoff

and layers of motion, 22, 23and metrical conflict, 15

Lester, Joeland accentuation, 23–25and metrical conflict, 15and nesting, 15, 29

loosening. See metrical processLorenz, Oswald, 218

Marseillaise, 219Mason, Daniel, 19Mendelssohn, Felix

St. Paul, 217"Song without Words," op. 102 no. 4, 15

Mereaux, AmadeusGrande Fantainie, 11-12

meterdefinition of, 22-23, 112-14

metric crossing, synonym for grouping disso-nance, 14, 18

metrical consonancedefinition of, 29-30early uses of term, 13, 17in early versions of Schumann's works,

118-21, 131, 134extramusical associations, 162, 173labeling of, 30in metrical processes, 86–88, 108–14in metrical progressions, 82–86, 148, 169,

233-34primary consonance, 30, 82, 84, 85, 87,

108, 109, 110, 111, 202, 207, 237,239, 240

See also metrical process (resolution)metrical dissonance

arithmetic conception of, 16–17compound, 57-58, 78–79, 96, 118, 122,

131, 141, 154, 169-70, 172-73, 178,196, 197, 198, 231, 233, 250

definition of, 59labeling of, 59

Schumann Metrical Dissonance - [PDF Document] (303)

288 Index

metrical dissonance (continued)

performance of, 182—84resolution of, 77, 111-12, 142, 170types, 59-60

direct, 45-46, 204-5, 210expressive use of, 4-5, 171-72, 184-85families of, 41-45, 51, 83, 99, 188, 192,

193-98, 203, 220, 224, 236, 244, 261geometric conception of, 17high-level, or hypermetrical, 10—12,

54-57, 71, 104, 199, 213, 214-16,218-19, 231, 238-42

indirect, 45-46, 140, 204-5, 210, 213, 215,222, 237, 239, 240, 241, 243, 261

definition of, 45distinct from subliminal dissonance, 46during resolution of direct dissonance,

45-46, 109intensity

contextual, 58–59inherent, 57–58

low-level, 53-54, 67, 144, 161, 200-1meanings of, 19, 20, 171-73, 184-85,

216-19motivic use of, 75-77, 82-83, 100-5, 131,

134-35, 137-40, 188-91, 192-98,203, 210-12, 221-24, 225-31,237-43

neighboring, 83

notation of, 4, 8-10, 178, 181, 204

passing, 84, 230and performance. See performance

and pitch structure. See pitch structure

prevalence in solo piano and chamber

music, 157simple, 59subliminal, 46-52, 83, 84, 96-99, 148,

170, 172, 188-90, 192, 198, 203, 205,211, 220, 225, 234, 244

as apparent consonance, 47, 204, 207,237-38

distinct from indirect dissonance, 46and intensity, 97performance of, 47, 97-98, 140, 180-82

surface-level, 46two basic types, 12-13, 17-18, 19, 21, 31,

178-79See also displacement dissonance, grouping


metrical layer. Sec layers of motionmetrical map, 85-86, 142, 166, 184, 206,


metrical narrative, 84-86, 188, 192, 203,211, 213, 220, 222, 225, 233, 234,237, 244

metrical process, 69, 264

augmentation, 41, 54, 73, 99-104, 105,

108, 149, 154, 203, 208, 238, 240,241, 267

deintensification, 91-94, 96, 107, 112, 132,140, 145, 167, 239-40

during resolution, 86, 110, 149diminution, 67, 72, 99-104, 105, 107, 132,

141, 190-91, 193, 195-96, 198, 199,203, 208, 210, 239, 241, 274

intensification, 66-67, 76, 78, 79, 86,

91-99, 107, 132, 135, 139, 144, 145,150-51, 167, 170, 208, 213, 225, 227,233, 240, 241

loosening, 72, 104-8, 148, 162, 193, 195,212, 241

during resolution, 111, 212and metrical revision, 139–41preparation, 87-91, 141, 184, 211-12resolution, 12-13, 15, 51, 70, 108-12, 147,

156, 162, 163, 167, 170, 171, 184,185, 188, 202, 205, 213, 214, 221,224, 228, 236, 237, 238, 240, 242-43,264

abrupt, 109-10coordination with pitch resolution, 5,

76, 142, 143-45deceptive, 110gradual, 76, 110-12, 142

submerging, 97-98, 108, 140, 201, 208,227, 237

surfacing, 97-98, 188, 195, 196-97, 212,227, 240

tightening, 67, 104-8, 112, 128, 141, 148,150, 162, 195, 226, 230

metrical progression, 82—85neighboring motion, 83passing' motion, 84, 230reduction of, 83—85See also metrical narrative

metrical revision, 117-41, 148, 149, 262,269-70

adding accents, 122-23, 228, 266adding voices, 118 — 19, 266altering dissonance type, 121, 266deleting a dissonant passage, 125deleting accents, 122, 125, 130, 180, 226,

