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. This movie shows how the two pairs of voices chart a path on a Mobius strip.

You can download the software used to create this video on my website: music.princeton.edu/~dmitri/ChordGeometries.html

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