Coming from the opposite direction, I'm quite curious as to where the linear algebra and combinatorics fit in. As a former mathematician (switched to computing after one post-doc) who has been trying to learn about music and to play the piano, I'm trying to make sense of how music and mathematics relate.
There's some stuff with group actions going on - I think you can think of a dihedral group acting on sets of triads or something along those lines and there are some articles out there about that, but I feel like I don't have a good mapping in my head as to the relationship between music and mathematics.
I can see combinatorics relating in the sense that exploring the space of potential compositions can be approached as a ‘combination of’ type problem for different elements.. chords as combinations of notes, chord progressions as combinations/orderings of chords, likewise for the order of notes in an arpeggio.. rhythms/grooves can be thought of as like combinations of emphasised beats (emphasis on 2 & the and of 3 vs. emphasis on 1 & the and of 3 for example) at different levels of beat-subdivision.. then the sounds each emphasised beat can take come from a discrete set (kick, snare etc.) so can be thought of as another combination-of type problem. many possibilities.
Perhaps this is not what the GP meant though, I’m curious about however it applies. No idea about where linear algebra could fit in, I have yet to see those parallels myself yet but interesting to think how it could relate
W.r.t. combinatorics: I was thinking of tuning systems and scales. I have always thought about the theory, but never written it down. Some other people actually did a much better job than me: http://andrewduncan.net/cmt/
W.r.t. linear algebra: mostly in relation to sound synthesis, but also in relation to music composition, theory of overtones, piano tunings... You ask, I'll explain.
Sound synthesis: mostly when I was playing with PD (Pure Data). Linear algebra comes up all the time in sampling theory.
Music composition: this is a bit more far fetched, but I always thought of composition as a combination of vectors which can vary semi-independently. We want to pick some plane through that vector space and move within the plane. For example, we can vary in harmonic complexity, melodic complexity, rhythmic complexity, dynamics, tempo. But it wouldn't make sense to do all at the same time. So we pick one plane, say harmonic complexity and dynamics, and move within that plane. This allows the listener to get used to the 'space' that is opened by the composition. We can then slowly add more vectors, to keep the interest.
A very visual representation of this is the trackpads that you can see on certain modular synthesizers. Often there is a complex setup, but the variables of the setup are reduced to two dimensions, which allows the composers to vary within this projected plane.
Piano tunings: well, basically you have a vector of 230 piano strings of which the overtones are all slightly out of tune. To tune a piano 'correctly', you need to minimise set of equations of strings and overtones (matrix).
There's some stuff with group actions going on - I think you can think of a dihedral group acting on sets of triads or something along those lines and there are some articles out there about that, but I feel like I don't have a good mapping in my head as to the relationship between music and mathematics.