Klarinet Archive - Posting 000204.txt from 2010/08

From: Jennifer Jones <helen.jennifer@-----.com>
Subj: Re: [kl] About clarinet acoustics
Date: Tue, 17 Aug 2010 08:57:10 -0400

Keith,

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 =3D radius. Is the complex
calculation something like L+C?.

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).

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 might depend upon how much different ambient temperature is from
the cold clarinet and the player. Perhaps you have looked at this
issue, having made the lattice-hole calculations in your bass
clarinet?

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 dist=
ance 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 =3D 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 t=
hat tone hole, D is the bore diameter at the open tone hole >and t is its d=
epth. h is a factor that may be taken as 0.75 for a completely open hole an=
d 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...

On Tue, Aug 17, 2010 at 3:30 AM, Keith Bowen <keith.bowen@-----.com> wrote:
> Because of the temperature gradient between the hot air from your mouth a=
nd
> the external temperature - which will be worse when the clarinet is cold,
> not better - one should not expect an accuracy better than about a semito=
ne
> in these experiments.
>
> And don't forget to do the end correction for the mouthpiece/barrel bit as
> well as the half-clarinet.
>
> When warmed up, the average temperature in the clarinet is about 25.5 C in
> an room at about 20 C, and the sound velocity is then 346 m/s.
>
> I think the mouthpiece node position will change somewhat between the two
> measurements. I can't estimate how much, but my feeling is less than a cm.
>
> Keith
>
> -----Original Message-----
> From: Jennifer Jones [mailto:helen.jennifer@-----.com]
> Sent: 17 August 2010 10:49
> To: The Klarinet Mailing List
> Subject: Re: [kl] About clarinet acoustics
>
> Nitai,
>
> The half clarinet measurement is easy. =A0If you have a tuner that can
> tell you what frequency you are playing. =A0Perhaps if it just tells you
> how many cents sharp or flat you are and relative to which frequency,
> it should work. =A0You 'll also need a thermometer and a ruler (metric
> is nice).
>
> The thought was to use just the upper segment of the clarinet, the
> barrel and mouth piece, measure the frequency played (cold clarinet-
> not warmed up) determine the wavelength corresponding to that
> frequency for the air temperature you have. =A0Then calculate 1/4
> wavelength. =A0Subtract that 1/4 wavelength from (the length of your half
> clarinet plus 0.6 times the radius) of the end and you get the distance
> between the tip of the mouthpiece and the first node in the clarinet.
> It is the same calculation that Diego did earlier, but without the
> complication of the bell.
>
> http://test.woodwind.org/Databases/lookup.php/Klarinet/2010/08/000059.txt
>
> Diego converted from concert A (B all closed with speaker key), which
> wouldn't be possible with a half clarinet, unless perhaps from high B
> (thumb, index finger, speaker key). =A0I was thinking of setting the
> tuner on C or C#, but I am not sure my tuner is that sophisticated.
> Then there is the issue of converting cents to hertz, which it looks
> like will be easy:
>
> http://www.sengpielaudio.com/calculator-centsratio.htm
> http://www.pianosupply.com/cents-hz/
>
> -Jennifer
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