I’m working on adding the ability to do frequency modulation in Minim. I didn’t figure it was a very complicated thing. I knew that I’d have to do it while generating each sample, so it couldn’t be done as an AudioEffect. But when I went looking online about how to do it, I found a number of articles that described the technique in words, with somewhat dense equations, but none that had easy to understand code examples. I did find this article, but the code in it is some form of Lisp, a language I am not familiar with. I thought I had it figured out a couple times, but every time I tried something new I still wasn’t achieving the correct result.
So today I asked my friend The Mysterious H how it works because he’s a smart guy and builds synths out of Atari sound chips and shit like that. He goes, “Oh it’s easy.”
Every time you want to generate a sample of the signal you are modulating (the carrier), generate a sample of your modulator and add that to the phase you use to generate your carrier sample.
Said another way: Say you’ve got a signal called f. At every time step t (which is your phase), you generate a sample s by evaluating f(t). If you want to modulate the frequency of f with a modulator called m, then at every t you will do this:
s = f(t + m(t))
The speed of the modulation is determined by the frequency of your modulator and the amount of the modulation (how many hertz above and below the frequency of your carrier signal the audible signal will swing) is determined by the amplitude of the modulator. In my tests I found that the amplitude had to be around 0.001 to achieve what one would consider vibrato. Setting it to 0.1 made for some pretty intense alien sounds when the frequency of the modulator was up in audio signal range (20 Hz and up, say).
It’s lots of fun to play with and will be coming soon!