71edo: Difference between revisions

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== 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.

71edo is a [[dual-fifth]] system, with the flat fifth (which is near the fifths of [[26edo]] and [[45edo]]) [[support]]ing [[flattone]] temperament with the 71c [[val]], and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]] with 71d. 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.

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=== 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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 == 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.
+edo is a [[dual-fifth]] system, with the flat fifth (which is near the fifths of [[26edo]] and [[45edo]]) [[support]]ing [[flattone]] temperament with the 71c [[val]], and the sharp fifth (which is near [[22edo]]'s fifth) supporting [[superpyth]] with 71d. 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.
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 === 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 ==