by Dmitri Tymoczko
A musical chord can be represented as a point in an orbifold. (An orbifold is a quotient manifold.)
Line segments join notes of one chord to those of another. Composers in a wide range of styles have exploited the (non-Euclidean) geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation.
(via Artemy Kolchinsky)