Klarinet Archive - Posting 000055.txt from 1996/05

From: Grant Green <gdgreen@-----.COM>
Subj:
Date: Fri, 3 May 1996 12:40:04 -0400

>Would some kind soul out there help me understand why the clarinet
>overblows a 12th while a bassoon, a flute, and an oboe overblow an
>octave.
>Please, no shooting from the hip, but serious knowledge about the
>phenomenon. Even better would be an explanation followed by a
>scholarly reference.

First, the scholarly reference: "Fundamentals of Musical Acoustics", by
Arthur H. Benade. My copy is at home at the moment, but I happened to have
a copy of the "Stranger Creek Productions" 1996 catalog, which carries the
tome (1-800-258-9528 to order).

Now, my recollection of his explanation: the difference between
oboe/bassoon/ sax/etc. and clarinet derives from the shape of the bore. Sax
et al. have conical bores, and play in the octave corresponding to their
length (e.g., the 2' octave for most soprano instruments, 8' for bassoon,
etc.). All reed instruments are treated as tubes closed at one end (by the
reed/mpc). These instruments produce a full overtone series, with the
differences in timbre resulting from muting or emphasis of particular
harmonics. If I remember right, the vibrating air column has a node at the
mpc and a node at the bell. The distance between the nodes determines the
frequency, i.e., the pitch.

Because clarinets have a predominantely cylindrical bore, they exhibit
"stopped pipe" harmonics. The air column has a node at the mpc, but due to
the physics of wave propagation cannot form a node at the bell. The wave is
then reflected back to the mpc, effectively doubling the length the wave
travels. The nodes are effectively twice as far apart (from the wave's
point of view) even though superimposed. A 2X distance results in half the
frequency, i.e., an octave lower than a conical pipe. This is why the
clarinet sounds nearly an octave lower than other soprano instruments of the
same length. The absence of a node at the bell prevents the air column from
vibrating in any of the even harmonic modes, which is why (1) the clarinet
has its characteristic harmonic structure (lacking the even harmonics) and
(2) why it overblows at the 12th (3rd harmonic).

The flute is different because it is open at *both* ends: there is no reed
to close the bore, and thus no node at the mpc (or embouchure hole). The
flute ends up with open pipe harmonics, like the conical bore instruments.

I'll try and review the text again this weekend, to make sure the above is
accurate (and perhaps explain it a bit better).

Grant D. Green
gdgreen@-----.com
http://www.crl.com/~gdgreen/index.html
Still hunting sarussophones!