Klarinet Archive - Posting 000064.txt from 1997/06

From: Jonathan Cohler <cohler@-----.net>
Subj: Re: Clarinet partials
Date: Sun, 8 Jun 1997 07:59:16 -0400

Ian Dilley wrote:

>A couple of days ago you said that I was wrong in assuming that the
>partials of a clarinet note were flat. I have just been reading an
>article on sneezy written by you that says the partials *are* flat! You
>even say that a note sounds flatter as you blow louder because you are
>introducing more flat partials.
>
>Which is correct?
>
>The article I refer to is at:
>http://sneezy.mika.com/clarinet/Study/Vibrato.html
>
>
>Ian Dilley.

Hi Ian,

Not exactly.

This is a confusing issue, because the partials (which are the components
of the generated sound) are different from the resonant modes of the
clarinet tube.

The resonant modes of the tube are flat. The partials of produced notes
are exactly harmonic. And these are not contradictory statements.

Here's what happens. Consider the resonant modes of the tube for a given
fingering on the clarinet. Let's the first resonance peek is a frequency
f. Then the next peek will be slightly below 3f, the next slightly more
below 5f, etc.

Now, when one blows on the clarinet, one is producing cooperative "regimes
of oscillation" (as Benade calls them) in which the resonant modes of the
tube support the vibration of the reed and vice versa. In order to get
clear speaking notes, you must have "good cooperation" between two or more
resonance peeks. Therefore the closer the peeks are to 3f and 5f etc, the
better.

However, because of other considerations these peeks are generally flat.

So what happens when we blow? At very soft levels, there is only the
fundamental, so we get a frequency of f controlled solely by the first
resonance peek. As we get louder, more of the first partial (around 3f)
comes into play. As this happens, the resonance peek at just below 3f
pulls the "regime of oscillation" slightly flatter. So we get a composite
note whose fundamental frequency is slightly below f and whose first
harmonic is exactly 3 times that and therefore slightly below 3f.

As we blow louder and louder, more of the successively flatter resonance
peeks effect the overall "regime of oscillation" pulling the fundamental
frequency ever lower. That's why clarinet goes flatter as it gets louder.

As you can see, this is not very easy to explain via E-mail! Perhaps some
of my previous messages were a bit unclear on the subject.

Sorry for any confusion.

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