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Science 19 January 2007:
Vol. 315. no. 5810, p. 330
DOI: 10.1126/science.1134163
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Technical Comments

Response to Comment on "The Geometry of Musical Chords"

Dmitri Tymoczko

The basic sonorities of traditional Western tonality divide the octave nearly evenly and are found near the center of the orbifolds Formula and Formula. 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.

Department of Music, Princeton University, Princeton, NJ 08544, USA.

E-mail: dmitri{at}princeton.edu

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Science. ISSN 0036-8075 (print), 1095-9203 (online)