12edo: Difference between revisions

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It is the smallest number of equal divisions of the octave ([[edo]]) which can seriously claim to represent [[5-limit]] harmony, and because it represents a [[meantone]] temperament (specifically {{frac|1|12}} Pythagorean comma meantone, or approximately {{frac|1|11}} syntonic comma or full schisma meantone).

It divides the octave into twelve equal parts, each of exactly 100 [[cent]]s each unless [[stretched and compressed tuning|octave stretching or compression]] is employed. It has a [[3/2|fifth]] which is quite accurate at 700 cents, two cents flat of just. It has a [[5/4|major third]] which is 13.7 cents sharp, which, while reasonable for its size, is unsatisfactory for some. The [[6/5|minor third]] is flat by even more, 15.6 cents.

It divides the octave into twelve equal parts, each of exactly 100 [[cent]]s each unless [[stretched and compressed tuning|octave stretching or compression]] is employed. It has a [[3/2|fifth]] which is quite accurate at 700 cents, two cents flat of just. It has a [[5/4|major third]] which is 13.7 cents sharp of 5/4, which, while reasonable for its size, is unsatisfactory for some. The [[6/5|minor third]] is flat of 6/5 by even more, 15.6 cents.

Historically, 12edo became dominant primarily due to practical considerations for keyboard instruments and its ability to handle modulation across all keys with reasonable intonation.

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 It is the smallest number of equal divisions of the octave ([[edo]]) which can seriously claim to represent [[5-limit]] harmony, and because it represents a [[meantone]] temperament (specifically {{frac|1|12}} Pythagorean comma meantone, or approximately {{frac|1|11}} syntonic comma or full schisma meantone).
-It divides the octave into twelve equal parts, each of exactly 100 [[cent]]s each unless [[stretched and compressed tuning|octave stretching or compression]] is employed. It has a [[3/2|fifth]] which is quite accurate at 700 cents, two cents flat of just. It has a [[5/4|major third]] which is 13.7 cents sharp, which, while reasonable for its size, is unsatisfactory for some. The [[6/5|minor third]] is flat by even more, 15.6 cents.
+It divides the octave into twelve equal parts, each of exactly 100 [[cent]]s each unless [[stretched and compressed tuning|octave stretching or compression]] is employed. It has a [[3/2|fifth]] which is quite accurate at 700 cents, two cents flat of just. It has a [[5/4|major third]] which is 13.7 cents sharp of 5/4, which, while reasonable for its size, is unsatisfactory for some. The [[6/5|minor third]] is flat of 6/5 by even more, 15.6 cents.
 Historically, 12edo became dominant primarily due to practical considerations for keyboard instruments and its ability to handle modulation across all keys with reasonable intonation.