Author: Luuk ★2017
Date: 2020-11-11 19:11
Keep in mind that the reed is small and stiff, and the bore is the major resonator.
The reed should be seen as a so-called perturbation, a secondary influence at best. Frequency spectrum of the clarinet will be 'mostly' (90%? 95%?) determined by the length, diameter and general cilindricity of the bore, and all other factors (chimney lengths, undercutting, bore diameter variations, stiffness of the reed, material used etc. etc.) will give second (third, fourth...) order effects. Nevertheless, they may be audible and relevant.
This paper gives an extended discussion of reed vibrations, and includes lots of pictures of vibrational modes of a reed on a mouthpiece:
https://hal.archives-ouvertes.fr/hal-00668277v1/document. Please note that this describes an experimental set-up, and that in real life the reed will behave different because of the dampening effect of the embouchure (not present in the experiments for this paper), and because the mouthpiece used in this research has a flat lay. But these 'perturbations' may also only be second or lower order. That being said, I expect the so-called transversal modes and the generic modes (see paper) are not present with embouchure added, or at least not wanted (chirping, squeaking).
Regarding the flute: the wind blown over the embouchure hole creates vortices. These vortices initiate vibrations in the pipe of the flute, and again (almost) all energy ends up in the resonant frequencies. Pipe length and basic construction (two-sided open pipe, in the case of a flute) determines the resonance spectrum, where material, subtle changes in diameter etc. have secondary influences, at most. This is why cheap clarinets with worthless reeds still sound as a clarinet, and not as a flute, sax, trumpet etc.
Harmonics do not result from the pipe material, but the precise location and intensity of the harmonics may be influenced in a subtle way by changing the material. 'Timbre' is the perceived quality of the mix of frequencies heard. This mix will be influenced by material, wall thickness etc. but again, only in a subtle way. Nevertheless, subtlety is very important in musical expression!
See f.i. https://link.springer.com/chapter/10.1007/978-3-030-19175-7_9 Effect of Wall Material on Vibration Modes of Wind Instruments: Having in mind theoretical considerations and numerous experimental approaches described in this chapter, we can mention that materials have a limited effect, if any, on the sound of acoustic specimens or experimental musical instruments. On the other hand, the vibration of a wind instrument wall can influence the feeling of a player for various reasons. It is evident that different materials provide very different amounts of damping, and therefore it is also evident that this phenomenon should be taken into consideration.
Regards,
Luuk
Philips Symphonic Band
The Netherlands
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The Clarinet BBoard
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