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

Reviews

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
*.*