316edo: Difference between revisions
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While not highly accurate for its size, 316et is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out the [[parakleisma]], {{monzo| 8 14 -13 }}, the [[undim comma]], {{monzo| 41 -20 -4 }}, and the [[maquila comma]], {{monzo| 49 -6 -17 }} in the 5-limit; [[3136/3125]], [[4375/4374]], [[10976/10935]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[9801/9800]] and [[14641/14580]] in the 11-limit; and using the [[patent val]], [[1716/1715]], [[2080/2079]] and [[4096/4095]] in the 13-limit; notably supporting [[abigail]] and [[semiparakleismic]]. | While not highly accurate for its size, 316et is the point where a few important temperaments meet, and is distinctly [[consistent]] in the [[11-odd-limit]]. It tempers out the [[parakleisma]], {{monzo| 8 14 -13 }}, the [[undim comma]], {{monzo| 41 -20 -4 }}, and the [[maquila comma]], {{monzo| 49 -6 -17 }} in the 5-limit; [[3136/3125]], [[4375/4374]], [[10976/10935]] in the 7-limit; [[3025/3024]], [[3388/3375]], [[9801/9800]] and [[14641/14580]] in the 11-limit; and using the [[patent val]], [[1716/1715]], [[2080/2079]] and [[4096/4095]] in the 13-limit; notably supporting [[abigail]] and [[semiparakleismic]]. | ||
It provides the [[optimal patent val]] for the rank-4 temperament tempering out 3388/3375. | It provides the [[optimal patent val]] for the rank-4 temperament tempering out 3388/3375, and [[triglav]], which also tempers out 3025/3024. | ||
316 factors into 2<sup>2</sup> × 79, with subset edos 2, 4, 79, and 158. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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[[Category:Parakleismic]] | [[Category:Parakleismic]] | ||
[[Category:Semiparakleismic]] | [[Category:Semiparakleismic]] | ||
[[Category:Triglav]] | |||