I've always been fascinated with how we can so quickly recognize music that we know -- from classical to pop and rock -- usually in just a few seconds even when that specific composition is being played in totally different styles, on different instruments, and in different tempos and keys. It has to be the relative note differences and relative note timing that's the answer, meaning it's mostly a matter of organic math. In fact, I've often noticed that when recognizing a piece that you can almost feel your brain "sliding" to sync and identify.
Technical analysis of music, like this one I happened to check out just an hour ago, spend so much time considering our own personal reactions to compositions, things like tension and expectation and payoff and call-and-response invitations to participate..
It makes me think that it's not so much recognizing the music itself or any math therein, but rather the pattern of our own responses.
Even with different tempos and such, we still recall the pattern, the order of our own reactions, and that leads us to [hopefully] recall the song on the tip of our tongue.
