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
of24
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 Tern
peram
ents
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.
21
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