You don't need math to enjoy or even perform music, or to understand it in a certain way. But there is another way to understand it that is purely mathematical,

You don't need math to enjoy or even perform music, or to understand it in a certain way. But there is another way to understand it that is purely mathematical, and it is quite enriching. The start of the rabbit hole is the pythagorean comma and it has a very real effect on the real-world messy compromises that are involved in tuning instruments to play with each other in multiple keys. The terrible beauty and ugliness that are one and the same stems from the simple fact that if you go up a fifth, say, C to G, it sounds the purest if the pitch is exactly 1.5 times as high, or 3/2. If you keep going up five notes at a time, eventually you get back to a C, having gone through all the other notes in the process. But the pure, good sounding way to get from a C to a higher C is to double its frequency. And you never can get to exactly a power of two by repeatedly multiplying by 1.5. So the C you get by going up by octaves and the C you get by going up by fifths come out different. A consequence of that is it is impossible to play all the different chords in a key as pure, perfectly-in-tune chords without at least one "floater" note (my term) that changes pitch depending on which chord it's part of at the time. See Just Intonation for more information. It's geeky stuff, but has an effect on the way real musicians play certain instruments, such as harpsichord and pedal steel guitar, and it has bothered and fascinated certain musicians ever since the ancient Greeks if not before.