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Equal temperament

Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). The best known example of such a system is twelve-tone equal temperament (sometimes abbreviated to 12-TET), which is nowadays used in most western music. Other equal temperaments do exist (some music has been written in 19-TET for example), but they are so rare that when people use the term equal temperament it is usually understood that they are talking about the twelve tone variety. The rest of this article concerns itself solely with 12-TET.

In an equal-tempered tuning, every note is 21/12 times the frequency of the note a semitone lower. Thus twelve equal-tempered semitones make exactly one octave, although all the intermediate intervals are slightly out of tune.

Equal temperament was designed to permit the playing of music in all keys with an equal amount of mis-tuning in each. True equal temperament was not available to musicians before about 1870 because scientific tuning and measurement was not available. Instead, they used approximations that emphasized the tuning of thirds or fifths in certain keys. There is some reason to believe that when composers and theoreticians of this era wrote of the "colors" of the keys, they described the subtly different dissonances of particular tuning methods.

Quite possibly, music from these eras will sound subtly different if played in historical tunings, rather than modern equal temperament.

The composer Terry Riley has been quoted as saying "Western music is fast because it's not in tune".

Ray Van De Walker, a wikipedian and amateur musician, has cut wind-chime bells in both pythagorean and equal-tempered tunings. He reports, "The pythagorean bells were cut on simple-fractional ratios. They were arguably in tune, because there were no beats to the pythagorean bells when they rang together. However, to my modern ear, and even my unsophisticated relatives, they sounded dramatically out of tune, like primitive non-western music."

The following is controversial: see the external link below:

However, equal temperament also made possible far more harmonically complex music, as it enabled musicians to move rapidly between keys without re-tuning: J. S. Bach wrote The Well-Tempered Clavier to demonstrate the musical possibilities of well temperament, a system similar in intent to just intonation, but one which did not create an octave of 12 identical semitones.

Interesting article in that link. Perhaps we should invite the author to explain it all here.

The interval 1:21/1200 is also known as a cent: one hundredth of an equal-tempered semitone.

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