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Science 7 July 2006:
Vol. 313. no. 5783, pp. 72 - 74
DOI: 10.1126/science.1126287
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Reports

The Geometry of Musical Chords

Dmitri Tymoczko

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.

Department of Music, Princeton University, Princeton, NJ 08544, USA, and Radcliffe Institute for Advanced Study, 34 Concord Avenue, Cambridge, MA 02138, USA.

E-mail: dmitri{at}princeton.edu

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THIS ARTICLE HAS BEEN CITED BY OTHER ARTICLES:
Generalized Voice-Leading Spaces.
C. Callender, I. Quinn, and D. Tymoczko (2008)
Science 320, 346-348
   Abstract »    Full Text »    PDF »
Comment on "The Geometry of Musical Chords".
D. Headlam and M. Brown (2007)
Science 315, 330b
   Abstract »    Full Text »    PDF »
Response to Comment on "The Geometry of Musical Chords".
D. Tymoczko (2007)
Science 315, 330c
   Abstract »    Full Text »    PDF »
VOICE LEADING IN SET-CLASS SPACE.
J. N. Straus (2005)
Journal of Music Theory 49, 45-108
   PDF »
SCALE NETWORKS AND DEBUSSY.
D. Tymoczko (2004)
Journal of Music Theory 48, 219-294
   PDF »


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Science. ISSN 0036-8075 (print), 1095-9203 (online)