Music Theory and Mathematics

Music Theory and Mathematics

Chords, Collections, and Transformations

Edited by Jack Douthett, Martha M. Hyde, Charles J. Smith


University of Rochester Press



Essays in diatonic set theory, transformation theory, and neo-Riemannian theory -- the newest and most exciting fields in music theory today.
The essays in Music Theory and Mathematics: Chords, Collections, and Transformations define the state of mathematically oriented music theory at the beginning of the twenty-first century. The volume includes essays in diatonic set theory, transformation theory, and neo-Riemannian theory -- the newest and most exciting fields in music theory today.
The essays constitute a close-knit body of work -- a family in the sense of tracing their descent from a few key breakthroughs by John Clough, David Lewin, and Richard Cohn in the 1980s and 1990s. They are integrated by the ongoing dialogue they conduct with one another.

The editors are Jack Douthett, a mathematician and music theorist who collaborated extensively with Clough; Martha M. Hyde, a distinguished scholar of twentieth-century music; and Charles J. Smith, a specialist in tonal theory. The contributors are all prominent scholars, teaching at institutions such as Harvard, Yale, Indiana University, and the University at Buffalo. Six of them (Clampitt, Clough, Cohn, Douthett, Hook, and Smith) have received the Society for Music Theory's prestigious Publication Award, and one (Hyde) has received the ASCAP Deems Taylor Award. The collection includes the last paper written by Clough before his death, as well as the last paper written by David Lewin, an important music theorist also recently deceased.

Contributors: David Clampitt, John Clough, Richard Cohn, Jack Douthett, Nora Engebretsen, Julian Hook, Martha Hyde, Timothy Johnson, Jon Kochavi, David Lewin, Charles J. Smith, and Stephen Soderberg.

An e-book version of this title is available (9781580467476), to libraries through a number of trusted suppliers. See here for a full list of our partners.


February 2008
114 line illustrations
278 pages
9x6 in
Eastman Studies in Music
ISBN: 9781580462662
Format: Hardback
University of Rochester Press
BISAC MUS020000, MAT003000
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Table of Contents

Introduction by Normal Carey, Jack Douthett, and Martha M. Hyde
Preface by Charles J. Smith
"Cardinality Equals Variety for Chords" in Well-Formed Scales, with a Note on the Twin Primes Conjecture - David Clampitt
Flip-Flop Circles and Their Groups - John Clough
Pitch-Time Analogies and Transformations in Bartók's Sonata for Two Pianos and Percussion - Richard Cohn
Filtered Point-Symmetry and Dynamical Voice-Leading - Jack Douthett
The "Over-Determined" Triad as a Source of Discord: Nascent Groups and the Emergent Chromatic Tonality in Nineteenth-Century German Harmonic Theory Nineteenth-Century German Harmonic Theory - Nora Engebretsen
Signature Transformations - Julian Hook
Some Pedagogical Implications of Diatonic and Neo-Riemannian Theory - Timothy Johnson
A Parsimony Metric for Diatonic Sequences - Jonathan Kochavi
Transformational Considerations in Schoenberg's Opus 23, Number 3 - David Lewin
Transformational Etudes: Basic Principles and Applications of Interval String Theory - Stephen Soderberg


These essays, by leading American music theorists, continue the development of some of the most important research of the last twenty years into mathematical models of basic musical structures. These models are elegant in the abstract, but they are also shown to have many practical applications in explaining a wide range of art music. Several of the contributions are bound to be classics in this literature. --John Roeder, Professor of Music Theory, University of British Columbia

Music Theory and Mathematics is a fitting memorial to John Clough, one of music theory's great pioneers. Clough was among the first scholars to introduce non-trivial mathematics into what has emerged as diatonic set theory or scale theory. This volume consists of essays by important theorists on a variety of topics ranging from scale and Riemannian theory to analysis of works by Bartók and Schoenberg. Building on Clough's research, Music Theory and Mathematics poses new questions and approaches to what are perhaps the most exciting directions in music theory today. --Robert Morris, Professor of Composition, Eastman School of Music, University of Rochester

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