Well temperament

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Well temperament (also circular or circulating temperament) is a type of tempered tuning described in 20th-century music theory. The term is modelled on the German word wohltemperiert which appears in the title of J.S. Bach's famous composition, Well-Tempered Clavier. The phrase wohl temperiert also occurs in the works of Bach's predecessor, the organ tuner and music theorist Andreas Werckmeister.



"Well tempered" means that the twelve notes per octave of the standard keyboard are tuned in such a way that it is possible to play music in most major or minor keys and it will not sound perceptibly out of tune. In most tuning systems used before 1700, one or more intervals on the twelve-note keyboard were so far from any pure interval that they were unusable in harmony and were called a "wolf". Until about 1650 the most common keyboard temperament was quarter-comma meantone, in which the fifths were narrowed to the extent that they were just usable, and would thereby produce justly tuned thirds. The syntonic comma was distributed between four intervals, with most of the comma accommodated in the sol to mi diminished sixth, which expands to nearly a minor sixth. It is this interval that is usually called the "wolf", because it is so far out of consonance. The term "mean tone", the basis for meantone temperament, refers to the mathematical averaging of thirds, in which the middle note (for example the D between C and E) is in the "mean" position between the notes making the third. Another example of this is equal temperament (which is actually eleventh-comma meantone if seen in the perspective as to how to divide the comma between the fifths.)

The wolf was not a problem if music was played in a small number of keys (or to be more precise, transposed modes) with few accidentals, but it prevented players from transposing and modulating freely. Some instrument-makers sought to remedy the problem by introducing more than twelve notes per octave, producing enharmonic keyboards which could provide, for example, a D and an E with different pitches so that the thirds B–D and E–G could both be euphonious.

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