[skybrian]

I'm interested in the algorithm for that, but it looks like for PolyTune, they just say "patented 'MonyPoly' algorithm."

So that's out. I wonder what other research has been done into detecting multiple notes at once?

[dspig]

Each string has it's fundamental frequency and harmonics. Some of them coincide or are very close in frequency, but some are unique to one string so can be picked out and their frequency measured with a FFT of sufficient resolution and used to indicate the tuning of the string it must be a harmonic of.

(Polytune is more robust than just doing this and does work really well, but if the guitar is really out of tune the method falls apart and you have to use its one-string-at-a-time mode)

[skupig]

Fourier Transform, identify the fundamentals by loudness and/or presence of harmonics?