- Exponentials and logarithms
- Harmonic series
- Combinatorics
- Chaos theory
- Some calculus
- Resonance
- Linear algebra
It also taught me about physics, cognitive psychology, learning theory, history and even some sociology.
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.
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. 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.
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).