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Science 7 July 2006:
Vol. 313. no. 5783, p. 13
DOI: 10.1126/science.313.5783.13c
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This Week in Science

In Western music, harmony--the selection of notes to create a chord--and counterpoint--how individual notes are connected in time to establish melodic voices--together form the basis for composition. The rules of harmony and counterpoint embody aesthetic norms but also represent constraints on the composer that can sometimes be difficult to reconcile. Tymoczko (p. 72; see the Perspective by Hook) discusses a mathematical system for organizing the 12 tones of the western scale that makes use of a topological structure called an orbifold, in which chords are points in the topological space and the segments connecting them indicate how chords progress. Examination of the geometry of these spaces provides an understanding of some long-standing puzzles in music theory.




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