Comment by elihu

Another multi-dimensional abstraction for music that's at a bit higher level is a musical lattice. The number of dimensions is limited by the largest prime you accept in the ratios you use. (Typical western music approximated by 12-tone equal temperament uses primes of 2, 3, and 5. Powers of 2 are often ignored because notes an octave apart are perceived to be sort of equivalent for harmonic purposes.)

https://en.wikipedia.org/wiki/Lattice_(music)