One narrow example is the *Hexachordal Theorem*, which in one version
says that a chord composed of any six notes on a twelve-tone scale
has the same "interval content" as the chord composed of the complementary
six notes. Some believed this underpinned
Schoenberg's use of hexachords.
The short abstract below provides a number of references to proofs of the theorem,
starting from Milton Babbitt in the 1950s, through to proofs by crystallographers
interested in distinct point patterns that lead to the same X-ray diffraction
patterns.
This could be considered an example where the mathematics that developed out of a musical
notion was perhaps more interesting than its musical origin.

Toussaint, Godfried. Abstract: "Interlocking rhythms, duration interval content, cyclotomic sets, and the hexachordal theorem." *Fourth International Workshop on Computational Music Theory*, Universidad Politecnica de Madrid, Escuela Universitaria de Informatica. 2006.
(PDF download)

And this illustrates the meaning of "interval content":

A Geometry of Musicby Dimitri Tymoczko, but I don't think it illustrates what you seek. $\endgroup$ – Joseph O'Rourke Jan 24 '15 at 17:16