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Response to Comment on "The Geometry of Musical Chords"

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Science  19 Jan 2007:
Vol. 315, Issue 5810, pp. 330
DOI: 10.1126/science.1134163

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The basic sonorities of traditional Western tonality divide the octave nearly evenly and are found near the center of the orbifolds Math and Math. Many common musical patterns exploit this fact, which permits efficient voice leading between structurally similar chords. In actual music, these patterns sometimes appear incompletely or are accompanied by additional notes. Using orbifolds in musical analysis therefore requires interpretive skill.

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