Klarinet Archive - Posting 000256.txt from 1999/11

From: "Edwin V. Lacy" <el2@-----.edu>
Subj: Re: [kl] KEYS
Date: Mon, 8 Nov 1999 14:32:51 -0500

On Mon, 8 Nov 1999, Dodgshun family wrote:

> I basically concluded that a difference in sound (or "colour") between
> keys is due to the tempered scale.

All that I have ever learned about this indicates that the exact reverse
is the case - it is precisely because we use the tempered scale that there
is less difference between the tonal characteristics of various keys than
there was in other types of temperament.

> This is because the intervals are not exactly equal from key to key.
> For instance (assuming the piano/organ is in tune), the perfect 5th
> between middle C and G beats at 105 beats per minute, but the perfect
> 5th between D and A beats at 120 beats per minute.

I'm having some trouble understanding this. The perfect 5th is one of the
two intervals in the tempered scale (the other being the perfect octave)
which can be tuned on the piano without any beats between the two notes.

I wonder if what you are describing is the frequency of the "difference
tone," a pitch or apparent pitch which is generated by the frequency
differential of two notes? The difference tone between the two notes of
any interval will be higher if the interval is transposed to a higher
pitch, so perhaps this is what you were mentioning.

It is true that there is a difference between the perfect 5th in the
tempered scale as compared to the Pythagorean scale (as well as others),
but the difference is relatively small in this case. The 5th in the
equally tempered scale will equal 700 cents, or 100ths of a semitone,
while in the Pythagorean, the 5th consists of 702 cents. However, even in
this case, the perfect 5th will produce beats at a frequency nowhere the
magnitude you described.

Having taken a course in acoustics many years ago, my memory could
certainly be faulty. But, your thesis as stated above is precisely
contrary to what I have taught and have read concerning the topic.

Ed Lacy
el2@-----.edu

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