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The Geometry of Music (Chopin)

submitted by doremifa

1 decade 7 years 1 week ago

Dimitri Tymoczko recently published an article in Science (313,72-4, 2006) about Western music chord cadences set to equations of string theory. There is another video which shows chord choices as intervals (2 different notes) and the 2-dimensional geometry superimposed. He uses Deep Purple's "Smoke on Water."

http://video.google.com/videoplay?docid=9174364106511581362&q=tymoczko

http://www.time.com/time/magazine/article/0,9171,1582330,00.html

http://www.sciencemag.org/cgi/content/full/313/5783/72

The article's abstract:

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.