Very interesting : I was actually thinking about redoing the spectrometer music visualization for MythTV to be use 'piano keyboard' pitches (rather than the FFT that they're using at the moment). And I came to the conclusion that some kind of recurrence (short) resonant filter would do the trick (with 88 different copies) - but never got further than that, since I had limited imagination about what algorithms to search for. Unfortunately, I've got overwhelmed with other projects now...
with N if it's highly composite. See, e.g. http://www.fftw.org/ which works fairly well even for non-powers of 2.