ChordGeometries 1.1


    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.  (Link temporarily removed pending publication.)

    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.
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

DOWNLOAD OLDER MAC VERSION 1.1

DOWNLOAD INTEL MAC VERSION 1.1

 DOWNLOAD WINDOWS XP VERSION 1.1

 WARNING: Macintosh users should use the program BOMArchiveHelper to unzip “ChordGeometries.zip”.  Control-click on the archive's icon and select “Open With ...”

MADE WITH MAX/MSP/JITTER.		 Screenshot