BACH'S TUNING

Manuel recently posted from the harpsichord list several points of
view on Bach's Tuning, one of which commented on Prof. Rudolf Rasch's
opinion that J.S. Bach composed in equal temperament.

I will quote part of my article *Bach's Tuning* from PITCH I:2 pp. 31-32
in reference to Rudolf Rasch's position on the equal temperament factor
and Bach, a position with which I disagree:

In a recently published essay, Rudolf Rasch of the Netherlands asks
the question "Does 'Well-Tempered' mean 'Equal-Temperament'?" Rasch
defines qualification of a tunng in which all tonalities can be
performed. Rasch believes, however, that Bach's *The Well-Tempered
Clavier* was conceived in equal temperament. He attributes this to
Werckmeister's later works which explicitly describe equal temperament.
Werckmeister wrote in his *Hypomnemata musica* of 1697 that:
Who, however, asks for a temperament in which all consonant
intervals are equal, must take care that all fifths beat 1/12th of a
comma downward, so that all major thirds beat 2/3 of a comma and
the minor third 3/4 of a comma... So far I have not been able to
agree with this view, because I prefer to keep the diatonic notes
which are used most often with the diatonic tonalities, as pure as
possible in tuning.
Werckmeister clearly does not fully support equal temperament at this
point in his life. Yet in Werckmeister's *Harmonologie musica* of 1702,
Rasch has determined that there is "a direct pleading for equal
temperament, based on the possibilities of unlimited transportation and
enharmonic changes." One problem with this interpretation is that all
circular keyboard tunings are, by definition, capable of unlimited
transposition and enharmonic changes. In this sense, equal temperament
fits well within the larger category of well-tempered tunings.
Werckmeister's last opus *Musicalische Paradoxal-Discourse* of 1707
was published posthumously. Based on Rasch's translated excerpts, it
would appear to the point of offering an apology "for his earlier
propaganda for unequal temperaments.
Werckmeister's attitude at the end of his life is summarized in a
book published posthumously (1707) where in effect he apologized
for not having included equal temperament among the various
circulating temperaments for which he had earlier published a
monochord diagram. (The incompetent engraver, he said, had
complained about dividing the narrow space of a comma into 12 parts.)
He quite approved of equal temperament, yet was willing "to have the
diatonic 3rds left somewhat purer than the other, less often used
ones," a procedure for which he had expressed clear preference in his
earlier writings.
What can be deduced for certain is that Werckmeister wrote about equal
temperament usage with increasing frequency in his later years. This
need not be interpreted as a dogmatic insistence on equal temperament,
nor as a preference, since Werckmeister was merely cataloging.

Manuel, please forward the above to the harpsichord list. Thank you.



Johnny Reinhard
Director
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com


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