Klarinet Archive - Posting 000117.txt from 1999/12

From: Neil Leupold <leupold_1@-----.com>
Subj: Re: [kl] cylinders & cones
Date: Sat, 4 Dec 1999 20:38:51 -0500

--- "Dee D. Hays" <deehays@-----.com> wrote:

> acoustically, some variance can occur before the sound
> waves "switch over" from the characteristics of the closed
> cylinder to the closed cone.

Followed by:

> For musicians and instrument designers, the important element
> isn't whether its a true cylinder but [how it acts] acoustically.

Based on these comments, I infer that the strict mathematical
definitions of cylinders and cones are not germane to a discus-
sion of instrumental acoustics, in the sense that modern instru-
ments are not typically manufactured to match these definitions.
Rather, you seem to be suggesting that the distinct acoustical
properties between cylindrical and conical instruments (more
particularly with respect to overblowing a 12th, as opposed to
an octave) hinge upon a specific relationship between the two
shapes, sharing a particular point at which the acoustics of
one no longer apply, but are supplanted by the acoustics of
the other. I'm still curious to know if there exists an ex-
act number -- a percentage of flare of an imperfectly cylin-
drical tube -- past which the cylinder ceases to function
like one acoustically. Does anybody know? How rapidly, and
to what minimum degree, must a tube flare outward from one
end to the other in order to cross over into the acoustics
of a cone?

-- Neil
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