Musical temperament

In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. "Tempering is the process of altering the size of an interval by making it narrower or wider than pure. A temperament is any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate pure octaves and produce certain sizes of major thirds." Temperament is especially important for keyboard instruments, which typically allow a player to play only the pitches assigned to the various keys, and lack any way to alter pitch of a note in performance. Historically, the use of just intonation, Pythagorean tuning and meantone temperament meant that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys.

The development of well temperament allowed fixed-pitch instruments to play reasonably well in all of the keys. The famous Well-Tempered Clavier by Johann Sebastian Bach takes full advantage of this breakthrough, with pieces written in all 24 major and minor keys. However, while unpleasant intervals (such as the wolf interval) were avoided, the sizes of intervals were still not consistent between keys, and so each key still had its own character. This variation led in the 18th century to an increase in the use of equal temperament, in which the frequency ratio between each pair of adjacent notes on the keyboard was made equal, allowing music to be transposed between keys without changing the relationship between notes.

Temperament, in music, the accommodation or adjustment of the imperfect sounds by transferring a part of their defects to the more perfect ones, in order to remedy, in some degree, the false intervals of those instruments, the sounds of which are fixed; as the organ, harpsichord, piano-forte, etc.
Temperament is what the Italians call participatione, or system temperato, because it is founded on temperature; that is, on the diminution of some intervals and augmentation of others, by which it partakes of the diatonic and chromatic systems.

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