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 unnamed 7c & 12c (or 19 & 64) temperament 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 [[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 unnamed 7c & 12c (or 19 & 64) temperament 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 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.

Still, the patent val [[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.

64be val is a tuning for the beatles temperament and for the rank-3 temperaments heimlaug and vili in the 17-limit. 64bccc tunes dichotic, although that is an exotemperament. 64cdf is a tuning for vibhu.

64be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].

=== Odd harmonics ===

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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 unnamed 7c & 12c (or 19 & 64) temperament 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 [[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 unnamed 7c & 12c (or 19 & 64) temperament 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 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.
+Still, the patent val [[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.
-be val is a tuning for the beatles temperament and for the rank-3 temperaments heimlaug and vili in the 17-limit. 64bccc tunes dichotic, although that is an exotemperament. 64cdf is a tuning for vibhu.
+be val is a tuning for the [[beatles]] temperament and for the [[rank-3]] temperaments [[heimlaug]] and [[vili]] in the 17-limit. 64bccc tunes [[dichotic]], although that is an [[exotemperament]]. 64cdf is a tuning for [[vibhu]].
 === Odd harmonics ===