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Physics of Chilly Magnus Chord Organs

Dear list -

Could someone please explain to me the relationship between the temperature of
an instrument and its pitch?  As you know, the pitch of an instrument is
usually low when it has been out in the cold.  Is this more a function of the
rigidity of the matter that is vibrating?  The slow speed with which particles
move in cold air?

A colleague of mine recently posed this question to me, in reference to a
Magnus Chord Organ (part of his message is below), and I thought this might be
an interesting question for the auditory list.

Thanks -
Timothy Justus

Part of my colleague's message:
 "... finding a Magnus Chord Organ... I was able to find
two of these organs, both in working condition.  Unfortunately, both are a
full half-step sharp in pitch.  Transposition while playing is an option
while using the keyboard, but not the push buttons that play chords, and
there's a gag in the piece that involves the push buttons. I believe these
organs are constructed as follows: when the organ is turned on, a fan provides
an air-stream; when a key is depressed, the air stream is released and
channelled in such a way as to vibrate the reed underneath the key (I suppose a
reed-organ or an accordian function the same way, with the air stream generated
manually).  I have a few questions:

"How would temperature affect pitch in such an instrument?  The temperature
in this shop was pretty cold; if the thing was warm, might the core pitch
change?  If it did, isn't it more likely to go higher, rather than lower?

"If the instrument's core pitch is indeed a half-pitch sharp, are there ways
to "tune" it?"

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