source file: mills2.txt
Date:         Thu, 21 Sep 1995 15:31:14 -0400

Subject:      Bach's keyboard temperament

From:         "j.s. mangsen" <smangsen@JULIAN.UWO.CA>

In the Early Music article from 1979, John Barnes develops a method
of counting the number of major thirds built on each note of the scale as
they occur in each of the WTC preludes, and then compares the resulting
distribution to the relative purity of those thirds if the instrument
were tuned in Werckmeister III.  It may sound naive, but he does go to
some trouble to assign "prominence values" to each of the thirds as
they occur in the music -- he uses a five-fold classification scheme,
based on several factors:  register, chordal context (if there are other
dissonances in the sonority, we won't be as disturbed by a particularly wide
third), duration.  He admits the resulting prominence value, which he will
use to give a weighted sum  of the total number of occurrences of
particular thirds in a passage, is somewhat subjective, and will be influenced
 by the performer's phrasing, tempo, etc.  His basic idea, to use his own
words, is  that "the avoidance of bad major thirds, sounded as such, in
music of a generally urbane character, appears to be the principal
constraint in the use of a circular temperament.  This should be an
influence on the composer which, in favourable circumstances, might
be recognizable as confirmation of the use of a circular temperament."

I can't see anything wrong with trying to make such a count, and to
correlate it with the character of the thirds in various temperaments.

But I would still not assume that WTC is conceived in one temperament, and
one only.  Tuning is an art, despite all the electronic boxes out there.
(also despite all the theorist's descriptions!)  Harpsichords can be tuned
for the particular piece one wants to play.  Also remember that at least
one of the preludes began life in a different key from the one in which
it ended up.  Moreover, unless you are convinced that the collection is a
cycle, always to be presented complete, there is no reason to assume that
only one temperament can be employed.

On the other hand, we all develop habits -- I tune Werckmeister III
often, I'm used to it, I may rely on it as my generic tuning for several
months at a time.  Maybe Bach did that too.  But if the concert is far
out on the flat side of things, I may not choose Werckmeister III.
If the concert has pieces far out on the flat and on the sharp side,
I may choose equal temperament.  I try not to program that way since I
enjoy suiting the tuning to the piece.

Sandra Mangsen
University of Western Ontario