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"Math" to most people means "numbers." "Math" to mathematicians means "relationships."

In a way, our understanding of higher math is hindered by our mastery of base 10 before we really deal with anything else. It's like learning to play with a capo. You'll get the fingerings that work, but you won't really get the relationship. This is why higher math rarely looks like "math" to normies; we can look at Fermat's last theorem and go "but that's just Pythagoras" and from the point of geometry, yeah. At least, Euclidian geometry at the scales we interact with it.

But to get to how a chord works you need to know how waveforms constructively and deconstructively interfere. You don't need that if you're just making songs. If you want to make a new way to make sound? Suddenly you're dealing on a different level.

Whenever math devolves to fractals or automata or stuff like that, you're dealing with the sound waves. They define what music *is*, not just how to play it. And by investigating the relationships that make up chords, you allow the creation of entirely new music, new ways to play music, new tools to make music with.

Some people ban augmented 4ths. Some people figure out why augmented 4ths drive people crazy. This is along the lines of figuring out what the interaction of an augmented 4th looks like and where else we might see that interaction play out in ways we haven't thought about before.