Well Temperament

Joseph L Monzo writes:
>The following table is the adjustment from equal temperament (in cents)
>used by Johnny Reinhard for the Werckmeister III temperament used in last
>week's performance by the Soho Baroque Opera.

C = +12
C#/Db = +2
D = +4
D#/Eb = +6
E = +2
F = +10
F#/Gb = 0
G = +8
G#/Ab = +4
A = 0
Bb/A# = +8
B = +4
C = +12

This is essentially the temperament that Dr. Al Sanderson published for
his manual and is labeled the Werckmeister III, Correct Temperament no. 1.
( Al is the inventor of the Sanderson Accu-tuner{SAT}, which has been a
tremendous help in restoration of the temperaments for piano techs).
Since the SAT has a resolution of .1 cent, Al's numbers are slightly more
specific, though I don't think the difference is audible, I will list them
below.
C = +11.7
C#= +2.0
D = +3.9
D# = +5.9
E = +2.0
F = +9.8
F# = 0.0
G = +7.8
G# = +3.9
A = 0.0
A# = +7.8
B = +3.9

As far as the most widely used temperament in the Baroque and Classical
era, that is hard to say. Experience says that the easiest one to tune was
probably the most common. The Kirnberger III is very close to the the Prinz,
or Aron-Neidhardt, which, according to Jorgensen, was quite close to the
temperament of L'Alembert, published in 1752 in the "Elemens De Musique".
The Prinz combines the two longest lasting practises of keyboards in one
tuning. i.e. the ancient Pythagorean fifths in the higher keys, and the pure
thirds and tempered fifths of the Pietro Aaron 1/4 comma meantone in the
simpler keys. I personally love this tuning. It has three thirds at the top
that are 21.5 cents wide.
The differences among the well temperaments, in practise, were possibly
less than we might recognize, as most tuning was done to achieve a goal of
progressively changing characters of the keys. In this respect, Valotti
probably was the ideal, though Thomas Young's alteration of Valotti's placed
the purest key at "C", instead of Valotti's "F". This distinction is lost on
us today, but perhaps 18th century ears accustomed to the tonal palette,
would have gone dancing with pin-headed angels over the difference.
Jorgensen does point out that there has never been any improvement in
temperament, as one facet is improved, ( say modulation), another is lost, (
key contrast).
Whereas the Young offered a very predictable rise in the speed of the
thirds as one modulated around the circle of fifths, the Prinz offered more
pure keys, and greater contrast. It is hard to say that one is better or
worse, and given that there was raging controversy over the various
temperaments of the time, it is also hard to say what was the most common
tuning.
Regards to all,
Ed Foote
Precision Piano Works
Nashville, Tn.