Mathematical Music Theory

Algebraic, Geometric, Combinatorial, Topological and Applied Approaches to Understanding Musical Phenomena

Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.

The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.

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Contents:

• Section I:

  • From Musical Chords to Twin Primes (Jack Douthett, David Clampitt and Norman Carey)
  • Hypercubes and the Generalized Cohn Cycle (Jack Douthett, Peter Steinbach and Richard Hermann)
  • Associahedra, Combinatorial Block Designs and Related Structures (Franck Jedrzejewski)
  • Rhythmic and Melodic L-canons (Jeremy Kastine)
  • The Fibonacci Sequence as Metric Suspension in Luigi Nono's II Canto Sospeso (Jon Kochavi)
  • One Note Samba: Navigating Notes and Their Meanings Within Modes and Exo-modes (Thomas Noll)
  • Difference Sets and All-Directed-Interval Chords (Robert W Peck)
  • Harmonious Opposition (Richard Plotkin)

• Section II:

  • Orbifold Path Models for Voice Leading: Dealing with Doubling (James R Hughes)
  • Reflections on the Geometry of Chords (Thomas A Ivey)
  • Theoretical Physics and Category Theory as Tools for Analysis of Musical Performance and Composition (Maria Mannone)
  • Intuitive Musical Homotopy (Aditya Sivakumar and Dmitri Tymoczko)
  • Geometric Generalizations of the Tonnetz and Their Relation to Fourier Phases Spaces (Jason Yust)
  • Deterministic Geometries: A Technique for the Systematic Generation of Musical Elements in Composition (Brent A Milam)

• Section III:

  • Flamenco Music and Its Computational Study (Francisco Gómez)
  • Examining Fixed and Relative Similarity Metrics Through Jazz Melodies (David J Baker and Daniel Shanahan)
  • In Search of Arcs of Prototypicality (Daniel Shanahan)

Readership: Students and researchers in Mathematical Music Theory.
Key Features:

• It includes the most prominent authors in the field
• It gathers a gamut of the most recent work in the field, which is something very difficult to find in one volume
• It will appeal to mathematicians, music theorists, and computer scientists. Within mathematics, it offers a variety of areas and techniques related to musical phenomena that cannot be found together in other volumes