> 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