The reason the ear can separate the two oboes is because an expected harmonic
relationship is known as a reference point for analysis. So the two "parts" can be
reconstructed by the brain to identify two oboes. So it looks like the ear-brain maybe does
know (pre-wired ) Fourier series ;-)

It's even more complex than that - the brain also keeps maintains a timbre map (vocal
tract resonances) of every speaker so you can hear individual speakers in a crowded room
(I do speech research work). Within the noisy signal, very weak individual speaker signals
can be easily correlated, extracted and decoded.

The brain is mostly tracking resonances rather then individual harmonics, but there is a lot
of evidence the human input transducers are spectral + time types. Experiments with
critical banding and masking indicate sine harmonics are being detected by the ear.

I'll have to see if I can find your reference in full somewhere. Sounds very interesting!

--- In Doepfer_a100@yahoogroups.com , "Doug" <dougc356@...> wrote:
>
> >
> > In your example, what are the "pitch parts" you're separating when
> analyzing the two
> > oboes SINE waves - right Not square or some other arbitrary
> function.
>
> The "oboe function" (steady state). I picked oboe, because it's not
> a sine. Each part is not a sine, yet the mind is easily able to
> separate them, and not in terms of equivalent sums of bell sounds.
> Just an example of how the ear is not hobbled by only being able to
> separate sounds into sines.
>
>
> >Which is not what the poster asked.
>
> Yeah, I went from the specific case he mentioned... using the set of
> square waves as a basis... to a set of *any* signals as a basis. And
> this is exactly what the paper addresses (well there are some
> assumptions about the candidate basis functions). It even goes so
> far to use tri waves as an example. There are even oboe graphs in
> there! It's a math paper in IEEE with music! Ha ha.
>
> >
> > I believe the poster was wondering if any function can be
> transformed from a non-circular
> > plane - like a square or rectangular one. Maybe it's just my
> limited knowledge, but I
> > haven't heard of such a thing. I can try to *approximate" a sine
> from a square plane...
>
> This is exactly what the paper is addressing.
>
> Doug
>