I'm trying to understand the math behind how computers make music! So to understand one type of synthesizer, FM synthesis, I found dexed, an emulator of the famous DX7 synth which popularized FM. Eventually I learned that the DX7 made the piano sound which you hear in Dire Dire Docks! So I thought to myself okay, I'll try to reverse engineer that sound, and it's going slowly as I try to figure out more and more what each dial corresponds to. I thought I had a handle on FM synthesis and envelopes, so I thought I understood it but then I discovered that the piano sample involves a sine wave modifying ITSELF. I have no clue what type of wave that makes. I MIGHT be able to figure it out by setting up a differential equation for FM synthesis and solving it? But then I'd have to solve a differential equation.
I wish I knew where to look for answers to these questions, but in the meantime it's a good rabbit hole to be stuck in.