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Klarinet Archive - Posting 000320.txt from 2001/02

From: (Tony Pay)
Subj: Re: [kl] Combination tones......
Date: Fri, 9 Feb 2001 19:50:45 -0500

On Fri, 09 Feb 2001 12:22:55 -0800, said:

> At 07:40 PM 2/9/01 +0000, Tony wrote:

> > This is a confusion of levels. Yes, the variation in amplitude is
> > visible, as you say, on an oscilloscope and in the math. But it
> > isn't *physically* there, because it doesn't 'waggle' anything real.
> > The pressure wave itself is already doing that.
> Please excuse me, but I don't exactly follow you. Are you saying that
> the beating effect isn't "physical" because it is a variation of
> something that is already varying? I'd say that the beats are as real
> as vibrato and tremolo, which are periodic variations in sound (which
> in turn is a periodic variation in air pressure).

The beating effect is an objective description of what happens to the
amplitude of the vibration of the eardrum. But the eardrum itself
doesn't notice that variation in amplitude -- it just responds to the
pressures on it, moment to moment.

Beats, vibrato and tremolo are all real -- to *us*. I have very little
idea of what's actually involved in our perception of those things,
though I'd have thought that some sort of memory at least comes into it.
You need to be able to compare what's happening with what has just

That's well beyond the competence of an eardrum -- though it may be part
of the competence of neural processors that deal directly with the
output from the basilar membrane.

The point is that such 'derived' things, however obvious and 'given'
they appear to us, cannot be a part of the explanation of how we derive

> Periodic variation in air pressure (within the hearing range) is
> perceived as sound, and a periodic variation of either the rate
> (frequency) or amount of the pressure variation (volume or amplitude)
> is perceived as vibrato or tremolo. They may only be characteristics
> of the underlying sound, but I wouldn't consider that as making them
> "non-physical."

To explain these things is essentially to show how perception of them is
possible from the physical inputs -- like forces on eardrums. To claim
'physicality' for them at this point begs the question.

> > A 'waggle' in a concept like amplitude isn't perceivable by an
> > eardrum -- it's already busy being waggled by something else: namely
> > the forces involved.
> How can one *not* hear a variation in amplitude?

It's a more difficult question to answer: how *can* we hear a variation
in amplitude?

As I said before, the difficulty is to explain in detail how the actual
vibrations of the eardrum can be processed so as to hear, not only the
variations in amplitude, but also other things: particularly, other
things that could have aided our survival in the past.

That would give a different sort of understanding of the details of
our ears and auditory systems.

> > You can see though, as I said in another thread, why the idea is
> > attractive. In fact, it was put forward by Young in 1784, but
> > contradicted by Helmholtz in 1877, who explained the picture
> > outlined by George Kidder here.
> >
> > This true explanation of why we perceive a difference tone is
> > actually much more suggestive, even though a bit difficult to
> > approach.
> Afraid I don't have a copy of Helmholtz handy (mine's at my office,
> while I'm stuck at home today): is it possible to summarize his
> explanation?

With all the reservations about summarizing, and not derived from
Helmholtz directly:

The ear is non-linear, and generates, even from a pure sine wave of
frequency P, the heterodyne frequencies 2P, 3P, etc. These are
represented in the basilar membrane.

In fact, a general non-linear system, from stimulation at two
frequencies P and Q, generates heterodyne frequencies 2P, 3P...; 2Q,
3Q...; P-Q, P+Q; (2P - Q), (2Q - P); (3P - 2Q).....etc. etc. etc,
including sums and differences of all of those. (Most of them are very
weak, of course.)

I think from your previous post you know how it goes from here:
multiples of (P-Q) are strongly represented in the above list. Our
neural processing systems are tuned to recognise, and group, *harmonic*
patterns; (survival value in that!-) and multiples of (P-Q) form the
harmonic series for the frequency (P-Q). So the upshot is that that
frequency (as well as others, more weakly) is perceived.

_________ Tony Pay
|ony:-) 79 Southmoor Rd
| |ay Oxford OX2 6RE GMN artist:
tel/fax 01865 553339

... Apple: "I know! Let's call it the Raincoat."

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