Translating Music Into Geometry (4 of 4) (IMAGE)

American Association for the Advancement of Science (AAAS)

Translating Music Into Geometry (4 of 4)

Caption

This is an image of the space of four-note chord types. Ordinary musical terms such as "dominant seventh chord" or "major seventh chord" refer to points in this space. This space is what mathematicians would call a "cone over the real projective plane," which, due to the limitations of our 3-D universe, here looks like a pyramid. The red sphere represents the "diminished seventh chord" and divides the octave evenly. The blue spheres represent chords whose notes are clustered together. Again, traditional Western music uses chords near the tip of the pyramid, which are close together. This image relates to article that appeared in the April 18, 2008 issue of the journal Science, published by AAAS. The study, by Dr. Clifton Callender of Florida State University and colleagues, was titled "Generalized Voice-Leading Spaces."

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Image courtesy of <i>Science</i>/AAAS

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