Owner`s manual

16
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.