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Encyclopedia of Microtonal Music Theory

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well temperament

[Joe Monzo, with contributions from Graham Breed]

A system of tuning in which the intervals between degrees are unequal, and in which the members of various chords approximate just ratios to various degrees of accuracy, depending on the "root" of the chord.

This produces a sound which gives a different "color" or affect to the different chords and keys.

The well-temperaments were developed specifically with keyboards in mind, so they are always closed systems, generally limited to 12 different pitches (as opposed to systems like just-intonation or meantone, which are "open" or theoretically infinite). Well-temperaments evolved mostly during the 1700s, out of the meantones that had been the primary tunings in use during the 1600s. Being closed systems, it was necessary to adjust certain pitches so that all keys would be useable, and thus that there would be no "wolves".

Modern research has reached somewhat of a consensus that J. S. Bach's infamous Well-Tempered Klavier was written for keyboards tuned in a well-temperament (hence the name of the work and the modern designation for the family of tunings), thus exploiting the different characters of the 24 major and minor keys in which the pieces are written, in contrast with the formerly-held opinion that this work demonstrated the "usefulness" of 12-edo. A unique well-tempered tuning has been devised by Herbert Anton Kellner, in which he presents speculative evidence supporting his contention that it was the keyboard tuning used by Bach.

A well-temperament is generally named after the theorist who first wrote about it. Three of the most famous are by Werckmeister, Valotti & Young, and Kirnberger.

Some theorists are of the opinion that equal temperaments should be considered as a special case of well temperaments.

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