Klarinet Archive - Posting 000266.txt from 1999/11

From: "Edwin V. Lacy" <el2@-----.edu>
Subj: Re: [kl] KEYS
Date: Mon, 8 Nov 1999 14:33:01 -0500

On Mon, 8 Nov 1999, Dodgshun family wrote:

> > > 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.
>
> This did strike me as being strange as well, but it fitted well into
> what I was writing about. Personally I do associate keys with
> colours, and I guess maybe it was that I wanted a logical answer for
> it.

If your paper served the purpose of getting the grade that you wanted in
the class, then it no doubt was successful. I'm still trying to figure
out the reference to "beats" in a perfect 5th. Earlier, I was writing
from home where I have no reference materials at hand. Now, I am in my
studio, and I have looked at a couple of acoustics books. They still
don't explain the values of 105 and 120 beats per minute. Actually, the
difference tone between the notes middle C and G would vibrate at 130.37
cycles per second, and the one between D and A would be at 146.34 Hz.
(In both cases, the difference tone is almost exactly one octave below the
lower member of the perfect 5th.) However, this is all based on the
tempered scale at A@-----. This makes C-zero (the C below the lowest note
of the piano keyboard) vibrate at 16.352 cycles per second. There is
another version of this tuning, sometimes referred to as "scientific,"
where this same low C is assumed to vibrate at exactly 16 cycles. This
very small difference is multiplied as the pitches go higher and higher,
until for example, A in the treble clef is not at 440, but rather
428.192Hz. Physicists have adopted the so-called "scientific" pitch
because it is easier for them to deal with the whole-number values of C -
16, 32, 64, 128, 256, etc. It is possible that the difference tone values
you listed, if that is what they were, would be much closer to 105 and 120
at that pitch level than they would be at the pitch we normally use.
However, in each case, no matter how many vibrations, they would be per
*second*, not per *minute.*

What is further perplexing is that you found your information in a book
about the pipe organ. Organists have an entirely different viewpoint
about tuning and temperament than do wind instrumentalists. The author of
that book could have had any one of several "takes" on the question.

Still puzzled,

Ed Lacy
el2@-----.edu

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