Introduction to Post-Tonal Theory

by Straus, Joseph N.

• ISBN13: 9780131898905
• ISBN10: 0131898906
• Edition: 3rd
• Format: Hardcover
• Copyright: 2004-08-18
• Publisher: Pearson

Summary

Emphasizing hands-on contact with the musicthrough playing, singing, listening, and analyzingthis book provides six chapters on theory, each illustrated with musical examples and fully worked-out analyses, all drawn largely from the "classical" pre-war repertoire by Schoenberg, Stravinsky, Bartok, Berg, and Webern.This book offers exceptionally clear, simple explanations of basic theoretical concepts for the post-tonal music of the twentieth century. Chapter topics include basic concepts and definitions; pitch-class sets; centricity, referential collections, and triadic post-tonality; basic twelve-tone operations; and more twelve-tone topics.Musicians and enthusiasts looking to explore advanced topics in music theory and analysis.

Author Biography

Joseph Straus is Distinguished Professor of Music at the Graduate Center of the City University of New York.  He taught for many years at the University of Wisconsin-Madison and Queens College (CUNY).  The author or editor of twelve books and numerous articles, mostly on topics in twentieth-century music, he is a former President of the Society for Music Theory.

Table of Contents

Preface	vii
Basic Concepts and Definitions	1	(32)
Octave equivalence	1	(2)
Pitch class	3	(1)
Enharmonic equivalence	3	(1)
Integer notation	4	(1)
Mod 12	5	(1)
Intervals	6	(1)
Pitch intervals	7	(1)
Ordered pitch-class intervals	8	(1)
Unordered pitch-class intervals	9	(2)
Interval class	11	(1)
Interval-class content	12	(1)
Interval-class vector	13	(3)
Exercises	16	(17)
Analysis 1	23	(10)
Webern, ``Wie bin ich froh!'' from Three Songs, Op. 25
Schoenberg, ``Nacht,'' from Pierrot Lunaire, Op. 21
Pitch-Class Sets	33	(46)
Pitch-class sets	33	(2)
Normal form	35	(3)
Transposition (Tn)	38	(6)
Inversion (TnI)	44	(3)
Index number (sum)	47	(2)
Inversion (Ix/y)	49	(3)
Set class	52	(5)
Prime form	57	(2)
Segmentation and analysis	59	(2)
Exercises	61	(18)
Analysis 2	67	(12)
Schoenberg, Book of the Hanging Gardens, Op. 15, No. 11
Bartok, String Quartet No. 4, first movement
Some Additional Relationships	79	(51)
Common tones under transposition (Tn)	79	(3)
Transpositional symmetry	82	(1)
Common tones under inversion (TnI)	83	(2)
Inversional symmetry	85	(6)
Z-relation	91	(2)
Complement relation	93	(3)
Subset and superset relations	96	(2)
Transpositional combination	98	(1)
Contour relations	99	(4)
Composing-out	103	(4)
Voice leading	107	(3)
Atonal pitch space	110	(4)
Exercises	114	(16)
Analysis 3	119	(11)
Webern, Movements for String Quartet, Op. 5, No. 4
Berg, ``Schlafend tragt man mich,'' from Four Songs, Op. 2
Centricity, Referential Collections, and Triadic Post-Tonality	130	(52)
Tonality	130	(1)
Centricity	131	(2)
Inversional axis	133	(7)
The diatonic collection	140	(4)
The octatonic collection	144	(3)
The whole-tone collection	147	(2)
The hexatonic collection	149	(1)
Collectional interaction	150	(4)
Interval cycles	154	(4)
Triadic post-tonality	158	(12)
Exercises	170	(12)
Analysis 4	174	(8)
Stravinsky, Oedipus Rex, rehearsal nos. 167--70
Bartok, Sonata, first movement
Basic Twelve-Tone Operations	182	(35)
Twelve-tone series	182	(1)
Basic operations	183	(9)
Subset structure	192	(3)
Invariants	195	(6)
Exercises	201	(16)
Analysis 5	205	(12)
Schoenberg, Suite for Piano, Op. 25, Gavotte
Stravinsky, In Memoriam Dylan Thomas
More Twelve-Tone Topics	217	(44)
Webern and derivation	217	(5)
Schoenberg and hexachordal combinatoriality	222	(9)
Stravinsky and rotational arrays	231	(3)
Crawford and her ``triple passacaglia''	234	(1)
Boulez and multiplication	235	(5)
Babbit and trichordal arrays	240	(6)
Exercises	246	(15)
Analysis 6	249	(12)
Webern, String Quartet, Op. 28, first movement
Schoenberg, Piano Piece, Op. 33a
Appendix 1 List of Set Classes	261	(4)
Appendix 2 Index Vectors	265	(4)
Index	269

Excerpts

Compared to tonal theory, now in its fourth century of development, post-tonal theory is in its infancy. But in the past three decades, it has shown itself to be an infant of prodigious growth and surprising power. A broad consensus has emerged among music theorists regarding the basic musical elements of post-tonal music--pitch, interval, motive, harmony, collection--and this book reports that consensus to a general audience of musicians and students of music. Like books on scales, triads, and simple harmonic progressions in tonal music, this book introduces basic theoretical concepts for the post-tonal music of the twentieth and twenty-first centuries.Beyond basic concepts, the third edition of this book also contains information on many of the most recent developments in post-tonal theory, including expanded or new coverage of the following topics: Transformational networks and graphs Contour theory Composing-out Atonal voice leading Atonal pitch space Triadic post-tonality (including voice-leading parsimony) Inversional symmetry and inversional axes Interval cycles Diatonic, whole-tone, octatonic, and hexatonic collectionsAs a result, this book is not only a primer of basic concepts but also an introduction to the current state of post-tonal theory, with its rich array of theoretical concepts and analytical tools.Although this book can make no pretense to comprehensiveness either, either chronologically or theoretically--there is just too much great music and fascinating theory out there--this third edition explores a much wider range of composers and musical styles than its predecessors. Although the "classical" prewar repertoire of music by Schoenberg, Stravinsky, Bart6k, Webern, and Berg still comprises the musical core, theoretical concepts are now also illustrated with music by Adams, Babbitt, Berio, Boulez, Britten, Cage, Carter, Cowell, Crawford, Crumb, Debussy, Feldman, Glass, Gubaidulina, Ives, Ligeti, Messiaen, Musgrave, Reich, Ruggles, Sessions, Shostakovich, Stockhausen, Varese, Wolpe, Wuorinen, and Zwilich.As with the previous editions of this book, I received invaluable advice from many friends and colleagues based on their teaching experience. I am grateful to Wayne Alpern, Jonathan Bernard, Claire Boge, Ricardo Bordini, Scott Brickman, Michael Buckler, Uri Burstein, James Carr, Patrick Fairfield, Michael Friedmann, Edward Gollin, Dave Headlam, Gary Karpinski, Rosemary Killam, Bruce Quaglia, Daniel Mathers, Carolyn Mullin, Catherine Nolan, Jay Rahn, Nancy Rogers, Steven Rosenhaus, Art Samplaski, Paul Sheehan, Stephen Slottow, David Smyth, Harvey Stokes, Dmitri Tymoczko, and Joyce Yip. My thanks go also to Chris Johnson and Laura Lawrie at Prentice Hall for their expert editorial work at every stage. Michael Berry provided additional editorial assistance. Closer to home, in matters both tangible and intangible, Sally Goldfarb has offered continuing guidance and support beyond my ability to describe or repay. Adam and Michael helped, too. Joseph N. Straus Graduate Center City University of New York