111ed12: Difference between revisions

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== Theory ==

111ed12 is nearly identical to [[31edo]], but with the [[12/1|12th]] [[harmonic]] rather than the [[2/1|octave]] being just. The octave is about 1.45 cents stretched compared to ~~31edo~~. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1|5th]] and [[7/1|7th harmonic]]s for improved [[3/1|3rd]] and [[11/1|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1|23rd harmonic]], which is now only 2.4 cents flat of just.

111ed12 is nearly identical to [[31edo]], but with the [[12/1|12th]] [[harmonic]] rather than the [[2/1|octave]] being just. The octave is about 1.45 cents stretched compared to just, or to any edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1|5th]] and [[7/1|7th harmonic]]s for improved [[3/1|3rd]] and [[11/1|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1|23rd harmonic]], which is now only 2.4 cents flat of just.

=== Harmonics ===

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 == Theory ==
-ed12 is nearly identical to [[31edo]], but with the [[12/1|12th]] [[harmonic]] rather than the [[2/1|octave]] being just. The octave is about 1.45 cents stretched compared to 31edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1|5th]] and [[7/1|7th harmonic]]s for improved [[3/1|3rd]] and [[11/1|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1|23rd harmonic]], which is now only 2.4 cents flat of just.
+ed12 is nearly identical to [[31edo]], but with the [[12/1|12th]] [[harmonic]] rather than the [[2/1|octave]] being just. The octave is about 1.45 cents stretched compared to just, or to any edo. Like 31edo, 111ed12 is [[consistent]] through the [[integer limit|12-integer-limit]], and like [[80ed6]], it optimizes for the [[11-limit]] by trading the accuracy of the [[5/1|5th]] and [[7/1|7th harmonic]]s for improved [[3/1|3rd]] and [[11/1|11th harmonics]]. The stretch is quite mild, but still considerable: the [[11/1|11th harmonic]] is only 4.4 cents flat of just (in comparison, 31edo's 11th harmonic is 9.4 cents flat). Also improved is the [[23/1|23rd harmonic]], which is now only 2.4 cents flat of just.
 === Harmonics ===