Jack Douthett & Martha Hyde 
Music Theory and Mathematics 
Chords, Collections, and Transformations

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 descentfrom 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.

Inhaltsverzeichnis

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