31-limit: Difference between revisions
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* The [[31-odd-limit|31-]], [[33-odd-limit|33-]], and [[35-odd-limit]]; | * The [[31-odd-limit|31-]], [[33-odd-limit|33-]], and [[35-odd-limit]]; | ||
* Mode 16, 17, and 18 of the harmonic or subharmonic series. | * Mode 16, 17, and 18 of the harmonic or subharmonic series. | ||
== Edo approximations == | |||
[[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]]. | |||
{{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. }} | |||
== Music == | == Music == | ||
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* [[No-twos 31-limit]] | * [[No-twos 31-limit]] | ||
* [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals | * [[User:Contribution/31-limit]] – Includes an enormous table of 31-limit intervals | ||
[[Category:31-limit| ]] <!-- main article --> | [[Category:31-limit| ]] <!-- main article --> | ||
[[Category:Listen]] | [[Category:Listen]] | ||