Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts

330 Pages·2008·3.42 MB·English

by  Michiel Schuijer

Analyzing Atonal Music
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Eastman Studies in Music
Ralph P. Locke, Senior Editor
Eastman School of Music
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in order of publication, may be found at the end of this book.
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Analyzing Atonal Music
Pitch-Class Set Theory and Its Contexts
michiel schuijer
University of Rochester Press
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Copyright © 2008 Michiel Schuijer
All rights reserved. Except as permitted under current legislation,
no part of this work may be photocopied, stored in a retrieval system,
published, performed in public, adapted, broadcast, transmitted,
recorded, or reproduced in any form or by any means, without
the prior permission of the copyright owner.
First published 2008
University of Rochester Press
668 Mt. Hope Avenue, Rochester, NY 14620, USA
www.urpress.com
and Boydell & Brewer Limited
PO Box 9, Woodbridge, Suffolk IP12 3DF, UK
www.boydellandbrewer.com
ISBN-13: 978–1–58046–270-9
ISBN-10: 1–58046–270-7
ISSN: 1071–9989
Library of Congress Cataloging-in-Publication Data
Schuijer, Michiel.
Analyzing atonal music : pitch-class set theory and its contexts / Michiel Schuijer.
p. cm.—(Eastman studies in music, ISSN 1071–9989 ; v. 60)
Includes bibliographical references and index.
ISBN-13: 978–1-58046–270–9 (hardcover : alk. paper)
ISBN-10: 1–58046–270–7 (alk. paper)
1. Musical analysis—Data processing. 2. Atonality. 3. Computer composition.
4. Musical pitch. 5. Set theory. I. Title.
MT6.S35294A63 2008
781.2'67—dc22
2008030245
Portions of chapters 2 and 3 first appeared as “Was ist ein pitch-class set?” in Wahrneh-
mung und Begriff: Dokumentation des Internationalen Symposions, Freiburg 2.–3. Juni 2000
(Kassel: Gustav Bosse Verlag, 2000). A large part of chapter 3 was published as
“T & I: A History of Abstraction” in Tijdschrift voor Muziektheorie 6/1 (February 2001).
A catalogue record for this title is available from the British Library.
This publication is printed on acid-free paper.
Printed in the United States of America.
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in liefdevolle herinnering
Korien de Boer
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Contents
List of Illustrations ix
Preface xv
Acknowledgments xvii
1 Pitch-Class Set Theory: An Overture 1
2 Objects and Entities 29
3 Operations 49
4 Equivalence 84
5 Similarity 130
6 Inclusion 179
7 “Blurring the Boundaries”: Analysis, Performance, and History 218
8 Mise-en-Scène 236
Reference List 279
Index 293
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Illustrations
Examples
1.1 Obvious and non-obvious combinations of tones in the opening
measures of Arnold Schoenberg’s Piano Piece, Op. 23, no. 3 5
1.2 Igor Stravinsky, Pas de Deux from Agon. An analysis of the
opening sonic fi eld, mm. 411–13 8
1.3 A device of progression. The Webern-group 10
1.4 The octatonic scale as the common ground between the materials
of Schoenberg’s piano piece and Stravinsky’s Pas de Deux 13
1.5 Heinrich Schenker’s analysis of a song by Robert Schumann:
“Aus meinen Tränen sprießen” from Dichterliebe 14
2.1 Pitch numbers 30
2.2 Conversion of pitch numbers to pitch-class (PC) numbers 30
2.3 Pitch intervals 37
2.4 Conversion of pitch intervals to pitch-interval classes (PICs) 37
2.5 PICs are order-dependent 38
2.6 PICs associated with PC pairs 39
2.7 PICs and interval classes according to Allen Forte 39
2.8 Schoenberg, Piano Piece, Op. 11, no. 1, mm. 49–50 42
2.9 Instances of a pitch-class set. An example from Joseph Straus’s
Introduction to Post-Tonal Theory 42
3.1 The transposition of a melody. A musical example from
Heinrich Christoph Koch’s Musikalisches Lexikon 53
3.2 Twelve-tone transposition. The beginning of the prelude from
Schoenberg’s Suite for Piano, Op. 25 54
3.3 PC-set transposition in Anton Webern’s Movement for String
Quartet, Op. 5, no. 5 56
3.4 Instances of T in Webern’s Opus 5, no. 5 58
9
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