64edo: Difference between revisions

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== Theory ==

64edo is a [[~~The Riemann zeta function and tuning #Valley_edos|~~zeta valley edo]] and is very bad at approximating [[JI]] for its size. It has two options of [[3/2|fifth]] almost equally far from [[just]]. The sharp fifth from the 64b [[val]] is inherited from [[32edo]] and produces a hard [[superpythagorean]] scale, while the slightly more accurate flat fifth from the [[patent val]] is within the [[meantone]]/[[flattone]] range. However bizarrely, the flat fifth does not [[support]] meantone or flattone in its [[patent val]], and instead supports the obscure {{nowrap|7c & 12c}} (or {{nowrap|19 & 64}}) temperament (named [[User:Jerdle/The_Ocean|meso]]{{idio}} by [[User:Jerdle|Jerdle]]) which reaches [[5/4]] as a double-diminished fourth. In order to interpret it as flattone, the 64cd val must be used.

64edo is a [[zeta valley edo]] and is very bad at approximating [[JI]] for its size. It has two options of [[3/2|fifth]] almost equally far from [[just]]. The sharp fifth from the 64b [[val]] is inherited from [[32edo]] and produces a hard [[superpythagorean]] scale, while the slightly more accurate flat fifth from the [[patent val]] is within the [[meantone]]/[[flattone]] range. However bizarrely, the flat fifth does not [[support]] meantone or flattone in its [[patent val]], and instead supports the obscure {{nowrap|7c & 12c}} (or {{nowrap|19 & 64}}) temperament (named [[User:Jerdle/The_Ocean|meso]]{{idio}} by [[User:Jerdle|Jerdle]]) which reaches [[5/4]] as a double-diminished fourth. In order to interpret it as flattone, the 64cd val must be used.

Still, the patent val [[tempering out|tempers out]] [[648/625]] in the 5-limit and [[225/224]] in the 7-limit, plus [[66/65]], [[121/120]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&64 temperament.

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* [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025)

* [https://www.youtube.com/shorts/cwEY-eXjMFw ''Servant of Evil - Mothy (microtonal cover in 64edo)''] (2026)

* [https://www.youtube.com/shorts/X9JjH40xCnU ''Waltz in 64edo''] (2026)

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 == Theory ==
-edo is a [[The Riemann zeta function and tuning #Valley_edos|zeta valley edo]] and is very bad at approximating [[JI]] for its size. It has two options of [[3/2|fifth]] almost equally far from [[just]]. The sharp fifth from the 64b [[val]] is inherited from [[32edo]] and produces a hard [[superpythagorean]] scale, while the slightly more accurate flat fifth from the [[patent val]] is within the [[meantone]]/[[flattone]] range. However bizarrely, the flat fifth does not [[support]] meantone or flattone in its [[patent val]], and instead supports the obscure {{nowrap|7c &amp; 12c}} (or {{nowrap|19 &amp; 64}}) temperament (named [[User:Jerdle/The_Ocean|meso]]{{idio}} by [[User:Jerdle|Jerdle]]) which reaches [[5/4]] as a double-diminished fourth. In order to interpret it as flattone, the 64cd val must be used.
+edo is a [[zeta valley edo]] and is very bad at approximating [[JI]] for its size. It has two options of [[3/2|fifth]] almost equally far from [[just]]. The sharp fifth from the 64b [[val]] is inherited from [[32edo]] and produces a hard [[superpythagorean]] scale, while the slightly more accurate flat fifth from the [[patent val]] is within the [[meantone]]/[[flattone]] range. However bizarrely, the flat fifth does not [[support]] meantone or flattone in its [[patent val]], and instead supports the obscure {{nowrap|7c &amp; 12c}} (or {{nowrap|19 &amp; 64}}) temperament (named [[User:Jerdle/The_Ocean|meso]]{{idio}} by [[User:Jerdle|Jerdle]]) which reaches [[5/4]] as a double-diminished fourth. In order to interpret it as flattone, the 64cd val must be used.
 Still, the patent val [[tempering out|tempers out]] [[648/625]] in the 5-limit and [[225/224]] in the 7-limit, plus [[66/65]], [[121/120]] and [[441/440]] in the 11-limit and [[144/143]] in the 13-limit. It provides the optimal patent val in the 7-, 11- and 13-limits for the 16&amp;64 temperament.
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 * [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025)
 * [https://www.youtube.com/shorts/cwEY-eXjMFw ''Servant of Evil - Mothy (microtonal cover in 64edo)''] (2026)
+* [https://www.youtube.com/shorts/X9JjH40xCnU ''Waltz in 64edo''] (2026)