These well temperaments share certain characteristics.
They all minimize the size of the
major thirds in the vicinity of C on the
circle of fifths, and keep the most extreme M3s to
exactly or just under the
"maximum" of 21.51 cents. These widest thirds are called
Pythagorean
Thirds because they are formed by the Pythagorean rule of tuning a series of
four perfect fifths. (For example, the sequence C-F-Bb-Eb-Ab is tuned with
perfect fifths,
resulting in a major third Ab-C that measures 21.51 cents wide
of just.
This principle can be observed exactly in Werckmeister, Kirnberger, and Prinz,
and
a fifth lower in Vallotti and Young.)
Werckmeister showed that excellent well-temperaments were possible with about
eight pure fifths. This version is 1/4 ditonic comma well, with tempered fifths on C, G, D and B.
Kirnberger: German theorist, composer, student of Bach.
C Major, G Major, E minor and B minor triads were all completely just,
achieved by compromising the D and A fifths.
Contains some of the purest harmony acoustically possible.
Vallotti: The fifths on the white keys CDEFGA are each one-sixth ditonic comma narrow.
The remaining six fifths are pure. A "very conservative" temperament.
Young: Jorgensen lavishes this praise on the Young
temperament: "Notice the complete symmetry…
the even changes in the sizes of thirds…the most perfect idealized form of well temperament
ever published…a summation of the best ideals of well temperament...the greatest perfection possible."
Prinz: The major third CE is just. This assured that the Prinz contains as much color-contrast as the original Kirnberger.