718edo: Difference between revisions
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718edo is [[consistency|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1|5]], [[13/1|13]], [[17/1|17]] and [[31/1|31]]. | 718edo is [[consistency|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1|5]], [[13/1|13]], [[17/1|17]] and [[31/1|31]]. | ||
As does 359et, 718et [[Tempering out|tempers out]] the 359-comma in the 3-limit, rendering a very accurate | As does 359et, 718et [[Tempering out|tempers out]] the 359-comma in the 3-limit, rendering a very accurate [[harmonic]] [[3/1|3]]. In the 5-limit it [[tempering out|tempers out]] the gammic comma, {{monzo| -29 -11 20 }}, and the [[monzisma]], {{monzo| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It [[support]]s [[gammic]], [[monzismic]] and [[abigail]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 718 factors into | Since 718 factors into {{factorization|718}}, 718edo contains [[2edo]] and [[359edo]] as subsets. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
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