Circulating temperaments (was Re: (no subject))

On Thu, 4 Mar 1999, Ara John Sarkissian wrote:
> I just got Enid Kahan's recording of Beethoven sonatas in the "Prinz"
> and Thomas Young's 1799 tuning (so the booklet tells me...). Could
> anyone suggest where I could get information about the construction of
> these particular tunings besides Barbour's "Tuning and Temeperament" ?

They're pretty popular tunings. Owen Jorgensen covers them both in his
Big Red Book, _Tuning_ (subtitled almost as lengthily as an 18th-century
novel), and they turn up lots of other places as well. Here's a short
breakdown:

Prinz, more commonly known as Kirnberger III, is tuned as follows: the
four fifths C-G-D-A-E are each tempered narrow by a quarter of a
syntonic comma; the fifth B-F# tempered narrow by a schisma; all other
fifths just.

Young goes like this: the six fifths C-G-D-A-E-B-F# each tempered narrow
by a sixth of a Pythagorean comma, the other six just. This is just
Vallotti's temperament transposed up a fifth. Vallotti's very easy to
remember, in that all the fifths which are tempered are between two
white keys.

HTH.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Well, so far, every time I break he runs out.
-\-\-- o But he's gotta slip up sometime . . . "

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