Klarinet Archive - Posting 000334.txt from 2000/08

From: Bilwright@-----.net (William Wright)
Subj: Re: [kl] Unloading.....
Date: Mon, 14 Aug 2000 13:40:10 -0400

=A0=A0 <><> Tony=A0Wakefield wrote:
Is this a question of psychology, ( the source of Will. Wright`s theory)
or is there some real scientific basis

Much of it is pure mathematics, Tony, not psychology. Please
forgive me if I'm repeating some stuff that is old hat, but I'm trying
to convey the 'big picture.'

It's a mathematical fact -- you can prove it with pencil and paper
and something called Fourier analysis -- that so long as we limit the
discussion to sine waves and their partials, every wave (no matter how
complex or irregular it may appear when graphed) can be described
accurately as the sum of a collection of sine waves.
The assertion is that 'musical sounds' are, in fact, close enough
to sine waves that this analysis applies. Experiment bears out this
assertion (but see "wavering" below). You may wish to call it
'psychology' in the sense that our minds create something, but this
assertion is verifiable and repeatable -- which is the essence of
'science'.

Our ears and neural circuits are built to respond to sine waves in
such a fashion that we 'hear' a single pitch even though musical sound
waves are a collection of many different frequencies. 'Tone color' is
the phrase that we use to describe the cumulative effect of the
additional frequency components that are not identical to the frequency
that we 'think' we are 'hearing.'
If the actual frequency that we 'think' we are hearing is filtered
out somehow (and isn't really there any longer), we still 'hear' the
same pitch anyway. Our brains will reconstruct the filtered-out
frequency by using all the other partials as clues.
In the real world, the frequency that we 'think' we are hearing is
distorted by echoes and reverberations, tremulos, heterodyned tones
(tones that were not part of the instrument's original sound wave but
were physically created -- and have been physically measured -- inside
our ears by the shape of our ear lobes and canals), and so forth.
Without all these clues that are provided by our unconscious assumption
of sine waves, we would hear disorganized cacophony -- not 'music.'
It's true that an absolutely pure sine wave sounds 'electronic' and
empty and hollow. Some small amount of wavering in frequency and
amplitude and phase makes a tone sound richer and fuller, but the sine
wave math still applies to most musical instruments.
Percussion is the major exception to all of this sine wave stuff,
of course.
The next step in the argument is that, mathematically, each of the
'component' sine waves (that make up a more complex sound wave) can be
described completely with just two numbers. One number describes the
amplitude, and the other number describes the phase. It turns out that
-- again, so long as we're discussing only sine waves -- all possible
elaborations on the fundamental tone A=3D440 can be described completely
and accurately with a collection of 50 two-number 'components'. If you
move an octave higher to A@-----. If
you move an octave lower to A=3D220, then you need 100 components in order=

to cover all the possibilities.
Again, slight wavering pitch and amplitude and phase and departures
from pure sine wave add to the 'beauty' of good music; but if you accept
the basic assertion that sine wave math still applies, then by simple
mathematic necessity, you must accept that all musical tones converge
towards sameness as the pitch increases.

My apologies if anyone didn't want to hear all of the above.

Cheers,
Bill

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