Re: Amplitude and pitch of sound waves

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

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