Three conceptions of musical distance

Research output: Chapter in Book/Report/Conference proceedingConference contribution

25 Scopus citations


This paper considers three conceptions of musical distance (or inverse "similarity") that produce three different musico-geometrical spaces: the first, based on voice leading, yields a collection of continuous quotient spaces or orbifolds; the second, based on acoustics, gives rise to the Tonnetz and related "tuning lattices"; while the third, based on the total interval content of a group of notes, generates a six-dimensional "quality space" first described by Ian Quinn. I will show that although these three measures are in principle quite distinct, they are in practice surprisingly interrelated. This produces the challenge of determining which model is appropriate to a given music-theoretical circumstance. Since the different models can yield comparable results, unwary theorists could potentially find themselves using one type of structure (such as a tuning lattice) to investigate properties more perspicuously represented by another (for instance, voice-leading relationships).

Original languageEnglish (US)
Title of host publicationMathematics and Computation in Music
Subtitle of host publicationSecond International Conference, MCM 2009, John Clough Memorial Conference, Proceedings
EditorsElaine Chew, Elaine Chew, Adrian Childs, Ching-Hua Chuan
Number of pages15
StatePublished - 2009

Publication series

NameCommunications in Computer and Information Science
ISSN (Print)1865-0929

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • General Mathematics


  • Fourier transform
  • Orbifold
  • Tonnetz
  • Tuning lattice
  • Voice leading


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