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Generalized Voice-Leading Spaces

Callender, Clifton ; Quinn, Ian ; Tymoczko, Dmitri

Science (American Association for the Advancement of Science), 2008-04, Vol.320 (5874), p.346-348 [Periódico revisado por pares]

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Título:
Generalized Voice-Leading Spaces
Autor: Callender, Clifton ; Quinn, Ian ; Tymoczko, Dmitri
Assuntos: Equivalence relation ; Exact sciences and technology ; Geometry ; Major chords ; Mathematical methods in physics ; Mathematical models ; Mathematical sequences ; Music theory ; Musical chords ; Musicology ; Octaves ; Optics ; Other topics in mathematical methods in physics ; Physics ; Quotients ; Sound pitch ; Theory ; Voice leading
É parte de: Science (American Association for the Advancement of Science), 2008-04, Vol.320 (5874), p.346-348
Notas: ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
Descrição: 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.
Editor: Washington, DC: American Association for the Advancement of Science
Idioma: Inglês

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