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Re: [Phys-l] Harmonics vs Overtones


Your hearing is fairly insensitive to frequency dependent phase shift, but
not when stereo comes into the question. At a 44kHz sampling rate a single
channel shift between left and right can be noticed as a shift in position
of the source. If you listen on headphones and the phase shift is great
enough you will experience sound in only one ear and you will think the
other channel is dead. I have been fixing some old recordings and have
experienced this with old stereo recordings of mono sources. It is really
perturbing to see that both channels visually have the same signal, but hear
sound from only 1 ear. True phase coherent speakers may sound better
because the left/right phase shift is tightly controlled.

Many lossy compression schemes remove nonlinear components, so that might be
one reason why they are distinguishable from the original recording. But
extra harmonic components are often unnoticed. There was an interesting
test of this where they put in a control on a radio that increased the
harmonic distortion, but labeled it bass. Most people would crank it up and
say it was better. Audiophiles would advance it some and say it was better.
Audio engineers would say it doesn't work, but it seems to increase
distortion. Most information about how you perceive sound comes from Bell
Labs experiments in the early 20th century.

As to the top end of hearing, I have proof that some adults can hear above
20kHz, and there are tests that show that small children can often hear well
above 20kHz. I had a friend who could hear the ultrasonic burgler alarms.
Some stores would leave the signal on, and just kill the alarm part. Most
of the sound above 10kHz is just "sparkle" in music and can't be
distinguished by pitch, so some lossy compression schemes regenerate the
upper end using an algorithm or a simple equation. They then transmit very
little information in the upper octave band between 10 and 20kHz. Such
schemes usually sound better and can achieve greater compression. I suspect
that most people on this list can no longer hear the 15kHz whistle that
analog TVs put out. The high end goes first.

Hearing is finely tuned to distinguishing certain things and not others.
Similarly vision really only distinguishes the change in color and
luminosity across boundaries, and not the absolute level. The result is
color constancy independent of the illumination. The usual 3 color
explanation of vision is basically incorrect for naturally illuminated
objects, but works fairly well for engineered products.

John M. Clement
Houston, TX


One of the interesting phenomena in hearing is that of turn-off (it can be
done in a gradual enough way that the turn-off edge doesn't introduce a
lot of high frequency components). A tone is present, but humans give no
indication of hearing it *until the tone is stopped*. Then they say, "Oh,
I WAS hearing something".
Hearing is tricky!


A question --

You claim (correctly) that ears have upper limits on what can be heard. I
have been told by people in music that although the ear cannot hear above,
say 20,000 Hz, the sound will be different if those higher frequencies are
there or not. Or, put another way, the trained ear can sense the higher
inaudible frequencies being present or not. Anyone have experience, or
knowledge in this area?


Are the "cross terms", "difference terms", etc. necessary to describe the
pressure fluctuations in the air, or do they apply only to the perception
of the sound?

I discussed a finite series, only, not an infinite series.
The problem is that in real instruments, nonlinearities are typically
present (there is argument that they make *all* the difference), and so
one hears "cross terms", "difference terms", and other bits which are
certainly not present in the signal originally used to drive the
instruments. The presence of these terms is, of course, dependent on the
volume at which the instruments are played, and that's not usually covered
by strictly modal decomposition.

As to your question about the possibility of an infinite series forming
the sum which is heard:
1) it's possible, so long as the sum is square-integrable (we have
to conserve energy, after all);
2) in principle, it doesn't matter, because our ears have upper
limits on what they can hear anyway.