267inserting a dissonant passage, 117—18

Schumann Metrical Dissonance - [PDF Document] (304)

Index 289

metrical process and, 132—41realigning voices, 119reasons for, 129-41, 146, 148, 149, 160,

162metrical states, 29-30, 39, 61, 82, 83, 86, 98,

114, 146-48, 155, 225, 238frequency of change of, 192, 203, 211, 213,

220, 225, 234, 237, 238, 240, 244proportions of, 83, 188, 192, 203, 211, 220,

224, 234, 237, 244Metternich, Prince Clemens, 217micropulse, 23, 30, 53Montag, Karl, 218Moscheles, Ignaz, 65, 77, 80

Twenty-Four Etudes op. 70, 66—67

Mozart, Wolfgang Amadeus, 14, 15, 18Don Giovanni, 217String Quartet in C Major, K. 465,

244String Quartet in D Minor, K. 421, 244

nesting, synonym for metrical consonance,15, 29-30

Neue Zeitschrift fur Musik, 72, 172, 216, 217,218

noncongruence, synonym for displacementdissonance, 14

Pagamm, Niccolo, 156Caprices for Solo Violin op. 1, 52

no. 3, 70no. 6, 69-70, 100-102, 142, 156no. 12, 70no. 13, 69

no. 16, 70, 80no. 24, 70

palindrome, 39—40Paul, Jean, 12, 177performance of metrical dissonance, 10, 20,

25, 29, 47, 51, 97-98, 108, 125, 140,167, 170, 177-86, 201, 204

role of subtle stresses in, 51, 97, 170,179-80, 182, 183-84

preparatory exercises, 178—79pitch-rhythm analogies, 262

dissonance analogy, 21, 29, 108, 150arithmetic approaches, 16—17geometric approaches, 17—18origins, 13, 15-18

embellishment analogyneighboring motion, 83passing motion, 84, 230

modulation analogy, 13, 223, 224, 231, 259sequence analogy, 11, 13

pitch structurecoordinated with metrical dissonance, 5,

79, 142, 145, 149-56, 227, 236coincidence of harmonic and metrical

parentheses, 155 — 56dissonance associated with an analo-

gous pitch state, 149-54, 156, 167,227

dissonance highlighting significant pitchevents, 153-54

metrical process associated with ananalogous pitch process, 154 — 55

recurring pitch events associated withsame metrical dissonance, 156

and the formation of layers of motion,25-27, 29, 241

and the formation of metrical dissonance,10, 12

polymeter, 20, 258polyrhythmic construction, synonym for

grouping dissonance, 244preparation. See metrical processprimary consonance. See metrical conso-

nanceprimary metrical layer. See layers of motionProphet Bird, 14, 22, 61, 141, 248pulse, 23

micropulse, 23, 53See also layers of motion

Reissman, August, 19resolution, metrical. See metrical processresultant rhythm, 16, 17, 39-44, 53, 95, 100,

246Rhine, 130, 131, 251rhythmic dissonance, 14, 15, 16, 17Richarz, Dr. Franz, 177, 243Riemann, Hugo, 8-13, 257

and large triplets, 10and layers of motion, 22and notation of metrical conflict, 8—11sequence analogy, 11

Roeder, John, 22, 259, 274Rosen, Charles, 19Rothstein, William, 18

Sabimri, Martha von, 177Schachter, Carl, 15Schaeffer, Julius, 220-21Schenkcr, Heinrich, 152-54

Schumann Metrical Dissonance - [PDF Document] (305)

290 Index

Schillinger, Joseph, 16-17Schnebel, Dieter, 19Schoenbcrg, Arnold, 244

"Valse de Chopin," 244-48

Schubert, Franz, 80, 215, op. 9, 71-73

Deutsche und Ecossaisen op. 33, 72, 263,272

Piano Trio in Bb Major, op. 99, secondmvmt., 72

Piano Trio in Eb Major, op. 100, fourthmvmt., 72

Schumann, Clara (nee Wieck), 22, 29, 36,51, 60-61, 65, 81, 82, 117, 129-32,149, 170, 171, 173, 177-86, 216-18,249, 252

"Geheimes Flustern," op. 23 no. 3, 210Piano Concerto in A Minor, op. 7, 209-10Piano Trio in G Minor, op. 17, 210-13

Schumann, Robertas conductor, 157, 251as critic, 5, 11-12, 68, 72, 199, 216-18,

219, 270conflicts in his life, 171-72, 217-19Foreword to Sechs Concert-Eluden op. 10,

