Barbour and Tuning cont.

Paul: Interesting, what formula did you use to approximate Barbour's RVF
tuning?

Ed: Barbour liked the 1/6-comma tuning under some circumstances. In the
"Meantone Temperament in Theory and Practice" record he and Fritz A.
Kuttner put out in the 1950's (Musurgia Records, Series A, No.2),
Barbour says of the recorded example of Bach's Prelude #6 in D-minor
from Book 1 of the Well-Tempered Clavier (in Silbermann's 1/6-comma
tuning (G#-Eb)):

"In fact, this Prelude sounds magnificent in the 1/6 comma tuning where
it is enhanced by a poignancy and beauty of interval coloration that
cannot easily be duplicated in equal temperament. The conclusion is
fully justified that equal temperament need not always be superior to
Silbermann's meantone system. It was for good reasons that this tuning
enjoyed popularity in the middle of the eighteenth century."

I might add tht most of the examples in the three recordings that were
released on the Musurgia series appear to have been chosen to highlight
the problems rather than the virtues of every tuning but 12-tet. He is
less effusive about 1/4 comma, even when he has chosen appropriate
examples and seems unwilling to admit that it may be anything other
than effective or smooth.

--John

John Chalmers wrote:

>Paul: Interesting, what formula did you use to approximate Barbour's RVF
>tuning?

John -- I just repeated the Barbour tuning as just reported by you, and my
tuning is just as I described before, but with a larger multiplier on the
cosine term (i. e. a bigger clock face).

>John Chalmers wrote:
>
>>Paul: Interesting, what formula did you use to approximate Barbour's RVF
>>tuning?
>
I wrote:

>John -- I just repeated the Barbour tuning as just reported by you, and my
>tuning is just as I described before, but with a larger multiplier on the
>cosine term (i. e. a bigger clock face).
>
Duh, of course you knew that. The formula for my tuning is:

fifthsize = 700 - 2.4752*cos(angle on circle of fifths)