Wow, theres so much I don't know. It would be great if you could let me know the names of some of the songs that Autechre uses math to create. Also, proggyman, if you could get me the name of that book, that would be awesome.
I love the Fibonacci sequence, it's another one of those things that is seen everywhere in the natural world and is an excellent example of how deeply everything is connected.
Physics is used widely with the timbre of instruments, there are many physics equations that deal with that, I however do not know much about the physical equations, I look more abstractly at the structures underneath.
And yes, Euclids algorithm to find the highest common factor of two numbers can also be used to find the largest measure of string segment that would fit into both. This is would have been extremely useful in tuning instruments in Euclids time since they talked about lengths of string rather then pitch and frequency.
This is awesome, keep throwing the ideas out there, what more does everyone know? Have you ever thought about what happens when you invert the notes of a chord mod 12? It's actually quite interesting. If you refer to the notes as numbers in the chromatic scale rather than by the note name, then all you have to do is negate each number of the chord and mod it by 12 and you will actually get the chord which is rooted on the minor third of the chord, and it will switch from major to minor, or vice versa.
E.g. Take C major (C,E,G) or in terms of the numbers on the scale (1,5,8). Now negate those (-1,-5,-8) and mod by 12 (11,7,4) This is an Eb minor chord. It works like this for any triad chord.
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