source file: mills2.txt
Date: Tue, 19 Sep 1995 05:03:47 -0700

Subject: Re: Was Bach Equal-tempered?

From: Paul Hahn <manynote@library.wustl.edu>

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."

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