pipe organ method [OT]
John Payson email (remove spam text)
| I know that this method seems funny (and Alice needled me) so I'm
|looking at the various problems: Turns out that no-one ever heard of pipe
|organs de-tuning themselves, that the resonant frequency is linearly
|proportional with the column height (strictly linearly) and that very
|small length changes give small but very constant frequency changes.
|Atmospheric pressure and temperature do not play a role as far as pipe
|organ experts know. So it should work even over changing temperature.
There are two primary types of organ pipes: flue pipes and reed pipes.
Flue pipes may be further subdivided into open and closed, and reed
pipes into full- and half-length.
An open flue pipe will produce a fundamental whose wavelength is equal
to the twice length of the pipe plus a small extra amount related to
its diameter. The overtones produced will have wavelengths of
2L/n + k
where 'L' is the pipe length, 'n' is a positive integer, and 'k' is
about the same for all overtones (note that the overtones produced are
not exact harmonics).
A closed flue pipe will produce a fundamental whose wavelength is equal
to four times the length of the pipe, plus a small extra amount related
to its diameter. The overtones produced will have wavelengths of
4L/(2n-1) + k
where the parameters are as above. Note that the fundamental pitch
will be about an octave lower than an open pipe of the same length, but
the pipe will have a much less "full" sound.
For flue pipes, the frequency is a function of wavelength (which in
turn is a function of pipe dimensions) and the speed of sound (which
can vary significantly with temperature). To the extent that changes
in temperature and humidity case the pipes to expand/contract, they
will probably contribute to non-uniform pitch changes since different
pipes are often made from different materials. If the organ is at a
uniform temperature, however, the speed of sound, will be uniform with-
in it. Changing the temperature of only part of the organ from 70F to
90F would cause it to be objectionably off-pitch compared with the rest
of the instrument, but changing the whole organ from 70F to 90F should
not pose much of a problem for the flue pipes.
Reeds, though, are another story. Unlike flue pipes which have no mov-
ing parts (other than the air molecules within them), reed pipes have
a vibrating reed a the bottom. The frequency output by the pipe is
mainly a function of the reed's resonant frequency (which is independ-
ent of the speed of sound in air); rather than affecting the frequency
produced, adjustments to the pipe length affect how well the pipe
Reeds can be and often are affected by temperature, but the specific
effects are hard to characterize. What is noticeable, though, is that
while flue pipes will sound good if they are at a uniform temperature,
regardless of how that temperature compares with the temperature at
which they were tuned, reed pipes will often not sound good at temper-
atures other than that at which they were tuned.
True anecdote: I was at a church service and practically cringed when
the organist turned on a certain reed stop during the final hymn. Af-
ter the service, I asked her about it and she said that's how she cues
the congregation that it's time again to spring for the twice-yearly
organ tuning. Cute, eh?
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