Gosh. For me, I think it abounds. If I look closely, I see it everywhere: why certain tonalities resolve or clash, the harmonic structure of everything, even rhythmic subdivisions. I don't necessarily think of math while I'm playing music. But if I take a closer look, I'm astonished by the beauty of it. Similar to the way I feel about Algebra.
Fair enough, that's all true.
It's weird, though. Thinking about harmony--as discussed ad nauseum in other threads, what we usually hear isn't pure pythagorean intervals, because of the compromises required by equal temperament, and the physics of vibrating strings, etc. And yet, it can still be beautiful and interesting, even when those compromises are audible. And there's more to harmony (and to music in general) than simple integer ratios.
I guess the way I'd put it is: yes, there's some overlap. But the parts of music that you can "explain" with math are just a small part of the world of music. And the parts of math that are useful for talking about music are just a small pretty well-trodden part of the world of mathematics. I can't recall seeing anyone produce really interesting results either by saying "here's some deep and interesting math, let me turn it into music somehow" or "here's some great music, let me see if I can get deep mathematics out of it". But I've likely overlooked things, of course, and wouldn't want to discourage anyone from trying!
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