Music and Twentieth-Century Tonality Routledge Studies in Music Theory 1 Music and Twentieth-Century Tonality Harmonic Progression Based on Modality and the Interval Cycles Paolo Susanni and Elliott Antokoletz Music and Twentieth-Century Tonality Harmonic Progression Based on Modality and the Interval Cycles Paolo Susanni and Elliott Antokoletz NEW YORK LONDON First published 2012 by Routledge 711 Third Avenue, New York, NY 10017 Simultaneously published in the UK by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2012 Taylor & Francis The right of Paolo Susanni and Elliott Antokoletz to be identified as author of this work has been asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Susanni, Paolo, author. Music and twentieth-century tonality : harmonic progression based on modality and the interval cycles / Paolo Susanni and Elliott Antokoletz. pages cm — (Routledge studies in music theory ; 1) Includes bibliographical references and index. 1. Music—20th century—Analysis, appreciation. 2. Musical analysis. I. Antokoletz, Elliott, author. II. Title. III. Series: Routledge studies in music theory ; 1. MT6.S87 2012 780.9'04—dc23 2011049874 ISBN: 978-0-415-80888-0 (hbk) ISBN: 978-0-203-11929-7 (ebk) Typeset in Sabon by IBT Global. To the Susanni and Antokoletz families Contents List of Tables and Figures ix Preface xi Acknowledgments xvii 1 General Concepts 1 2 Interval Cycles 21 3 Compound Cyclic Collections 43 4 Inversional Symmetry and the Axis Concept 63 5 Modes 81 6 Modal/Cyclic Relationships 102 7 Harmonic Structures, Pitch Cells, and Cyclic Tetrachords 128 Notes 147 Bibliography 153 Index to Compositions 155 General Index 157 Tables and Figures FIGURES 1.1 Webern, Piano Piece Op. Posth. (mm. 1–5). 5 1.2 Debussy, La Cathédrale engloutie (mm. 1–2). 6 1.3 Messiaen, Le baiser de l’Enfant-Jesus (mm. 39–44). 9 1.4 Schoenberg, Three Piano Pieces Op. 11, No.1 (mm. 1–3). 10 1.5 Crumb, Spiral Galaxy fi rst “A” section. 17 1.6 Crumb, Spiral Galaxy fi rst “B” section. 18 1.7 Crumb, Spiral Galaxy “C” section. 19 2.1 Ligeti, Cordes à vide (mm. 1–4). 28 2.2 Bartók, Study No. 1 (mm. 107–114). 31 2.3 Bartók, Suite Op. 14 (mm. 1–8). 33 2.4a Lutoslawski, Étude (mm. 1–3). 35 2.4b Lutoslawski, Étude (mm. 5–6). 35 2.5 Ives, Psalm XXIV (mm. 1–4). 40 2.6 Ives, Psalm XXIV (mm. 23–24). 41 3.1 Ives, Psalm XXIV (mm. 16–19). 53 3.2 Takemitsu, Rain Tree Sketch (mm. 1–6). 54 3.3 Busoni, Sonatina Seconda (mm. 1–4). 56 3.4 Muszynski, Toccata Op. 15 (mm. 1–7). 58 3.5 Ginastera, Piano Sonata No. 1, Mvt. II. (mm. 25–31). 61 4.1 Bartók, Bagatelle No. 2 (mm. 1–6). 68 4.2a Debussy, Voiles (mm. 1–2). 70 4.2b Debussy, Voiles (mm. 5–9). 70 4.3 Bartók, The Night’s Music (m. 1). 71 4.4 Ives, Psalm XXIV (mm. 16–18). 75 4.5 Bartók, Mikrokosmos No. 141, Subject and Refl ection (mm. 1–3). 76 4.6 Penderecki, Threnody to the Victims of Hiroshima. 79 x Tables and Figures 5.1 Kodaly, Valsette (mm. 6–11). 85 5.2 Copland, The Cat and the Mouse: Scherzo Humoristique (mm. 1–4). 86 5.3 Lutoslawski, Melodie (mm. 25–28). 89 5.4 Bartók, In the Hungarian Style (mm. 1–4). 91 5.5a Stravinsky, Hymne (mm. 1–2). 92 5.5b Stravinsky, Hymne (mm. 12–14). 92 5.6 Adams, Phrygian Gates (mm. 234–238). 94 6.1a Ravel, Laideronnette, Imperatrice des pagodes (mm. 1–6). 109 6.1b Ravel, Laideronnette, Imperatrice des pagodes (mm. 12–13). 109 6.2a Bartók, Piano Sonata, Mvt. III (mm. 1–4). 112 6.2b Bartók, Piano Sonata, Mvt. III (mm. 7–8). 112 6.3 Ligeti, Désordre (mm. 1–5). 116 6.4a Bartók, Piano Sonata, Mvt. I (mm. 1–7). 117 6.4b Bartók, Piano Sonata, Mvt. I (mm. 13–16). 117 6.5a Debussy, L’isle Joyeuse (m. 1). 120 6.5b Debussy, L’isle Joyeuse (mm. 8–9). 120 6.6a Scriabin, Op. 74, No. 3 (mm. 1–3). 125 6.6b Scriabin, Op. 74, No. 3 (mm. 23–26). 125 7.1 Bartók, Sonata for Piano Mvt. III (mm. 71–76). 131 7.2 Bartók, Sonata for Piano Mvt. III (mm. 82–90). 132 7.3 Bartók, From the Isle of Bali (mm. 1–2). 