Klarinet Archive - Posting 000385.txt from 2003/04

From: b1rite@-----. Rite)
Subj: Re: [kl] Fun & games with "barrel blank"
Date: Sat, 26 Apr 2003 00:35:21 -0400

<><> Doug=A0Sears wrote:
Some time ago, I made a crude spreadsheet model of Benade's perturbation
equations (which are described, but not given explicitly, in
"Fundamentals of Musical Acoustics"). Making some rough guesses about
your clarinet and barrel, I figure your low register would be about 50
cents flat, from low E up to E at the bottom of the staff. From that E
up into the throat would gradually improve, up to 0 cents flat at throat
A. The clarion long B would be only a couple of cents sharp, getting
worse as you go up the scale, 50 cents sharp at E, all the way to 100
cents sharp (a semitone!) at clarion A through C above the staff. How
did I do? I'm eager to hear how accurate the prediction was.

I'm surprised at how close your spreadsheet predictions are, Doug!

As you'll notice below, the upper clarion & lower altissimo don't fall
apart as badly as predicted, but I'm not a virtuoso up there, and
perhaps if I were, then the sharpness would be more extreme?

Given the major discontinuities where the 'barrel blank' joins the
mouthpiece & upper joint.... well, I'm surprised. I didn't think that
mathematics could come so close.

Does your spreadsheet deal with volumes & diameters only, or possibly
can it offer information about the shape of interior curves?

.....anyway, I was expecting that the 'barrel blank' would not play a
steadily increasing scale (albeit out of tune) for all the chromatic
fingerings up into the altissimo, but it does. So that was the first
surprise for me.

When we were discussing putting an oboe reed on a clarinet, Tony Pay
explained how 'uncoupling' the mouthpiece & reed from the remainder of
the instrument caused discontinuous results up and down the scale. I
was expecting similar results with my 'barrel blank', but it didn't
happen that way.

For the following results, I played each fingering with my normal barrel
first, and I tried my best to 'remember' the embouchure that put my
tuners' needles (I have two tuners) 'right on'. Then I played, as best
I could, the same fingering and embouchure (and same mouthpiece & reed,
of course) with the blank.

I played all of these with my spherical bell, just because I am used to
it. I will re-do some of these over the weekend with my flared bell
just to see if something unexpected happens.

In general, my tuners bounced around more with the blank. Presumably
the sharp-edged change in bore diameter (where blank meets mouthpiece &
joint) accounts for this.

low E 45 cents flat
F 55 cents flat
F# 50 cents flat
G 40 cents flat
G# 35 cents flat
A 30 cents flat
A# 40 cents flat
B 40 cents flat
C 40 cents flat
C# 45 cents flat
D 55 cents flat
D# 45 cents flat
E (*really* bounces around!) 60 cents flat
F 65 cents flat
F# 65 cents flat
G (open G) 60 cents flat
G# 40 cents flat
A 35 cents flat
A# 60 cents flat (first use of register key)
B (long fingering) 30 cents flat
C 10 cents flat
C# 5 cents flat
D 0 cents flat
D# 0 cents flat
E 5 cents sharp
F 5 cents sharp
F# 5 cents sharp
G 10 cents sharp
G# 25 cents sharp
A (first leger line) 30 cents sharp
A# 40 cents sharp
B 40 cents sharp
C 40 cents sharp
C# ...... well, it's my bedtime......

Cheers,
Bill

<who *is* impressed what math can do>
<Doug received no hints from me off-list>

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