Pitch Perception, Dynamical Systems, Nonlinear Model

Hi Carl, Mike, and all,
have you read the papers by Cartwright, Gonzalez and Piro, e.g.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.64.9129&rep=rep1&type=pdf

http://www.pnas.org/content/98/9/4855.full.pdf+html

If so, what do you think? They use ideas from dynamical systems to arrive at a formula for the virtual fundamental which is in good agreement with the 1st pitch shift effect.

I see the papers are about ten years old (and were briefly discussed here about then) but I can't access anything that looks like a further development of it.

Steve M.

(P.S. I posted this before, or so I thought, but it didn't appear in the forum, so...)

Steve wrote:

> have you read the papers by Cartwright, Gonzalez and Piro, e.g.
>
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.64.9129
> &rep=rep1&type=pdf
>
> http://www.pnas.org/content/98/9/4855.full.pdf+html
>
> If so, what do you think? They use ideas from dynamical systems
> to arrive at a formula for the virtual fundamental which is in
> good agreement with the 1st pitch shift effect.
> I see the papers are about ten years old (and were briefly
> discussed here about then) but I can't access anything that
> looks like a further development of it.

Thanks for pointing these out, Steve. I had a quick look.
It's beyond my expertise to evaluate whether their results
are correct. My gut feeling is that the appeal to dynamical
systems is unjustified. 'Hey, Helmholtz thought residue
was caused by nonlinearities, and even though his proposal
was wrong maybe we can save it!' Just how hard is it to get
one of these fancy oscillators to reproduce the psychoacoustic
data? I don't know. Would be a good question for John
Starrett, but I don't think he reads the list these days.

-Carl

Sorry for my lack of reply. I had read these papers when Steve first
posted them, but I guess I didn't respond. I thought the same thing
that Carl wrote here:

On Tue, Jan 4, 2011 at 4:42 AM, Carl Lumma <carl@...> wrote:
> My gut feeling is that the appeal to dynamical
> systems is unjustified. 'Hey, Helmholtz thought residue
> was caused by nonlinearities, and even though his proposal
> was wrong maybe we can save it!'

It still doesn't explain why a column of sine waves in a harmonic
series disappears and we only perceive the fundamental.

I also did an experiment a while ago - I started playing "Happy
Birthday" with a timbre that was made up of only 1's and 3's, and I
made the 1's as soft as possible. I kept lowering the 1's until they
were gone. Although this took a few times to get the hang of it, I
could eventually hear the 3's still as 3's, even when the 1 was
totally removed - that is, I heard the phantom 1 although the only
thing that was playing was a single sinusoid at 3.

Nonlinear models don't generally predict that this is possible, but
something like harmonic entropy does - a single sine wave could be
1/1, or 2/2, or 3/3, etc. Although 1/1 is most probable, you can hear
it as something else under different circumstances (e.g. priming,
which is the trick I used here).

-Mike