> (You might think, for example, that you could just snip your 5-minute song 
> into, say, 50 ms chunks and take the Fourier transform of each chunk. 
> Alas, snipping it up introduces phantom frequencies that aren't really 
> there.)

Use something other than a rectangular window function then, that helps with 
the phantom frequencies.

> I've spent a significant amount of time trying to come up with some 
> mathematics for analysing sound the way that the human auditry system 
> does... So far, nothing works.

If you don't need it in realtime then just run a band-pass filter over the 
whole song at varying frequencies, you can then read off the amplitude at 
any frequency at any time during the song.

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