64edo: Difference between revisions

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== Theory ==

64edo has two options of fifth equally far from just. The sharp fifth is inherited from 32edo and produces a hard superpythagorean scale, while the flat fifth is within the meantone/flattone range, ~~supporting~~ flattone temperament.

64edo has two options of fifth almost equally far from just. The sharp fifth is inherited from 32edo and produces a hard superpythagorean scale, while the slightly more accurate flat fifth 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~~, which would perhaps be of more interest if it was lower in badness~~.

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.

64edo is a [[zeta valley]] EDO and is very bad at approximating JI for its size.

=== Odd harmonics ===

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 == Theory ==
-edo has two options of fifth equally far from just. The sharp fifth is inherited from 32edo and produces a hard superpythagorean scale, while the flat fifth is within the meantone/flattone range, supporting flattone temperament.
+edo has two options of fifth almost equally far from just. The sharp fifth is inherited from 32edo and produces a hard superpythagorean scale, while the slightly more accurate flat fifth 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, which would perhaps be of more interest if it was lower in badness.
+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.
+edo is a [[zeta valley]] EDO and is very bad at approximating JI for its size.
 === Odd harmonics ===
 {{Harmonics in equal|64}}