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
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.
And this illustrates the meaning of "interval content":