Klarinet Archive - Posting 000148.txt from 1995/02

From: Jon Delorey <Jon_Delorey@-----.COM>
Subj: Caution More Physics!
Date: Tue, 7 Feb 1995 10:26:07 -0500

The posting from Jonathan Cohler was great. I love the depth of these
discussions and find that a lot can be learned. Every *definitive answer* does
seem to bring up more questions and these subjects are never straight forward,
not even the physics let alone the metaphysics. Of course, this means I have
several questions about the physics.

Regarding Non-Harmonics.
>6. Now to answer the seeming paradox about
> how you can get inharmonic (or non-integer-multiple
> harmonics) from a driven system.
> The answer is that the driving force coming into
> the clarinet is not a simple sinusoidal driving force.
> If it were, then as I described in 4 above, the air
> column would vibrate ONLY at that sinusoidal driving
> frequency at an amplitude determined
> by the input force and the resonance curve.

I don't understand this statement. A non-linearity is needed in order to
produce non-harmonic partials. Maybe the reed acts as this non-linearity,
changing the effective impeadance of the tube with time, but I still don't
understand the non-harmonically related partials. I would also assume there
are still harmonically related partials propagating in the tube, creating a
kind of natural vibrato. I have tried to envision a fourier transform of a
noise generator and filter that would produce this result but I can't come up
with one.

As far as the reed being a white noise generator this makes sense, but since the
tube is not ideal, the reed in combination with the tube is not a white noise
generator in the strictest sense. The shape of the noise must vary with the
keying used for the particular note. This would affect the harmonic content of
the resulting waveform.

The non-harmonic partials has to also make the manufacturing of a clarinet that
is *in tune* for nearly four octaves very difficult (never mind having to
accomadate a non-harmonically related even-tempered scale). It's the kind of
problem that makes engineering interesting and a good day job.

Speaking of boundary conditions, there was a posting a while back that stated
the harmonics in an organ pipe were dependent on position. Would this be due
to the proximity of the floor or ceiling, and is this a factor in the harmonic
output of a clarinet?

Do you have a bibliography for some of these results? That may be an easier way
to answer these questions since the physics can get long winded since equations
and pictures of spectrums are hard to reproduce on a text based posting.

Jon_Delorey@-----.com
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