Was Bach Equal-tempered?

On 18 Sep 1995, Dick Wisan wrote:
> In article <199509180332.XAA07038@svcs1.digex.net>, candlerg@CPCUG.ORG
> (George Candler) writes:
> > ...I believe he was
> > "extolling the virtues" of well temperament with its different "flavors" for
> > each key."
>
> How similar were those differences from temperament to temperament? Surely,
> they were different for ill-tempered tunings, but perhaps you never used
> one of those except for the keys it wasn't ill for. But well-but-not-
> equal temperament tunings must also have given the same keys different
> flavors. Or would the criterion for well-temperedness be precisely that
> these differences would be trivial?
>
> What bothers me --and this goes beyond WTC-- is this: Since composers
> had no control over the tuning of anybody else's instrument, how could
> they have counted on the flavor of a key?

Actually, virtually all the circulating or "well" temperaments I've
worked with have some fairly significant characteristics in common:

1. The best available major third is always between C and E, or, if
there are more than one "best" third, C-E is invariably one of them.

2. The _worst_ available major third (or one of them if there are
more than one) is directly opposite C-E on the circle of fifths, or
nearly so; usually F#-A#/Bb or C#/Db-F.

3. Between these two extrema, the quality of the thirds progresses
without backtracking; i.e. on the sharp side, any particular major
triad will have as good a third, or better, than its dominant, and
on the flat side, the reverse is true.

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "Foul? What the hell for?"
-\-\-- o "Because you are chalking your cue with the 3-ball."

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Tue, 19 Sep 1995 14:33 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id FAA24334; Tue, 19 Sep 1995 05:33:46 -0700
Date: Tue, 19 Sep 1995 05:33:46 -0700
Message-Id: <00996A253C7F6F88.1A7C@ezh.nl>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu