Music Theory and Mathematics : Chords, Collections, and Transformations

Preface vii Charles J. Smith Introduction 1 Norman Carey, Jack Douthett, and Martha M. Hyde 1 "Cardinality Equals Variety for Chords" in Well-Formed Scales, with a Note on the Twin Primes Conjecture 9 David Clampitt 2 Flip-Flop Circles and Their Groups 23 John Clough 3 Pitch-Time Analogies and Transformations in Bartok's Sonata for Two Pianos and Percussion 49 Richard Cohn 4 Filtered Point-Symmetry and Dynamical Voice-Leading 72 Jack Douthett 5 The "Over-Determined" Triad as a Source of Discord: Nascent Groups and the Emergent Chromatic Tonality in Nineteenth-Century German Harmonic Theory 107 Nora Engebretsen 6 Signature Transformations 137 Julian Hook 7 Some Pedagogical Implications of Diatonic and Neo-Riemannian Theory 161 Timothy A. Johnson 8 A Parsimony Metric for Diatonic Sequences 174 Jonathan Kochavi 9 Transformational Considerations in Schoenberg's Opus 23, Number 3 197 David Lewin 10 Transformational Etudes: Basic Principles and Applications of Interval String Theory 222 Stephen Soderberg Works Cited 245 List of Contributors 253 Index 257