Klarinet Archive - Posting 000336.txt from 1998/01

From: Jonathan Cohler <cohler@-----.net>
Subj: Re:reed tip closing
Date: Wed, 7 Jan 1998 10:02:26 -0500

Roger Shilcock wrote:

>>From what I'm beginning to remember, the reed
>is initially vibrating at its own frequency immediately after attack by
>the tongue - the air column then *forces* the reed to vibrate at its own
>or some compatible frequency. Given the difference in the materials, it is
>hard to believe that the reed at this stage is vibrating in exactly the
>same modes as the air column, though. Again - what happens with
>multiphonics?
>Roger Shilcock
>

Here's a bit more detail on how it works without getting into too much physics.

First, for a given fingering, the tube by itself has resonance peaks at
certain frequencies. If the lowest peak is at frequency F, then the
subsequent peaks are at frequencies slightly below 3F, 5F etc., getting
flatter as they go higher.

Second, the reed all by itself (if you put it in a vice and twang it, for
example) has it's own completely different set of resonance peaks (which
are modified when yet again when one puts their lip on the reed with
varying degrees of pressure and positioning). The lowest natural mode
frequency of the reed by itself is roughly in the range of 2,000 to 3,000
Hz.

When the reed is put on a mouthpiece/clarinet and blown to produce tones,
the reed and the air column work together. The fundamental frequencies of
the produced tones lie neither at the resonant frequency of the reed or at
the resonant peaks of the tube, although they tend to lie very close to the
lowest of the resonant peaks of the tube.

Since Benade says it so well, here are some sections quoted from
Fundamentals of Musical Acoustics (Dover, pg 436):

1. The resonance frequencies of an air column terminated by a reed
are always lowered by the reed's presence, and they are never higher
than the natural frequency with which the reed cane itself would
vibrate if plucked like a tuning fork. (Note: this natural frequency
is NOT the one obtained by blowing on an oboe or bassoon reed or on a
clarinet mouthpiece; in all these cases there is present inside the
reed cavity a miniature air column that has significant influence.)

2. Changes in the reed's natural frequency (produced for example by
changes in the way in which it is pressed onto its mouthpiece by
the player) produce small but parallel changes in the air-column modes
that lie far below the reed's natural frequency. These changes become
progressively larger for higher modes that lie nearer to the reed
frequency.

Now, the issue of multiphonics and squeaks is much more complex.
Multiphonics arise out of the fact that airflow through the reed into the
mouthpiece is not a linear function of the air pressure differential
between inside the mouth and inside of the mouthpiece. This curve, which
can be drawn for a given embouchure setting, is what Benade calls the
"flow-control characteristic curve". Without getting into the
mathematics/physics behind it, here are Benade's basic conclusions (pg 439):

9. The fact that the flow-control characteristic curve is not straight
(or, equivalently, the fact that the slope varies from point to point
along the curve) is an indication that heterodyne effects can take
place. It is this nonlinear feature of the flow-control behavior that
leads to the existence of regimes of oscillation in which oscillation
is maintained by excitations taking place simultaneously at several
frequencies.

10. Due to resonance phenomena, the flow-control sensitivity of the
reed itself becomes large in the frequency region just below its own
natural frequency. If the reed is insufficiently damped (e.g. by
the players lips), high-pitched squeaks may take place at the frequency
of the reed even though the air column itself may be above cutoff and
so lack a resonance peak in this region.

---------------------------
Jonathan Cohler
cohler@-----.net