Why topology?

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Abstract

Music theorists have modeled voice leadings as paths through higher-dimensional configuration spaces. This paper uses topological techniques to construct two-dimensional diagrams capturing these spaces’ most important features. The goal is to enrich set theory’s contrapuntal power by simplifying the description of its geometry. Along the way, I connect homotopy theory to “transformational theory,” show how set-class space generalizes the neo-Riemannian transformations, extend the Tonnetz to arbitrary chords, and develop a simple contrapuntal “alphabet” for describing voice leadings. I mention several compositional applications and analyze short excerpts from Gesualdo, Mozart, Wagner, Stravinsky, Schoenberg, Schnittke, and Mahanthappa.

Original languageEnglish (US)
Pages (from-to)114-169
Number of pages56
JournalJournal of Mathematics and Music
Volume14
Issue number2
DOIs
StatePublished - May 3 2020

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Music
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Topology
  • contextual inversion
  • geometrical music theory
  • neo-Riemannian theory
  • voice leading

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