77influenced by

Bach, J. S., 71-72Beethoven, 73 — 77early nineteenth-century pianists,

65-69, 77Paganini, 69-70Schubert, 72-73

mental illness, 20, 53, 91, 99, 173, 177,185-86, 187, 209, 243, 246-48,249-52

on metrical conflict, 4, 5, 11-12, 13and Vienna, 216-19works. See List of Cited Works by Robert

SchumannSedlnitzky, Count Joseph, 217Seeger, Charles, 16—17subliminal dissonance. See metrical dissonancesubmerging. See metrical process

surfacing. See metrical processsyncopation, 10, 12, 13, 19, 20, 33, 60, 66,

102, 103, 109, 112, 126, 128, 133,159, 162, 163, 183, 213, 240

See also displacement dissonance

Tausch, Julius, 132, 149, 173text, and metrical dissonance, 156-71

dissonance coordinated with poetic form,233

dissonance highlighting significant text,159-60, 169-70, 171

dissonance related to poetic meter, 164-65dissonance representing emotional states,

161-64, 167, 170-71dissonance suggesting different levels or

dimensions, 160 — 61metrical mimicry, 157-58, 170, 171, 210

tightening. See metrical processtype A dissonance, synonym for grouping

dissonance, 31type B dissonance, synonym for displace-

ment dissonance, 33

Verschiebung, synonym for displacement dis-sonance, 18, 94

Verwechslung, synonym for grouping disso-nance, 18

Vienna, 216-19

Wagner, Johann Ernst, 12, 219waltz, 33, 72, 215, 248, 263Wieck, Clara. See Schumann, Clara (nee

Wieck)Wieck, Friedrich, 44, 65, 171-72, 173

Yeston, Mauryand cycles, 32and layers of motion, 22and resultant rhythm, 261and rhythmic consonance and dissonance,

17, 34

Zwickau, 185

Schumann Metrical Dissonance - [PDF Document] (2024)


What are the different types of metrical dissonance? ›

[2.1] Krebs (1999) identifies two basic types of metric dissonance: displacement dissonance, in which the grouping of units remains the same but the position of the first unit is shifted either forward or backward in time, and grouping dissonance, in which the grouping of units changes, as in a hemiola (Example 2a).

What is displacement dissonance? ›

Displacement dissonance, in which two or more layers with the same meter (or grouping structure) are displaced against each other. Grouping dissonance, in which two or more layers with unique grouping structures (that are not simple multiples/factors of each other) can be heard simultaneously.

What is rhythmic dissonance? ›

Rhythmic dissonance is the compositional tool of organiz- ing and layering different qualities of rhythm (such as meter Page 7 What is Rhythmic Dissonance? — 7/22 and tempo) to create tension within a piece of music.

What are the different types of dissonance? ›

These species of dissonances are seven: semitone, tritone, major third plus fifth; tone plus fifth, minor third plus fifth; tone and semitone plus fifth.

What is the most common metrical pattern? ›

This type of metrical foot is called an iamb and there are five of them here. Since “penta” is the prefix for five, we call this metrical form “iambic pentameter,” the most common meter in English poetry.

What is the paradox of cognitive dissonance? ›

Cognitive dissonance is considered as emerging between the social identity of persons and that of their acts. An analysis is made of the paradoxical consequences of a double bind: Those who are A are supposed not to do B and are also supposed not to think that those who are A would be allowed to do B.

What are the five primary types of cognitive dissonance? ›

There are five primary types of cognitive dissonance: post-decisional dissonance, dissonance from wanting something we can't have, dissonance due to inconsistency between attitude and behavior, dissonance due to inadequate justification, and dissonance due to inconsistency between commitment and information.

What is a cadential hemiola? ›

Hemiola is a rhythm device that occurs when there are 3 beats in a measure to bring attention to musical cadences. A cadence is a musical arrival point. Hemiola is a grouping of accented beats that forms a rhythmic flow that is twice as slow as the main beat. ( Or half as fast)

How many types of metrical are there? ›

Metrical systems

The four major types are: accentual verse, accentual-syllabic verse, syllabic verse and quantitative verse. The alliterative verse found in Old English, Middle English, and some modern English poems can be added to this list, as it operates on somewhat different principles than accentual verse.

What are the types of poetry metrical tale? ›

Definition o Metrical tale is a narrative poem which is written in verse that relates to real or imaginary events in simple, straight forward language, from a wide range of subjects, characters, life experiences, and emotional situations.

What are the metrical patterns? ›

A metrical foot consists of one beat (accented syllable) and either two or three unaccented syllables. The most common metrical patterns in poetry are iambic pentameter, blank verse (which is unrhymed iambic pentameter), and free verse.

What is an example of dissonance in a poem? ›

In Macbeth, Shakespeare employs poetic dissonance to convey Macbeth's stress and desperation: “Of all men else I have avoided thee. With blood of thine already.” The consonants and vowels of Macbeth's lines clash and sound unpleasant to the ear.

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