Author: Tony Pay ★2017
Date: 2020-11-18 21:44
I don't really want to engage with the various things that have been said on this topic. Some of them strike me as being helpful, others not so much.
About this 'paper', though, I can be quite clear. It's not defective because of its mathematics, of which actually there is very little. It's defective because it doesn't SAY anything; and what it seems to be trying to say is based on a misconception.
It seems to be trying to assess experimentally the harmonicity of the overtones in a steady clarinet sound of varying pitches. This is a wild goose chase because we already know that steady, driven oscillations are necessarily periodic and therefore harmonic. The measurements therefore say more about defects in the experimental setup than about anything real related to clarinets.
You note that the paper is unpublished. I don't know where it came from, but it strikes me as a graduate student effort that would never pass peer review in any reputable journal of musical acoustics.
The point is implicit in something I wrote here a couple of years ago. This Board is cluttered with so much opinionated noise that the point's subtlety passed by many, though not all, of its readers.
What is the point?
It is that though a reasonably expert player can excite the normal modes of oscillation of a clarinet (the so-called 'bugle calls'), these notes are not harmonics (whole number multiples) of the chalumeau note being fingered.
BUT, when you play the chalumeau note steadily, the overtones ARE whole number multiples of the chalumeau note frequency. What happens in actual clarinet playing does not correspond directly to the normal modes of oscillation of the tube.
It's surprising, perhaps; but there it is. A child looking at an old-fashioned 78rpm gramophone disc is said to have asked, "How do they get a whole orchestra into that wiggly line?"
Michelle Gingras wrote a whole mini-chapter of a book claiming that you could hear these bugle call notes in steady clarinet playing, and it took some effort on my part to persuade her and her publisher that they were in error. And, not because of ME, as I pointed out, but because of Mother Nature herself.
Therefore, I suggest that when Karl writesQuote:
A sounding clarinet's air column vibrates in multiple modes at once ...he immediately lays himself open to confusion.
A sounding clarinet is a system entire. Everything affects everything else. You can tinker with bits of it, but looking for a simple prediction as to the precise effects of that tinkering is very likely impossible, particularly where the reed is concerned.
By the way, I would no longer wish to be counted a mathematician. That part of my life evaporated many years ago:-)
Tony
Post Edited (2020-11-19 01:07)
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