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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.


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in reply to @hillexed's post:

Digital synthesis is discrete, so continuous math will give you a different answer from what the DX7 produces. Oscillator feedback is always delayed by some amount, often a single sample. The best way IMO to get a sense of what kind of noise a given algorithm produces is to dial it up and look at it/listen to it.

There's a book called FM Theory & Applications by John Chowning and David Bristow that goes into detail on how the sounds are generated (as well as how they are affected by the limitations (namely the sample rate) of the DX7)