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Ancient Temperaments
Pythagorean: Pythagoras (582-500 B.C.) was a brilliant Greek theorist and
mathematician. The Pythagorean temperament is characterized by pure fifths
and fourths. The Pythagorean theory founded a diatonic scale which served as
a model throughout the Middle Ages.
Mean-Tone: Mean-Tone temperament improves on the Pythagorean tuning by
slightly contracting each of the four fifths needed to generate a major third.
Major thirds and in-tune fifths are slightly narrow, and the differences between
the major and minor seconds are smoothed out. Many artists now prefer Mean-
Tone temperaments when performing 15th through 17th century repertoire.
J.S. Bach’s Well Tempered Clavier, written in 1722 and 1738-42, is a collection of 24 paired preludes
and fugues written in every major and minor key. The title refers to the use of a temperament in which all
keys are satisfactorily in tune, but not necessarily an absolutely equal temperament.
Well Temperaments
Kirnberger: Johann Philipp Kirnberger (1721-1783) was a German composer
and pupil of Bach from 1739-41. His temperament favored pure fifths, as in
the Pythagorean model, but performance was improved in many keys.
Werckmeister I and III: Andreas Werckmeister experimented with
temperaments in the latter part of the 17th century. In Werckmeister I he
further refined the Mean-Tone temperament. In Werckmeister III, four tones
are practically tuned identical to Equal Temperament (C, D#, F# and A).
Young I and II: Young Temperaments offer further refinements to the Mean-
Tone model, except with slightly higher pitched sharps.
Equal: Equal Temperament is the modern standard which utilizes a succession
of 12 semitones of equal size, allowing performance in all keys successfully.
The fifths are slightly narrowed and the upward thirds are considerably sharp,
but unlimited modulation from key to key is possible.
