111ed12: Difference between revisions
→Theory: expand on its tuning characteristics |
→Theory: "to any edo" isn't best here because you're probably using it as stretched 31edo |
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== Theory == | == 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 | 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. 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 === | === Harmonics === | ||
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* [[80ed6]] – relative ed6 | * [[80ed6]] – relative ed6 | ||
* [[87ed7]] – relative ed7 | * [[87ed7]] – relative ed7 | ||
* [[107ed11]] – relative ed11 | |||
* [[138ed22]] – relative ed22 | |||
* [[204ed96]] – close to the zeta-optimized tuning for 31edo | |||
* [[39cET]] | * [[39cET]] | ||
[[Category:31edo]] | |||