31-limit: Difference between revisions

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[[311edo]] is the smallest edo that is [[consistent]] to the [[31-odd-limit]]. [[1600edo]] is the smallest edo that is [[distinctly consistent]] to the 31-odd-limit.

Edos with increasingly better approximations of the 31-limit ([[monotonicity limit]] ≥ 31 and decreasing [[TE error]]): {{EDOs| ~~99ef~~, 121ik, 130, 140, 149, 152fgj, 159, 183, 190g, 217, 243e, 270, 311, 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, 954hj, 1205g, 1289, 1308, 1395, 1578 }}, etc. For a more comprehensive list, see [[Sequence of equal temperaments by error]].

Edos with increasingly better approximations of the 31-limit ([[monotonicity limit]] ≥ 31 and decreasing [[TE error]]): {{EDOs| 99efk, 121ik, 130, 140, 149, 152fgj, 159, 183, 190g, 217, 243e, 270, 311, 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, 954hj, 1205g, 1289, 1308, 1395, 1578 }}, etc. For a more comprehensive list, see [[Sequence of equal temperaments by error]].

{{Note| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "~~99ef~~" means taking the second closest approximations of harmonics 11 and 13. }}

{{Note| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "99efk" means taking the second closest approximations of harmonics 11, 13, and 31. }}

== Music ==

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 [[311edo]] is the smallest edo that is [[consistent]] to the [[31-odd-limit]]. [[1600edo]] is the smallest edo that is [[distinctly consistent]] to the 31-odd-limit.
-Edos with increasingly better approximations of the 31-limit ([[monotonicity limit]] ≥ 31 and decreasing [[TE error]]): {{EDOs| 99ef, 121ik, 130, 140, 149, 152fgj, 159, 183, 190g, 217, 243e, 270, 311, 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, 954hj, 1205g, 1289, 1308, 1395, 1578 }}, etc. For a more comprehensive list, see [[Sequence of equal temperaments by error]].
+Edos with increasingly better approximations of the 31-limit ([[monotonicity limit]] ≥ 31 and decreasing [[TE error]]): {{EDOs| 99efk, 121ik, 130, 140, 149, 152fgj, 159, 183, 190g, 217, 243e, 270, 311, 388, 422, 525, 566gj, 571, 624jk, 639hj, 643ijk, 653, 692ik, 718, 742i, 863efgjk, 882, 908, 954hj, 1205g, 1289, 1308, 1395, 1578 }}, etc. For a more comprehensive list, see [[Sequence of equal temperaments by error]].
-{{Note| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "99ef" means taking the second closest approximations of harmonics 11 and 13. }}
+{{Note| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "99efk" means taking the second closest approximations of harmonics 11, 13, and 31. }}
 == Music ==