Tonality and Transformation 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 Tonality and Transformation STEVEN RINGS 1 1 Oxford University Press, Inc., publishes works that further Oxford University’s objective of excellence in research, scholarship, and education. Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offi ces in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Th ailand Turkey Ukraine Vietnam Copyright © 2011 by Oxford University Press Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 www.oup.com Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Rings, Steven. Tonality and transformation / Steven Rings. p. cm.—(Oxford studies in music theory) Includes bibliographical references and index. ISBN 978-0-19-538427-7 1. Music theory. 2. Tonality. 3. Musical intervals and scales. 4. Musical analysis. I. Title. MT6.R682T66 2011 781.2—dc22 2010019212 Publication of this book was supported by the AMS 75 PAYS Publication Endowment Fund 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 CONTENTS Acknowledgments vii Note to Readers ix A Note on Orthography x i Introduction 1 P ART I Theory and Methodology Chapter 1: Intervals, Transformations, and Tonal Analysis 9 Chapter 2: A Tonal GIS 41 Chapter 3: Oriented Networks 101 PART II Analytical Essays Chapter 4: Bach, Fugue in E major, W ell-Tempered Clavier , Book II, BWV 878 151 Chapter 5: Mozart, “Un’aura amorosa” from C osì fan tutte 171 Chapter 6: Brahms, Intermezzo in A major, op. 118, no. 2 185 Chapter 7: Brahms, String Quintet in G major, mvt. ii, Adagio 203 Aft erword 221 Glossary 223 Works Cited 231 Index 239 This page intentionally left blank ACKNOWLEDGMENTS Th anks are due fi rst to my wife Gretchen, for her prodigious patience and grace; though she remains blissfully innocent of this book’s contents, she has been a lim- itless source of inspiration. My son Elliott served as a sort of inadvertent quality control: this volume would have been completed at least a year sooner had he not come along. I hope my thinking is a year more refi ned than it would have been without him; my life is certainly immeasurably richer. Th e book is dedicated to them. I also thank my mother Linda, my father Dale, and my brother Mike for their unwavering love and support. My Doktorvater Daniel Harrison oversaw the fi rst iteration of many of these ideas; his spirit imbues this work. David Clampitt introduced me to this style of music theory and off ered trenchant observations on ideas new to this book. My other teachers at various stages in my graduate work—in particular, Pat McCreless, Allen Forte, James Hepokoski, Leon Plantinga, Craig Wright, Michael Cherlin, and David Damschroder—all played crucial roles in shaping my theo- retical and critical outlook. Ian Quinn saved me from myself at one very early stage, pointing out a rather hilarious, exhaustion-induced slip (I had decided for several pages that there were only 11 chromatic pitch classes). Ramon Satyendra and Julian Hook both read the manuscript and provided invaluable comments on matters large and small. Henry Klumpenhouwer off ered critical perspectives on the conceptual foundations of Lewinian theory, while Peter Smith and Frank Samarotto lent insight into matters Schenkerian. Dmitri Tymoczko has been a valued sparring partner and friend; this book has benefi ted greatly from his criti- cal perspective. Th e anonymous readers for Oxford challenged me on several important points and forced me to clarify my thinking. Lucia Marchi answered questions on Da Ponte’s verse. My assistant Jonathan De Souza has done yeoman work as a design consultant, typeface expert, punctuation cop, indexer, and editor extraordinaire (his passion for the Chicago Manual almost exceeds my own). All of these individuals helped improve this book. Th e errors that inevitably remain are mine, not theirs. Richard Cohn has been a supporter of this work from the beginning—he has in many ways opened the theoretical space within which my ideas have unfolded. As the editor of this series, he also helped acquire the book for Oxford. I cannot thank him enough. Suzanne Ryan has been a model editor, enthusiastic and patient in equal measure; her confi dence and understanding helped me weather a couple rough patches. Norm Hirschy and Madelyn Sutton at Oxford have also vii (cid:2) viii Acknowledgments been a delight to work with, making the whole process run more smoothly than I could have hoped. I would also like to thank the Mrs. Giles Whiting Foundation for supporting the year’s research leave necessary to complete the book, and the American Musicological Society for a generous subvention from the AMS 75 PAYS Publication Endowment Fund. My scholarly home during this book’s writing has been the University of Chicago. I would like to thank the chairs of the music department during this time—Robert Kendrick and Martha Feldman, as well as interim chairs Anne Robertson and Larry Zbikowski—for providing unstinting support and helping to create the ideal intellectual environment for a junior faculty member. My fel- low theorists at Chicago—Larry Zbikowski and Th omas Christensen—are the best professional and intellectual role models I could hope for; they are also good friends. My colleagues in historical musicology, ethnomusicology, and composi- tion have at once inspired me with their own achievements and helped to keep my thinking productively unsettled. Th e same can be said for the remarkable cohort of graduate students that I have had the pleasure to work with over the last fi ve years. Finally, I would like to thank Berthold Hoeckner for many hours of stimulating conversation and for his valued insights into the balance between work and family. While I cannot imagine a better personal home than the one I described in the fi rst paragraph of these acknowledgments, I cannot imagine a better intellectual home than the one created by my friends and mentors in the University of Chicago Department of Music. NOTE TO READERS I have sought to make this book both accessible and formally substantive. It is a tricky balance: one risks disappointing both specialists (who wish there was more math) and nonspecialists (who wish there was less). Th e latter readers may indeed wonder why any math is needed at all.1 While I hope that the book will speak for itself in this regard, I will answer here that statements in transformational theory gain their musical suggestiveness in signifi cant part from the formal structures that support them. Th ose structures situate each musical interval or gesture within a richly developed conceptual space; the algebraic contours of that space contribute in important ways to the character of the interval or gesture in question. Th is underlying formal context is some- times operative only “behind the scenes”; at other times it is thematized in the foreground of an analysis. In either case, an awareness of the pertinent under- lying structure adds considerably to the allusiveness of any observation made in the theory, sensitizing us to the expressive particularity of a given musical rela- tionship. Moreover, the theory’s formalism can act as a generator of insights: once a basic musical observation has been rendered in transformational terms, the technology can lead the analyst toward new observations. Th e formal pre- cision of the apparatus assures that the new insights will be related to the old, oft en in compelling ways. I have nevertheless limited the amount of formalism in the book, and not only out of ethical concerns for accessibility. Th e simplicity of the book’s math results from my conviction that much of the fascination in this style of music theory resides in the reciprocal interaction that it aff ords between formal ideas and musical experience. One does not need to delve very far into the math to explore that interaction. My interest has thus been to employ only as much formalism as needed, and to expend somewhat greater eff ort seeking out the ways in which the resulting technical ideas may be brought to bear on musical experience—modeling or shaping it—in ways that are at once concrete and immediate. For the specialist wishing for more mathematical development, I hope the basic ideas introduced 1. In addition to my comments here, readers may wish to consult John Clough’s eloquent answer to this question in his review of David Lewin’s Generalized Musical Intervals and Transformations ( Clough 1989 , 227) . ix