Author: Bob Phillips
Date: 2010-04-25 16:16
There are a few academic studies of the effects of body material on the sound characteristics of woodwinds.
One made a few rudimentary flutes of thick and thin silver, gold, and (perhaps) aluminum. The spectral structure of the noises made were indistinguishable by spectrographic analysis.
The Fox article suggests to me that three material properties may be significant in the performance of a clarinet:
Specific stiffness is the ratio of Elastic modulus to density. Stiffness tends to force a distorted material back to its natural shape, and density tends to keep a moving section of material moving. The square root of this ratio [ sqrt(Stiffness/density) ] will almost always factor out of a mathematical expression for the vibration frequency(ies) of an object. The rest of the formula will reflect the dimensions and constraints of the vibrating object.
I'm pretty certain that the vibration characteristics of a reed depends upon the "cut/shape" and its specific stiffness. Can is stiff and light, so it vibrates rapidly, while simple plastic is not so stiff and much denser. Can is also directional in that the fibers run lengthwise, so that it is stiffer wrapping around the mouthpiece facing then in bending away from the mouthpiece table. Similarly, a wooden clarinet is stiffer in bending than it is in "swelling".
Another property of importance is specific damping, which is the ratio of energy dissipation to the product of stiffness and density. A stiffer material stores more energy when deflected a given amount than a softer material. A denser material stores more energy when it is moving, so these effects combine to establish how much energy is captured in the vibration. The damping determines how rapidly the material's vibration dissipates --and how rapidly it can be established or changed.
One would expect that specific damping would have a great effect on a clarinet body's transient response. For certain, the specific damping is significant in how well a reed will respond to a change in fingering in the altissimo register.
The third material property that is probably significant is its thermal diffusivity. This is the ratio of thermal conductivity to the product of density and specific heat. Unfortunately to an investigator, this is probably not independent of specific damping, as the energy dissipation involves the internal generation and transfer of heat. The amount of thermal energy in the material depends upon how much of it there is (density) and how much heat is required to change the material temperature a given amount. So thermal diffusivity is a measure of how rapidly a change in thermal energy propagates through the material.
As in stiffness, wood will have quite different values of thermal diffusivity along and across its grain.
As guidance for experimentation with clarinet bodies, one should probably compare measurable performance metrics with specific stiffness, specific damping and thermal diffusivity. One interesting experiment would be to compare two clarinets --one with the growth rings perfectly concentric with the bore, and another with the growth rings running across the bore.
Of course, the shape of the clarinet body (limited mostly to wall thickness, as the bore and tone holes can't be changed much) affects its vibration characteristics; so that needs to be controlled in the experimentation.
Of interest to me: carbon fiber and ceramic clarinets
Bob Phillips
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The Clarinet BBoard
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