Klarinet Archive - Posting 000059.txt from 1996/05

From: "Kirby W. Fong" <kfong@-----.EDU>
Subj: Why overblow at a twelfth
Date: Fri, 3 May 1996 19:53:54 -0400

Dan Leeson asked for an explanation of why the clarinet overblows at a
twelfth. While it is true that in theory a stopped cylindrical pipe does not
support even harmonics, this is a restatement of the phenomenon, not an
explanation. I don't really know if there is an explanation brief enough to
put in an electronic mail message, so I will resort to citing substantive
documents. John Backus is a professor of physics who has written several
articles about clarinet acoustics in the Journal of the Acoustical Society
of America; however, for the layman, the best place to start is his book
"The Acoustical Foundations of Music" published by W. W. Norton & Company,
New York in 1969. I don't know if there is a newer edition; I bought my
copy more than 20 years ago for $9.75. The discussion of the harmonics of
a stopped pipe is on page 64, but you will have to read the material
leading up to it. There is only a modest amount of mathematics involved,
and I think a grasp of high school algebra is all that is necessary to
understand the explanation. If you get that far, be sure to look at the
comments about the clarinet in particular on pages 188 to 194.
As long as you're patronizing your friendly local bookdealer, you
might want to order a copy of "Horns, Strings, & Harmony" by Arthur H. Benade.
Dr. Benade was also a professor of physics well known for his work and
experience in musical acoustics. My copy of this book was published by Anchor
Books, Doubleday & Company, Garden City, New York in 1960. It is a paperback
that cost me $1.45 30 years ago. This has almost no mathematics and so
explains in only qualitative terms how musical instruments work. This is
insufficient for explaining why a clarinet overblows at a twelfth, but it
is an enormously readable book about musical acoustics. I do not know if
there is a newer edition.

Kirby Fong
kfong@-----.edu