I'm currently just looping and calling sin() a lot. I use trivial 4-way symmetry of sin() and build a "mipmap" of progressively octave-higher versions of a wave, to play for higher notes, by copying samples off the lowest-frequency waveform. That still is only 8x faster than the naive way to do it.
I know in theory that a FFT or DFT will turn a CONTINUOUS graph of frequency into a graph of time, and vice versa, but if I don't have a a continuous graph of frequency but rather an array of strengths, can I still use it? I thought of making a continuous graph of frequency from my harmonics, but 1) sounds quite imprecise and 2) I note real FFT graphs have smooth "hills" where harmonics are, rather than point peaks, and am wondering whether I'd get expected output if I didn't generate those hills.
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