Length - Frequency ratio for wooden instruments

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Bob Thomson - 26 Jul 2006 15:01 GMT

Hi,

I originally posted this message on the newsgroup
rec.music.makers.woodwind, but I'd appreciate getting
feedback from acousticians also.

I'm wondering about the suitable length of the fujara
(bassoon type recorder) that I'm working on (as a
hobby).

I know the frequency is inversely proportional to the
length. I found a scale (about didgeridoos) that I used
to make one in PVC and I thought I would use it again
for the fujara:

http://www.didjshop.com/physicsDidj.html

As a fujara plays mostly with undertones (and uses a
diatonic scale), I decided to make a fujara with key F
so as to enable me to play in key C (that fits with lots
of other instruments, including my didge and one I
made for a friend).

My issue is that it does not seem the infos in a plan of
fujara I have (once published on a reference Web site
about fujaras made in Slovakia) exactly matches the
length calculation info of didgeridoos given above -
unless this Web site deliberately publishes slightly
approximate length values so as to confuse us mere
mortals:

http://www.fujara.sk/faq/keys.htm

The plan I have can be displayed at:

http://chorand.nerim.net/fj/fj.gif

So according to didge physics, a wooden tube that
will play a F should be 1970 mm long.

And a fujara with a key F is presented as being only
(around) 75" or 1900 mm long on this site.

At this frequency, this difference would make half
a semitone. But this does not take into account the
"whistle" part of the fujara that includes the square
opening and goes up to the upper tip.

Furthermore, I think the reference length of a fujara
should be the distance between the end of the pipe
and the beginning of the aperture of the tip of the
edge (labium).

There is a nice drawing on:
http://en.wikipedia.org/wiki/Recorder

OK, at this stage, I could simply build the instrument
with the maximum length and assess the frequency
with a small chromatic tuner that I have, allowing
myself the option to shorten the instrument, but I'd
like to be sure I understand what's at stake ...

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Bob Thomson

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Savant - 28 Jul 2006 00:39 GMT

Bob,

> I'm wondering about the suitable length of the fujara
> (bassoon type recorder) that I'm working on (as a
> hobby).

I don't know the answer off the top of my head, but Dr. Olson probably
does:

http://www.amazon.com/gp/product/0486217698/sr=8-1/qid=1154043291/ref=sr_1_1/103
-0990225-0907061?ie=UTF8

If you don't have it/haven't read it already, it's more or less a must
have if your hobby is instrument building. ;-)

Arthur Benade is also a potential must-have:

http://www.amazon.com/gp/product/048626484X/sr=1-1/qid=1154043450/ref=sr_1_1/103
-0990225-0907061?ie=UTF8&s=books

I hope this helps!

---Savant---

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Bob Thomson - 28 Jul 2006 11:44 GMT

Savant a écrit :

> Bob,
>
[quoted text clipped - 17 lines]
>
> ---Savant---

Thanks ! It can't be harmful to read such reference books.

That said, I thought my issue was a very basic one... in fact,
when I think about it again, I feel there is simply no way a
given pipe may escape the law that says its frequency (pitch
of its base note) is inversely proportional to its length.

So my lengish post could be summed up as:
When calculating the frequency of a recorder type flute, are
there specifics to know, or should the applicable length of
the pipe be measured from the labium (square hole of the
fipple part) ?

Another possibility would be that the measurement must be
made starting from the inner wall - the (nearly) blocked end
of the fipple.

In the lack of any accurate answer, I'll start with the safest
option (longest value of the pipe), measure the frequency of
the sound with my little chromatic tuner, then decide if I'm
to shorten the pipe.

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Bob Thomson

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Natural Science Forum / Physics / Acoustics / July 2006

Length - Frequency ratio for wooden instruments