Sunday, March 9, 2008

The Geometry of Music

Dmitri Tymoczko is a composer and music theorist who explores the geometry of music. His site includes visualizations of musical patterns including "Smoke on the Water" on a Möbius strip (mov) and Chopin's prelude in E minor on a circle (mov) and in 4D space (mov). His ChordGeometries 1.1 application represents chords and voice leadings in a variety of 3D geometrical spaces.

From Science News:

Music theorists have long found Chopin's E minor prelude puzzling. Although the chord progressions sound smooth to the ear, they don't quite follow the traditional rules of harmony. When Tymoczko looked at the piece and watched the composition's motion through his geometrical space, he saw that Chopin was moving in a systematic way among the different layers of the four-dimensional cubes. "It's almost as if he's an improviser with a set of rules and set of constraints," Tymoczko says.
The image above is from Andrew Lipson's Lego Page.

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