134 TABLES 2.1 Complex of Interval Cycles 22 3.1 Compound Cyclic Collections 44 Preface The vast majority of those who study western art and popular music from an early age are fi rst schooled in the fundamental principles that underlie the music of the traditional tonal system. The journey commences with the study and application practice of the major and minor scales, which form the core of this system. This entails the identifi cation and building of intervals, primary triads, and the more complex tertian constructions such as seventh chords. These triads and larger tertian constructions represent the principal harmonic elements of the system. Once these are mastered, the study of tra- ditional harmonic function harmony is undertaken. Students spend most of the time allotted to music theory studies, learning the principles of harmonic function and concepts of voice-leading that dictate all pitch relations in tradi- tional tonal music. The subject is taught in the minutest of details and is still considered the core of essential musical knowledge. In typical western musical education, the contrapuntal modal music of the Middle Ages and Renaissance is given little priority in comparison to that given to the music of the common practice era. It also is usually reserved for special studies at an advanced educational stage. This non sequitur is at odds with the actual historical sequence of developments from modality to major/minor tonality. Most often, the principles that underlie the music of the common practice era are given little if any historical context, that is, that which underlies the changes in the perception of such musical concepts as consonance and dissonance. 20th century music is dealt with in much the same way as that of the Middle Ages and Renaissance, even though so much of it has become part of the standard musical repertoire and the subject of intense theoretical and musicological scrutiny. Only a small fraction of the total time spent in the study of musical theory and harmony is devoted to it. Most performers and scholars leave the university with only a marginal knowledge of 20th century music. No amount of in-depth study of traditional tonal music such as that of Bach, Beethoven, and Brahms can prepare one for the analysis of music as wide-ranging in style as that of Debussy, Stravinsky, and Ligeti. The music of the latter composers cannot be analyzed using the canons of the traditional xii Preface tonal system. The traditional scales of the common practice period are part of an open system of transpositions and modulations, their interactions forming the core of analytic methods that theorists and composers used in their work. The new musical language is based on a new conception of the identity and structure of scales and their interactions. In contrast to the openness of the traditional major/minor system, the scales used in 20th century music tend to represent closed entities (discrete and contrasting structures), and their interactions diff er from those found in traditional major/minor scales. A short explanation of some of the fundamental diff erences between tra- ditional tonal music and modal or scalar based 20th century music might highlight the diffi culties encountered in the analysis of the music of the latter category. In traditional tonal music based on the major/minor scale system and ter- tian harmony, each degree of the major or minor scale occupies a particular position that indicates the known functions such as tonic, subdominant and dominant, and the notion of a leading tone. In this music, individual scale degrees play diff erent melodic and harmonic roles in creating motion. In the sphere of traditional tonal progression, each note fulfi lls a specifi c tonal function relative to its contextual position. The level of musical tension and function of each note in the tonal composition creates a hierarchical system based primarily on these two aspects. Traditional tonal hierarchy is largely created by the unequal subdivision off the octave into the major and minor modes as well as their triadic substructures. At the end of the 19th century and beginning of the 20th century, the weakening and eventual dissolution of tonal hierarchy led to the equalization of the twelve tones. Thus, tonality relies on the unequal subdivision of the octave while the dissolution of tonal function relies on the equal or symmetrical subdivision of the octave. Traditional tonal music is limited to a single type of harmonic structure (i.e., the triad derived exclusively from the major and minor scales), whereas the works by 20th century composers are often based on diverse types of harmonic constructions derived from a host of diff erent scalar formations that include the seven diatonic modes, special non-diatonic modes, hybrid modes, and the system of interval cycles.