Klarinet Archive - Posting 000208.txt from 2010/08

From: "Keith Bowen" <keith.bowen@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Tue, 17 Aug 2010 13:15:25 -0400

Jennifer

>The node location estimate for notes with open tone holes in
cylindrical bored portions of clarinets seems to be missing a
parameter. The equation you sent looks like it is only the end
correction. Where does the length of the clarinet come into it? The
simple calculation was L + 0.6a where a = radius. Is the complex
calculation something like L+C?.

The length of the clarinet only comes into it for the fully-closed notes.
The equation isn't missing a parameter.

The correction you mention is the correction for a cylindrical tube open at
the end. The equation I gave is different: it is the correction for the tube
length when some of the fingers are closing holes and there are open holes
below this position, e.g. low Bb with T/L123/R1 down, the rest open. The
full equation is the equation I gave.

>I have another question. Is the temperature gradient that critical in
a cold instrument? The gradient in the air may affect the speed of
sound within the bore and may result in a rapid dumping of water from
the humid air into the bore surface, resulting in an increased air
density (water is less dense than nitrogen, the main component of
air).

Yes, according to Benade and Nederveen it is. And we know from playing that
we are flat when the instruments are cold. My point was that with a cold
clarinet and hot air blowing in, there is a completely unknown and
irreproducible temperature gradient. Nothing to do with the water. The
velocity of sound depends quite strongly on temperature.

>I don't see why the gradient would be worse when the clarinet is cold;
it might be less stable because the heat exchange has not reached a
steady state, but with a probably less than 1 minute measurement of
pitch for the wavelength calculation, everything else is independent
of breath; the length measurement of the clarinet, ambient temperature
measurement. It seems like measuring the initial velocity of an
enzyme catalyzed reaction (forgive the biochemistry reference); a
measurement that requires attention and planning, but is quite doable
when done in a timely fashion.

It is obviously a higher gradient when you go from body temp to cold as
compared with body temp to something warmed up a bit. And the measurements
of thermal dynamics are much less well controlled than in your planned
biochemistry experiment, unless you have a very heavily instrumented
clarinet. What I am saying is that without attention to this sort of detail,
it will be a sloppy, irreproducible experiment, and there is never any point
in wasting time taking bad data.

>It might depend upon how much different ambient temperature is from
the cold clarinet and the player.

Definitely.

>Perhaps you have looked at this issue, having made the lattice-hole
calculations in your bass clarinet?

No, I took the average sound velocity in a warmed-up instrument.

On 16 Aug 2010, at 22:40, Keith Bowen wrote:

>> The end effect must be taken into account as it can be more than the
distance between tone holes. The correction formula is on >page 450 of
Benade (Fundamentals of Musical Acoustics) and is also given in my masters'
thesis that I sent you recently.

>>"The acoustic length is longer than the physical length to the last closed
tone hole by the amount

>>C = z/2{sqrt[1 +(4/z)(t+hd)(D/d)^2]-1}

>>where z is the distance to the next open tone hole, d is the diameter of
that tone hole, D is the bore diameter at the open tone hole >and t is its
depth. h is a factor that may be taken as 0.75 for a completely open hole
and 1.0 for an average padded hole."

>This can be used to estimate the first node location without removing
the bottom of the clarinet, but it requires a narrow ruler that can
get in through the tone holes...

Well I didn't say that you could use a ruler. I used a vernier caliper with
depth gauge. There are accurate plastic ones available (used in the car
industry for measuring without scratching), which are the types that one is
allowed to use on museum specimens. Using a ruler would be taking bad data
:-).

Keith

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