Author: mschmidt
Date: 2007-04-27 17:53
It would be great if someone actually understood the physics of the crow. I doubt that anyone does, at least not to my satisfaction.
First we must consider the reed as a musical instrument--a very short oboe, with a more-or-less conical bore up to where the cane starts. If the staple dominated this instrument, the pitch would be rather fixed, and overblow in octaves. But the staple is only 47/70 of the instrument, the top of the bore isn't conical, and the sides of this bore are not rigid. Given all these complications, it is remarkable that the instrument does rather consistently give a "C" despite the many variations in cane width, cane thickness, gouge, and whatever between different makers and players. I have some very vague ideas of why this might be, but they are too vague to express at this point.
The "double crow" is not two tones sounding simultaneously; otherwise it would be like an organ stop that plays two pipes simultaneously, and would be a sweet, continuous tone. Instead, it seems to be a "bi-stable system" that goes back and forth between sounding the high tone and the low tone many, many times per second. All reeds are cyclical systems, in which the reed closes by the Bernoulli effect of the air velocity, stops the air flow, reopens under the pressure of stopped air, and allows the air velocity to increase to restart the cycle. This sort of system is a "non-linear" system. For there to be a cycling between the low and high note in a crow, there has to be another non-linear system that cycles between the low and high crow.
One speculative hypothesis is that the high crow (or the middle crow in a three-tone crow) is due to the vibration of the tip; this vibration feeds energy into the back portion of the reed, which has a different, lower fundamental frequency. As the amplitude of this vibration increases, it becomes dominant, forcing the principal (tip) vibration to a lower tone. The sounding of the lower tone dissipates energy quickly, so that the amplitude of the low frequency modes of the reed dies out, and the reed returns to the vibration dominated by the tip (the higher tone).
This speculative hypothesis would have to be thrown out if a French-cut reed, that has no separate "back" portion, were to easily give a two-tone or three-tone crow. I have no experience with such reeds, so I would welcome any data on this point. If such a reed does generate double or triple crows, then we have to have a new hypothesis for the crow, one that probably involves a bistable system that is purely about intereference of pressure waves in the air inside the reed.
Anyway, this post is probably more helpful to me in sorting out my own thoughts than it is for you, but who knows.
Mike
Still an Amateur, but not really middle-aged anymore
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