Temperaments

are the various alterations of strict tuning necessary for practical purposes. Equal temperament, now in general use, involves the division of the octave into twelve equal semitones, a procedure that necessitates some modification of intervals from their true form, according to the ratios of physics. Equal temperament, exemplified in Johann Sebastian Bach's 48 preludes and fugues for the well-tempered clavier, won gradual acceptance in the 18th century, replacing earlier systems of tuning. It has been plausibly suggested that the system of equal temperament was borrowed from China, where its mathematical basis was published towards the end of the 16th century.