Re: Amplitude and pitch of sound waves

[Michael Edmiston <edmiston@BLUFFTON.EDU>]

I think Chuck Britton is mostly correct.  While the "well-tempered"
scale could mean "equal temper," it typically did not mean that.

Experiments with tempering had the purpose of trying to make every
scale "usable," but the various tempering techniques did not make every
scale sound the same.  So the well-tempered scale that Bach used
allowed the composer to get a slightly different sound (perhaps even
mood) by writing something in a particular key.

The equal-tempered scale has every scale equal.  When a piece is
transposed to a different key it is higher or lower, but otherwise
unaffected.  Various well-tempered scales were close to that, but not
exactly that.

As Chuck suggests, I have heard concerts (or portions of concerts) in
which period instruments and pieces were played with tuning appropriate
for the period.  These are quite interesting.  I'm never sure how well
I like it, being an equal-tempered piano player myself, but it is
indeed interesting.

BTW, I didn't want to have to write too much here, so I looked on the
WWW to see if anyone else wrote about well-tempered scales.  I found
this one:

http://www.mcn.net/~jimloy/scale.html

I do not know Jim Loy, have never been to his site before, and can't
even figure out for sure what his occupation is.  But his site is
interesting.  There is funny stuff there, wise stuff there, artistic
stuff there...  Anyway, I think his description of scales is correct.

Michael D. Edmiston, Ph.D.              Phone/voice-mail:       419-358-3270
Professor of Chemistry & Physics        FAX:                    419-358-3323
Chairman, Science Department            E-Mail                  edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817



-----Original Message-----
From:   John Mallinckrodt [SMTP:ajmallinckro@CSUPOMONA.EDU]
Sent:   Monday, November 29, 1999 5:59 PM
To:     PHYS-L@lists.nau.edu
Subject:        Re: Amplitude and pitch of sound waves

On Mon, 29 Nov 1999, Chuck Britton wrote:

> Have you ever experienced a 'well-tempered' piano. It is said to
> sound LOUSY, UNLESS it is playing in it's correct key.
>
> I seem to recall a Mozart (?) piece that was intended to be played on
> such a beast.

I think you are confusing a couple of things.  Here is my (hopefully
not
too fractured) history:

First the term "well-tempered" is archaic and refers (I think) to the
same
scale that we now call "equal tempered," one that exhibits *no*
preferred
key.

Bach wrote a number of works collected under the title "The
Well-Tempered
Clavier" to demonstrate the superiority of the tempered scale in
allowing
unrestrained modulation, something that was not aesthetically possible
using the "scale of just intonation" (based on low integer fraction
frequency ratios) that had been almost exclusively used up to that
time.

On the other hand, music that doesn't stray from its key sounds
remarkably
pure--some with a modern ear say sterile--when played in just
intonation.
Furthermore, different key signatures convey different moods--whence
the
appearance of "modes"--when played on a just intoned scale.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm