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Science. 2006 Jul 7;313(5783):72-4.

The geometry of musical chords.

Author information

1
Department of Music, Princeton University, Princeton, NJ 08544, USA. dmitri@princeton.edu

Abstract

A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries and suggest different musical uses.

PMID:
16825563
DOI:
10.1126/science.1126287
[Indexed for MEDLINE]
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