Putting Music on the Map

Mathematics and music have long been closely associated. Now a
recent mathematical breakthrough uses topology (a generalization of
geometry) to represent musical chords as points in a space called
an orbifold, which twists and folds back on itself much like a
Mobius strip does. This representation makes sense musically in
that sounds that are far apart in one sense yet similar in another,
such as two notes that are an octave apart, are identified in the
space.This latest insight provides a way to analyze any type of
music. In the case of Western music, pleasing chords lie near the
center of the orbifolds and pleasing melodies are paths that link
nearby chords. Yet despite the new connection between music and
coordinate geometry, music is still more than a connect-the-dots
exercise, just as mathematics is more than addition and
multiplication. For More Information: The Geometry of Musical
Chords, Dmitri Tymoczko, Science, July 7, 2006.