Mathematics and Computation in Music

1. Front Matter

   Pages I-XI

   PDF

2. Algebraic Models

   1. Front Matter

      Pages 1-1

      PDF

   2. Primal-Circular Substitutions

      • Marcus D. Booth

      Pages 3-12

   3. On the Group of Transformations of Classical Types of Seventh Chords

      • Sonia Cannas, Samuele Antonini, Ludovico Pernazza

      Pages 13-25

   4. Pairwise Well-Formed Modes and Transformations

      • David Clampitt, Thomas Noll

      Pages 26-37

   5. Homometry in the Dihedral Groups: Lifting Sets from \( \mathbb {Z}_{n}\) to \( D_{n}\)

      • Grégoire Genuys, Alexandre Popoff

      Pages 38-49

   6. A Symmetric Quantum Theory of Modulation in \(Z\!\!Z_{20}\)

      • J. David Gómez-Téllez, Emilio Lluis-Puebla, Mariana Montiel

      Pages 50-62

   7. Almost Difference Sets in Transformational Music Theory

      • Robert W. Peck

      Pages 63-75

   8. Algebra of Harmony: Transformations of Just Consonances

      • Marek Žabka

      Pages 76-88

3. Computer Assisted Performance

   1. Front Matter

      Pages 89-89

      PDF

   2. Developing Software for Dancing Tango in Compás

      • Emmanuel Amiot, Jean-Philippe Lerat, Bérenger Recoules, Valérie Szabo

      Pages 91-103

   3. Using Inharmonic Strings in Musical Instruments

      • Kevin Hobby, William A. Sethares, Zhenyu Zhang

      Pages 104-116

   4. Real-Time Compositional Procedures for Mediated Soloist-Ensemble Interaction: The Comprovisador

      • Pedro Louzeiro

      Pages 117-131

4. Fourier Analysis

   1. Front Matter

      Pages 133-133

      PDF

   2. Strange Symmetries

      • Emmanuel Amiot

      Pages 135-150

   3. Interval Content vs. DFT

      • Emmanuel Amiot

      Pages 151-166

   4. Probing Questions About Keys: Tonal Distributions Through the DFT

      • Jason Yust

      Pages 167-179

5. Gesture Theory

   1. Front Matter

      Pages 181-181

      PDF

   2. Abstract Gestures: A Unifying Concept in Mathematical Music Theory

      • Juan Sebastián Arias

      Pages 183-200

   3. Mathematical Music Theory and the Musical Math Game—Two Creative Ontological Switches

      • Guerino Mazzola

      Pages 201-212

This book constitutes the thoroughly refereed proceedings of the 6th International Conference on Mathematics and Computation in Music, MCM 2017, held in Mexico City, Mexico, in June 2017. The 26 full papers and 2 short papers presented were carefully reviewed and selected from 40 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in topical sections on algebraic models, computer assisted performance, Fourier analysis, Gesture Theory, Graph Theory and Combinatorics, Machine Learning, and Probability and Statistics in Musical Analysis and Composition.

• developing variation
• discrete Fourier transform
• geometric approaches to music
• hierarchical structure in music
• Markov model
• microtonal
• music notation
• music representation
• musical patterns
• musical performance theory and analysis
• musical scales and tuning
• musical similarity and contrast
• operations research in music
• post-tonal music analysis
• time-span tree
• transformation spaces
• music information retrieval
• signal processing
• artificial intelligence
• machine learning

• UNCA and UTM, Oaxaca, Mexico

  Octavio A. Agustín-Aquino

• UNAM, Mexico City, Mexico

  Emilio Lluis-Puebla

• Georgia State University, Atlanta, USA

  Mariana Montiel

Policies and ethics