Re: Amplitude and pitch of sound waves

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

Thanks to Michael Edmiston, I stand corrected on the issue of "well"
versus "equal" temperament and the related issues of the tone coloring of
different keys.  I looked at the relevant link that Michael provided but
was frustrated by its lack of a specific example of a well-tempered scale.
Accordingly I did my own brief search (which I should have done in the
first place!) and found an exhaustive piece by Margo Schulter entitled
"Pythagorean Tuning and Medieval Polyphony" at

   http://www.medieval.org/emfaq/harmony/pyth.html

In particular, I found that a section entitled "Well-temperaments, triadic
and trinic"  at http://www.medieval.org/emfaq/harmony/pyth5.html#5 made a
lot of cents.  (Sorry!)

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

On Tue, 30 Nov 1999, Michael Edmiston wrote:

> 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.