Re: Physics of Chilly Magnus Chord Organs

[Jont Allen <jba@xxxxxxxxxxxxxxxx>]

The frequency depends on the acoustic length L and the velocity of sound c, where

        f=c/L

The velocity of sound is porportional to the square root of temperature,
in degrees Kelvin. Thus c \propto sqrt(C+273) where C is the temperature
in degrees C.

The pitch, as I use the term, is the psychological frequency. This depends
on a lot of factors. Thus "pitch" is not relevant to the question.

As I use the term, pitch is not the same as frequency. However, in the casual
speech literature, they use the term to mean the fundamental frequency
of the vocal cord vibration.

This is from my dictionary (AHD)
8. a. Acoustics The distinctive quality of a sound,
dependent primarily on the frequency of the sound waves produced by its source.
b. Music The relative position of a tone within a range of musical sounds,
as determined by this quality.
c. Music Any of various standards for this quality associating
each tone with a particular frequency.


Timothy C. Justus wrote:
>
> 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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