Klarinet Archive - Posting 000399.txt from 1996/10

From: Roger Shilcock
Subj: Re: CO2 and Pitch (fwd)
Date: Wed, 16 Oct 1996 03:47:38 -0400

---------- Forwarded message ----------
Date: Fri, 11 Oct 1996 11:59:04 +0200
From: Leonardo Fuks <leonardo%SPEECH.KTH.SE@-----.UK>
Subject: Re: CO2 and Pitch

Charette wrote:
>Most of the assumptions on pitch change concerned the CO2 in the
>clarinet air column changing the density. In reality, the amount of
>air expelled to produce a tone for a relatively short time is
>significantly smaller in volume than the air column contained in the
>clarinet. Therefore, diffusion of the CO2 over time would have to be
>taken into account, along with the effective length of the clarinet
>air column (which depends on the holes covered and exposed for the
>note).

Dear Mr. Charette:

The length of a clarinet is approx. 63 centimeters and the inside diameter
is in average lower than 1.5 cm .
The volume of air inside the instrument (bell and tone-holes would not add
too much) :
V@-----., d - diameter, ^2 - to
the power of two
V~ 111 cm3 ~ 0.11 liters

The air-flow through a clarinet reed (if no major leakeage is present), the
flow into the clarinet bore may assume tipically values that range from 0.12
to 0.40 liters per second (Bouhuys&Jonson, JASA 22:1086, 1967).

Your lungs contain very pessimisticaly 4.0 liters of vital capacity . Most
of healthy adults, males, higher than 5'9" - 1.75 m, breathing at sea
level, in a standing position, holding a black clarinet (:)), will have a
V.C. of more than 4.8 liters .

>From the former paragraphs you can conclude that the gas mass inside the Bb
clarinet will be "updated" almost every second, or even more often; that the
instrument will be filled dozens of time by every breath, with increasing
contents of CO2 (not in this message but I wrote about that some days ago).

CO2 is not a type of gas that diffuses as quickly as O2 or H2, in an
air-like mixture. So it is not likely to escape so quickly through your
clarinet holes.

I hope it makes sense.
Best regards,
Leonardo
No - it doesn't make much sense.
1) Clarinets are full of holes. The instrument is only going to fill up
if the player is blowing continuous low Es!
2) The said holes are several mm in diameter. CO2 molecules are not going
to emerge from such holes any more slowly than any other molecules.
Clarinets are not made of microporous membranes or unglazed ceramic,
normally, so the common "laws" of diffusion are irrelevant. In any case,
the forced draught changes all the rules.
(Don't ask me exactly how, though).
Roger Shilcock