equal temperamentArticle Free Pass equal temperament, in music,
a tuning system in which the octave is divided into 12 semitones
of equal size. Because it enables keyboard instruments to play
in all keys with minimal flaws in intonation, equal temperament
replaced earlier tuning systems that were based on acoustically
pure intervals, that is, intervals that occur naturally in the
overtone series. For a more technical explanation of overtones,
see sound: Standing waves. The search for satisfactory tuning
systems parallels the development of the Western tonal system,
with its reliance on enharmonic equivalence (for example, having
the notes F♯ and G♭ sound the same) and multiple major and minor
keys. In 1581 the Florentine music theorist Vincenzo Galilei
(father of the astronomer Galileo) proposed a system of equal
intervals for tuning the lute. The Chinese prince and
musicologist Zhu Zaiyu in 1596 and the French philosopher and
mathematician Marin Mersenne in 1636, among others, wrote of
such a system. The ide