Audacious Euphony 00-Cohn-FM.indd i 10/13/2011 12:38:43 PM 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 00-Cohn-FM.indd ii 10/13/2011 12:38:43 PM Audacious Euphony C hromaticism and the Triad’s Second Nature Richard Cohn 1 00-Cohn-FM.indd iii 10/13/2011 12:38:43 PM 1 Oxford University Press, Inc., publishes works that further Oxford University’s objective of excellence in research, scholarship, and education. 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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 00-Cohn-FM.indd iv 10/13/2011 12:38:43 PM in memoriam John Clough David Lewin 00-Cohn-FM.indd v 10/13/2011 12:38:43 PM This page intentionally left blank 00-Cohn-FM.indd vi 10/13/2011 12:38:43 PM 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 00-Cohn-FM.indd vii 10/13/2011 12:38:43 PM (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 00-Cohn-FM.indd viii 10/13/2011 12:38:43 PM 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 00-Cohn-FM.indd ix 10/13/2011 12:38:43 PM