Klarinet Archive - Posting 001373.txt from 1999/05

From: "Edwin V. Lacy" <el2@-----.edu>
Subj: Re: [kl] Even Partials (was Bradley's Question)
Date: Sun, 30 May 1999 01:03:55 -0400

On Sat, 29 May 1999, Dee D. Hays wrote:

> As far as the altissimo A, that's easy. That partial is so flat
> compared to the even tempered scale that you do indeed have to play
> what ought to give you the next higher note. This even works out
> mathematically. Calculate the frequency of A based on partials only
> starting at the fundamental chalumeau note and you get a value that
> would result from a Pythagorean scale approach. This is quite flat
> compared to the even tempered scale.

And, On Sat, 29 May 1999, Roger Garrett wrote:

> I was very much hoping that Jim Pyne would respond to the questions
> posed to him regarding the strong opinion that the overblown A (that
> he mentioned in his earlier post as being an example of his argument)
> is actually a very flat Bb and, therefore, is not a very strong
> example supporting his arguement.

It seems to me that both of these messages imply a disagreement with what
James Pyne first posted, but in fact, neither one of them seem to me to
directly address the points he made.

First, it is easy to see that altissimo A, as we usually play it, is
fingered as a note in the harmonic spectrum of chalumeau C. In fact, it
is the seventh partial of that series. This can be discerned from the
similarity of the fingerings of the notes in the low C series. From low
C, the second partial would be C one octave higher. However, as Mr. Pyne
indicated, we cannot make the instrument respond in that mode with the
fingering of the fundamental. Then, the 3rd partial would be G just above
the treble clef, And the correspondence of the fingerings is obvious - one
needs only to open the register key, thereby setting the air column to
vibrating in a new mode. Next, the fourth partial would be C, two ledger
lines above the staff, another partial which we cannot produce with the
fundamental fingering. The 5th partial would be altissimo E, and again
the relationship to the fundamental fingering is apparent. In this case,
the venting consists of opening both the register key and the first finger
hole of the left hand. Continuing with this process to the 7th partial,
another mode in which the air column can be induced to vibrate, would
produce a very flat Bb (very flat only in relationship to the tempered
scale). In fact this note is so flat that the clarinetist uses this
particular variation of the fundamental C fingering to produce the note
altissimo A.

However, as far as I can determine, none of this refutes the arguments of
Mr. Pyne. I think he was propounding the arguments that (1) contrary to
popular belief, even numbered partials *are* present in the harmonic
spectrum of the clarinet, and (2) when a tone is played on the clarinet,
regardless of the fingering or the position in the harmonic spectrum of
some lower note, the note being played functions acoustically as a
fundamental. In other words, every note on the clarinet or any other
instrument will produce its own harmonic spectrum, and its partials will
show the intervallic structure which we expect of the overtone series -
P8, P5, P4, M3, m3, etc., etc.

This is a concept which is often misunderstood by woodwind players. For
example, when we play a note such as clarion F, if the resulting tone is
subjected to spectral analysis, it will show an overtone series based on
the F, not on the chalumeau Bb. The tone quality of the F is determined
by its own spectrum, not that of some other note. Now, the *pitch* of an
upper register note may be affected by its position in the harmonic series
of a lower note. For example, the clarion F, if played in tune to the
harmonic spectrum of low Bb, would be higher than the lower fundamental by
an interval of 1,702 cents. To be in tune with the tempered scale, that
interval should be 1,700 cents. Naturally, the player can accomodate and
adjust to a discrepancy of 2 cents. But still, no matter what the pitch
of the F, it will generate its own harmonic series.

So, if I may be so presumptuous, my interpretation of Mr. Pyne's statement
is that while the clarinet does function as a pipe closed at one end, the
result is not the total attenuation of the even-numbered partials, but
rather only that the air column can be made to vibrate only in the
odd-numbered modes of any given fundamental range fingering.

What I would like to see are more representative spectra of the Fourier
analysis of clarinet tone. Mr. Pyne, did you select the one which you
gave on the basis of it being representative of clarinet tone in general,
or was it one in which the even-numbered partials were particularly
prominent?

Ed Lacy
el2@-----.edu

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