Temperament is a system of tuning the musical scale in which “pure,” acoustically ideal intervals are deliberately altered a little (narrowed or widened) in order to overcome the natural mathematical contradictions of the scale and make it possible to play freely in any key.
The most widespread today is equal temperament, by which the octave is divided into twelve absolutely identical semitones. This is an ingenious compromise: no interval (except the octave) sounds perfectly pure, but all keys become equal, and the composer can modulate freely from one to another. The idea of playing freely in all keys is championed by Johann Sebastian Bach's famous cycle “The Well-Tempered Clavier” (which modern scholars believe was intended for an unequal well temperament rather than equal temperament) — 24 preludes and fugues in all the major and minor keys. Temperament made possible the entire subsequent harmonic language of European music.
