Generalized voice-leading spaces

Clifton Callender, Ian Quinn, Dmitri Tymoczko

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


Western musicians traditionally classify pitch sequences by disregarding the effects of five musical transformations: octave shift, permutation, transposition, inversion, and cardinality change. We model this process mathematically, showing that it produces 32 equivalence relations on chords, 243 equivalence relations on chord sequences, and 32 families of geometrical quotient spaces, in which both chords and chord sequences are represented. This model reveals connections between music-theoretical concepts, yields new analytical tools, unifies existing geometrical representations, and suggests a way to understand similarity between chord types.

Original languageEnglish (US)
Pages (from-to)346-348
Number of pages3
Issue number5874
StatePublished - Apr 18 2008

All Science Journal Classification (ASJC) codes

  • General


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