Egregoros

pitch recognition methods seem to be completely dominated these days by machine learning, but I'd really like to make something where I understand all the math involved instead of relying on preset weights

maybe instead of the holy grail being instrument-agnosticism, maybe it would be better to be instrument-hyper-specific. What about asking for samples of the kinds of instrument being analyzed? That would allow for a closest-fit harmonic analysis without the guesswork of instrument agnosticism.

Yeah theoretically it's more cumbersome to use ("what do you mean I need to give you samples of each instrument and not just the file?") but on the other hand it seems like there would be less knob-fiddling and potentially more accurate results even if the initial work for the user is higher.

@binkle youre going to have to look at and understand FFT, if you say you want to know the maths behidn it . there is no way around or over it really.
but once you understand FFT (or atleast, the output of the fast fourier transform), after that should be a series of logic puzzles to match. on top of this is what the machine learning pitch recognitions and other older autotunes are built on.

i have yet to understand the FFT algo but i havent really given it a good shot at it (i am not an intelligent man)

@lebronjames75 I wrote a complex FFT from scratch with the fancy bit-twiddling in college once. I can't say I remember a TON about the bit-twiddling but the rest of it is still pretty fresh. The intersection of the various fourier transforms, sampling theory, etc is probably my favorite part of math I ever learned

if you want a recommendation I think the class I took was based around Ken Steiglitz's "A Digital Signal Processing Primer". Not having read it independently of the course I couldn't tell you if it's as handy without the additional instruction, but I have fond memories of it, which is at least something