Klarinet Archive - Posting 000454.txt from 2001/02

From: Grant Green <gdgreen@-----.com>
Subj: Re: [kl] Combination tones......
Date: Mon, 12 Feb 2001 15:13:52 -0500

Tony said:
>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
>happened.

I think you're right: this is a confusion of levels. I wouldn't
define "hearing" as limited to what happens at the eardrum, although
the cochlea apparently does some of the processing (like frequency
and amplitude detection). I agree that the signal probably requires
processing by the nervous system "downstream" from there. If the
auditory system parallels the visual processing system, there are
probably neurons that detect changes in frequency, changes in
amplitude/volume, etc., similar to the visual processing neurons that
detect edges and simple shapes in the visual field.

>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
>them.

Here I don't completely follow you, as I am not sure exactly what you
mean by "derived." I realize that a degree in chemistry with a minor
in music doesn't exactly qualify me as an expert in acoustics, but I
was taking the sine wave addition as a description of the physical
change in air pressure. In other words, the wave pattern that
results is the physically measurable sound, regardless of the ear's
nonlinearity. If you run both sine waves into a speaker, the added
waveform is what the speaker produces (assuming a perfect speaker, of
course).

> > 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?

All I meant here is that we constantly hear variations in amplitude:
this is why we write dynamics into our music. Regardless of *how* we
hear, and how the audible signals are processed by our nervous
systems, we *do* hear variations 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.

Further off topic, but this is particularly interesting when one
considers that some fraction of the brain's wiring is apparently due
to environmental input and learned behavior. The "ear" is trainable.

>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.

Yes, the description above also appear in Benade (which I *can*
locate). It explains why you hear beats between a sine wave (which
has no upper harmonics) at 200 Hz when played against a tone at 403
Hz. You "shouldn't" hear beats between two frequencies that far
apart: one does, however, because the ear nonlinearity results in a
series of harmonics, so that the 200 Hz sine wave has a *perceived*
400 Hz harmonic to beat against the 403 Hz test tone. However, if
you use a musical instrument (or basically anything other than a sine
wave or a noise spectrum), you don't have to invoke the ear's
nonlinearity: the harmonics are already physically present. The
heterodyne effect occurs whether you detect the sound with an ear or
an oscilloscope.

I think my original statement regarding different tones and beats
wasn't sufficiently precise (although it does describe what one
hears). The waveform of two close sources that are slightly out of
tune resembles a single wave at the average frequency that rises and
falls in amplitude: this is what the ear hears. If you play 440 Hz
while the musician on the next stand plays 442 Hz, you hear 441 Hz
that beats once per second (1 Hz). If you gliss the pitch from 442
Hz up to 660 Hz, you'd hear the frequency of beating increase to a
burr, eventually ending up with a difference tone. Both the beating
and the difference tone are produced by the same physical phenomena,
although the ear perceives them somewhat differently.

Grant

++++++++++++++++++++++++++++++++++++++++++++++++
Grant Green gdgreen@-----.com
ecode:contrabass http://www.contrabass.com
Professional Fool -> http://www.mp3.com/ProFools
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