86edo: Difference between revisions

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86 = 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo~~|43~~]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.

== Theory ==

86 = 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 & 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.

86edo is closely related to the [[delta scale]], which is the equal division of the [[16/15|classic diatonic semitone]] into eight parts of 13.9664 cents each.

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=== Odd harmonics ===

=== Subsets and supersets ===

86edo contains [[2edo]] and [[43edo]] as subsets. [[258edo]], which triples it, is a notable tuning.

== Interval table ==

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 {{EDO intro|86}}
-= 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo|43]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 &amp; 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.
+== Theory ==
+= 2 × 43, and the [[patent val]] is a [[contorted]] [[43edo]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out [[245/242]], [[540/539]] and [[4000/3993]], and in the 13-limit [[144/143]], [[196/195]] and [[676/675]]. It provides the optimal patent val for the 13-limit 9 &amp; 86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.
 edo is closely related to the [[delta scale]], which is the equal division of the [[16/15|classic diatonic semitone]] into eight parts of 13.9664 cents each.
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 === Odd harmonics ===
 {{Harmonics in equal|86}}
+=== Subsets and supersets ===
+edo contains [[2edo]] and [[43edo]] as subsets. [[258edo]], which triples it, is a notable tuning.
 == Interval table ==
 {{Interval table}}