71edo: Difference between revisions

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71edo ~~is the 20th [[prime EDO]]. It~~ is a [[dual-fifth]] system, with the flat fifth (which is near the fifths of [[26edo]] and [[45edo]]) ~~supporting~~ [[flattone]] temperament, and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth~~]] and [[archy~~]]. Unlike small dual-fifth systems such as [[18edo]], both fifths are close approximations of 3/2.

== Theory ==

71edo is a [[dual-fifth]] system, with the flat fifth (which is near the fifths of [[26edo]] and [[45edo]]) [[support]]ing [[flattone]] temperament, and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]]. Unlike small dual-fifth systems such as [[18edo]], both fifths are close approximations of 3/2.

Using the [[patent val]], the equal temperament [[tempering out|tempers out]] 20480/19683 and [[393216/390625]] in the [[5-limit]], [[875/864]], [[1029/1024]] and [[4000/3969]] in the [[7-limit]], [[100/99]] and [[245/242]] in the [[11-limit]], and [[91/90]] in the [[13-limit]]. In the 13-limit it supplies the optimal [[patent val]] for the 29 & 71 and 34 & 37 temperaments.

== ~~Theory~~ ==

=== Odd harmonics ===

~~It tempers out 20480/19683~~ and ~~[[393216/390625]] in~~ the [[~~5-limit~~]], ~~875/864, 4000/3969 and 1029/1024 in the~~ [[~~7-limit~~]]~~, 245/242~~ and [[~~100/99~~]] ~~in the~~ [[~~11-limit~~]], ~~and 91/90 in the [[13-limit]]. In the 13-limit~~ it ~~supplies the optimal [[patent val]]~~ for the ~~29&71 and 34&37 temperaments~~.

=== Subsets and supersets ===

71edo is the 20th [[prime edo]], following [[67edo]] and before [[73edo]]. [[142edo]], which doubles it, provides correction for the harmonic 3.

== Intervals ==

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 {{EDO intro|71}}
-edo is the 20th [[prime EDO]]. It is a [[dual-fifth]] system, with the flat fifth (which is near the fifths of [[26edo]] and [[45edo]]) supporting [[flattone]] temperament, and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]] and [[archy]]. Unlike small dual-fifth systems such as [[18edo]], both fifths are close approximations of 3/2.
+== Theory ==
+edo is a [[dual-fifth]] system, with the flat fifth (which is near the fifths of [[26edo]] and [[45edo]]) [[support]]ing [[flattone]] temperament, and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]]. Unlike small dual-fifth systems such as [[18edo]], both fifths are close approximations of 3/2.
+Using the [[patent val]], the equal temperament [[tempering out|tempers out]] 20480/19683 and [[393216/390625]] in the [[5-limit]], [[875/864]], [[1029/1024]] and [[4000/3969]] in the [[7-limit]], [[100/99]] and [[245/242]] in the [[11-limit]], and [[91/90]] in the [[13-limit]]. In the 13-limit it supplies the optimal [[patent val]] for the 29 &amp; 71 and 34 &amp; 37 temperaments.
-== Theory ==
+=== Odd harmonics ===
 {{Harmonics in equal|71}}
-It tempers out 20480/19683 and [[393216/390625]] in the [[5-limit]], 875/864, 4000/3969 and 1029/1024 in the [[7-limit]], 245/242 and [[100/99]] in the [[11-limit]], and 91/90 in the [[13-limit]]. In the 13-limit it supplies the optimal [[patent val]] for the 29&amp;71 and 34&amp;37 temperaments.
+=== Subsets and supersets ===
+edo is the 20th [[prime edo]], following [[67edo]] and before [[73edo]]. [[142edo]], which doubles it, provides correction for the harmonic 3.
 == Intervals ==