Doepfer

> Sine functions can be represented as Taylor series. 
 
Perfect example of a sine being constructed. 
 
>I'm guessing, the
> human ear naturally decomposes a wave into its Fourier components, 
absorbing
> the energy from the lower frequencies in sine form, and then 
passing off the
> rest down the tube.

I'm sticking with sines and cosines as a convenient analytical 
representation (that includes a mathematical analysis of vibrations 
in the ear too). I don't think the ear knows diddly about Fourier ;) 
I would go back to the idea that your ear/mind can separate the 
parts of a musical sound based on the timbres of the constituent 
instruments, not only in the case that they are pipes or flutes, or 
whatever particular timbre is closest to a sine. I think the 
ear/mind is really good at this, actually. If there is a bird 
chirping and a lion roaring at the same time, I bet some of the 
Fourier terms are overlapping, but there would be no doubt in 
mentally separating the sounds according to timbre. Should I go 
further and say that spectrally rich tones are easier for the mind 
to categorize than "pure" ones?

> 
> This leaves open the question of a synthesizer filter based on a 
different
> resonance waveform.  Any thoughts on whether that's possible, what 
it would
> sound like?

Not a designer, but I bet there are contexts in which using tri or 
square is more convenient than sines. Especially in digital 
synthesis. 

Doug