Audacious Euphony: Chromaticism and the Triad’s Second Nature

256 Pages·2012·6.736 MB·English

by  Richard Cohn

Audacious Euphony
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OXFORD STUDIES IN MUSIC THEORY
Series Editor Richard Cohn
Studies in Music with Text, David Lewin
Music as Discourse: Semiotic Adventures in Romantic Music , Kofi Agawu
Playing with Meter: Metric Manipulations in Haydn and Mozart’s Chamber Music
for Strings , Danuta Mirka
Songs in Motion: Rhythm and Meter in the German Lied , Yonatan Malin
A Geometry of Music: Harmony and Counterpoint in the Extended Common
Practice , Dmitri Tymoczko
In the Process of Becoming: Analytic and Philosophical Perspectives on Form in Early
Nineteenth-Century Music, Janet Schmalfeldt
Tonality and Transformation , Steven Rings
Audacious Euphony: Chromaticism and the Triad’s Second Nature , Richard Cohn
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Audacious Euphony
C hromaticism and the Triad’s Second Nature
Richard Cohn
1

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1

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Library of Congress Cataloging-in-Publication Data
Cohn, Richard Lawrence, 1955-
Audacious euphony : chromaticism and the consonant triad’s second nature / Richard Cohn.
p. cm. — (Oxford studies in music theory)
ISBN 978-0-19-977269-8 (hardback : alk. paper) — ISBN 978-0-19-983282-8 (companion website)
1. Harmony. 2. Triads (Music) I. Title. II. Series.
MT50.C736 2011
781.2΄5—dc22 2011008754
Publication of this book was supported by the Otto Kinkeldey Endowment of the
American Musicological Society.
1 3 5 7 9 8 6 4 2
Printed in the United States of America
on acid-free paper
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in memoriam
John Clough David Lewin
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CONTENTS
Introduction ix
About the Companion Web Site xviii
1 Mapping the Triadic Universe 1
Th ree Ways to Calculate Triadic Distance 1
Triads in Chromatic Space 8
Remarks on Syntax and Maps 13
2 Hexatonic Cycles 17
A Minimal-Work Model of the Triadic Universe 17
Th e Hexatonic Trance 20
Contrary Motion and Balance 24
Hexatonic Progressions, Tonnetz Representations,
and Triadic Transformations 25
Near Evenness, Minimal Voice Leading, and the
Central Role of Augmented Triads 33
Remarks on Dualism 37
Triadic Structure Generates Pan-Triadic Syntax 39
Triads Are Homophonous Diamorphs 40
3 Reciprocity 43
Th e Historical Emergence of Augmented Triads 43
Consonance/Dissonance Reciprocity 46
Two Early-Century Examples: Beethoven and Schubert 48
Th ree Late-Century Examples: Liszt, Rimsky-Korsakov, Fauré 49
Reciprocity in Weitzmann’s Der Ubermässige Dreiklang 56
4 Weitzmann Regions 59
Th e Structure of a Weitzmann Region 59
Weitzmann Transformations and N/R Cycles 61
Remarks on the Tonnetz 65
Historical Origins of Weitzmann Regions 67
Th e Double-Agent Complex 72
Expanded N/R Chains 76
Weitzmann Regions without Sequences: Wagner and Strauss 78
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(cid:2)
viii Contents
5 A Unifi ed Model of Triadic Voice-Leading Space 83
How Hexatonic and Weitzmann Regions Interact 83
Chromatic Sequences 89
Transformational Substitutions 95
Voice-Leading Zones 102
Remarks on Disjunction and Entropy 106
6 Navigating the Triadic Universe: Th ree Compositional Scripts 111
Neighborhoods and Pitch Retention Loops 113
Departure → Return Scripts 121
Continuous Upshift s 131
7 Dissonance 139
Four Eighteenth-Century Approaches to Dissonance 139
Reduction to a Triadic Subset 142
Hexatonic Poles in Parsifal 145
Th e Tristan Genus as Nearly Even Tetrachord 148
Circumnavigating the Tristan-Genus Universe 159
Scriabin’s Mystic Species and Generalized Weitzmann Regions 166
8 Syntactic Interaction and the Convertible Tonnetz 169
Some Previous Proposals 169
Th e Diatonic Tonnetz 175
Horizontal Extensions 179
Vertical Extensions 184
Th e Convertible Tonnetz 186
Two Analytical Vignettes: Wagner and Brahms 189
9 Double Syntax and the Soft Revolution 195
A Summary Example from Schubert 195
Double Syntax and Its Skeptics 199
Code Switching and Double Determination 201
Cognitive Opacity 203
Th e Soft Revolution 205
On Musical Overdetermination 208
Glossary 211
Bibliography 215
Index 229
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INTRODUCTION
Th e admittedly audacious but eff ective and euphonious progression shown [above]
defi es defi nition in terms of an older doctrine of key. But . . . it consists only of
closely related chords contrasted with the tonic triad.
— Hugo Riemann, s.v. “Tonalität,” M usik-Lexicon , 1909
Two questions arise. First, what notion of harmony underlies Hugo Riemann’s
judgment that these chords are closely related? Current textbooks have inherited
the eighteenth-century formulation that triads are closely related if their epony-
mous scales are identical to within one degree of diff erence: they share at least six
out of seven tones. Th ese harmonies don’t come close to qualifying: their associ-
ated scales share three tones out of seven. Riemann’s conception of harmonic dis-
tance is evidently rather diff erent from our own. How can we construct and
represent that conception? Second, if the triads are closely related, why does
Riemann call the progression “audacious”? Close relations are unmarked, well
formed, normal— n ot the stuff of audacity. Th ese questions lead to diff erent kinds
of responses. Th e fi rst is susceptible in principle to a systematic inquiry. If we can
establish that Riemann and his contemporaries calculated harmonic distance in a
consistent way, even if distinct from the way we do so, then we might have a chance
to understand the basis for his judgment. Th e second, because it identifi es a para-
dox, is an invitation to an interpretation.
Audacious Euphony reconstructs conceptions of triadic distance that were
proper to nineteenth-century harmonic thought but have since been stripped
from music theory’s inheritance. What eff ect do these alternative conceptions have
on our understanding of how the nineteenth-century ear understood harmonic
relations and how nineteenth-century composers craft ed strategies and made
choices that both appealed to and molded that ear? How did these alternative
conceptions, and the strategies and choices they motivated, contribute to the
charismatic, entraining, and sublime qualities that we still hear in many compositions
of that era?
H armonic theorists of the nineteenth century provided a partial response to
these questions. Th is book expands that sketch into a fully realized proposal using
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