ChordGeometries 1.1

Trichord Prism

ChordGeometries represents chords and voice leadings in a variety of 3D geometrical spaces. You can enter chords on a MIDI keyboard or using the Keyboard window. Voice leadings between successive chords are represented by continuous paths in the spaces. The program is meant to accompany the paper "The Geometry of Musical Chords" [Science 313 (2006): 72-74]. Further information can be found in "Generalized Voice-leading Spaces," with Clifton Callender and Ian Quinn.

Three movies demonstrate the program, using the opening of Chopin's E minor prelude. The first shows Chopin's piece as it appears in circular "pitch class space." The second shows how the two pairs of voices chart a path on a Mobius strip. The third depicts Chopin's piece as it travels through a slice of the four-dimensional space containing seventh chords. You can also watch Deep Purple on the Mobius strip.

ChordGeometries Demo: Chopin - Circular "pitch class space" from Dmitri Tymoczko on Vimeo.

ChordGeometries Demo: Chopin on a Mobius strip from Dmitri Tymoczko on Vimeo.

ChordGeometries Demo: Chopin through four-dimensional space from Dmitri Tymoczko on Vimeo.

ChordGeometries Demo: Deep Purple on the Mobius strip from Dmitri Tymoczko on Vimeo.

Download Now

WARNING: It got too hard to support the standalone applications, so I have started distributing Max/MSP source code instead. To install, download Max/MSP/Jitter from cycling74 (there is a free runtime version). Then install the Lobjects from Peter Elsea. Then set the filepaths and run ChordGeometries.maxpat. It might take some fiddling but it should work.

Made with Max/MSP/Jitter

System Requirements

Macintosh

  • OS 10.3 or higher
  • 256 MB of RAM
  • Quicktime 6 or higher
  • OpenGL 1.5 or higher

Windows XP

  • 256 MB of RAM
  • 1 GHz processor or higher
  • OpenGL hardware-accelerated video card
  • QuickTime 6 or higher
  • OpenGL 1.5 or higher

About Me

Dmitri Tymoczko (b. 1969, Cambridge, Massachusetts) is a composer and music theorist who teaches at Princeton University. His book A Geometry of Music (Oxford) has been described as "a tour de force" (The Times Literary Supplement), a "monumental achievement" (Music Theory Online), and, potentially, a modern analogue to Schoenberg's Harmonielehre (The Musical Times). His first three CDs, Beat Therapy ("far reaching yet utterly entertaining," Newmusicbox), Crackpot Hymnal ("ebullient ... polystylistic ... kinetic ... vividly orchestrated and vibrantly paced," Sequenza21), and and Rube Goldberg Variations ("foot tapping," "sassy," Limelight), are available from Bridge Records. A fourth, Fools and Angels is available from New Focus.