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Klarinet Archive - Posting 000229.txt from 2001/02

From: (William Wright)
Subj: Re: [kl] Organs and combination tones
Date: Wed, 7 Feb 2001 17:24:32 -0500

<><> I wrote:
So far as I know, the word "hear" is very important because (so far as I
have read) a difference tone is manufactured by flesh in the human ear,
not by interference or summation of sound waves outside of the ear. (See
Arthur Benade, "Horns, Strings, and Harmony", Chapter IV, pg. 80+ in the
Dover paperback edition.)

<><> Somebody else wrote:
You may be misreading Benade or something [snip] A difference tone
does not need to be manufactured; it exists in the air, as surely as two
pebbles dropped in a pond will cause interfering waves in the water.

Tony Pay has cited a reference besides the one that I cited, and I'm
pretty sure that this is a clear-cut issue:

A 'difference tone' does not exist outside the person's ear,
whereas the 'beat' produced by two mismatched notes does exist outside
the ear.

A 'difference tone' is manufactured inside the ear because tissue
inside the ear begins to vibrate at a frequency other than any of the
incoming components. This vibration is translated to electric
discharges and processed by our brain, and hence we 'hear' something
that doesn't exist outside the ear.

Is it disturbing to think that we hear things that don't exist?
It disturbs me, that's for sure, but measuring instruments say that it's
true. Over the last year, thanks partly to conversation here and
partly to reading --- "Maestro, I read" --- "Oh you! You need to
practice more" --- I've had to change (reluctantly) my thought process
about such things.
I've read about an optical illusion that is based on similar
principles (manufactured perception rather than simply ambiguous input).
In this illusion, a neurologist claimed that I would see a piece of
paper rise up from the floor, float on edge in mid-air and dance
non-stop for me. This was a little bit too much for me to believe
..... until I tried it!

....anyway, the confusion between 'difference tone' and
'interference' is this: When two waves add (or subtract), they are
merely combining their amplitudes to create larger and smaller
amplitudes as they drift 'into phase' and then 'out of phase'. They
are not creating a new frequency component. They are only reinforcing
or cancelling existing peaks and valleys.
When we hear the rise and fall of amplitude (fluctuating loudness),
we say that we hear a 'beat'; but this is only a change in volume or
loudness, not a new frequency component. So long as the two
frequencies are close enough together, we don't believe that we hear a
new frequency, only a rising and falling volume. And when the
frequencies *do* get far enough apart, then we begin to hear separate
notes (perhaps in harmony or discord) and the sensation of 'beat' begins
to fade.

What does this have to do with the reading on a tuner? Not much
except that unless some part of the tuner responds in the same way as
the ear does, then something else besides 'difference tone' is happening
that accounts for the discrepancies that someone asked about in the
beginning of this thread.


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