64edo: Difference between revisions

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~~'''64 equal divisions of the octave''' ('''64edo''') is the tuning system that divides the octave into 64 equal parts of exactly 18.75~~{{~~cent~~}} ~~each.~~

== 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.

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.

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 ===

~~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~~.

=== Subsets and supersets ===

64edo is the 6th power of two edo, and it has subset edos 1, 2, 4, 8, 16, 32.

== Intervals ==

{| class="wikitable center-all right-2"

{| class="wikitable mw-collapsible mw-collapsed center-all right-2"

|-

![[Degree|#]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''64 equal divisions of the octave''' ('''64edo''') is the tuning system that divides the octave into 64 equal parts of exactly 18.75{{cent}} each.
+{{EDO intro|64}}
 == 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.
+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.
+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 ===
 {{Harmonics in equal|64}}
-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.
+=== Subsets and supersets ===
+edo is the 6th power of two edo, and it has subset edos 1, 2, 4, 8, 16, 32.
 == Intervals ==
-{| class="wikitable center-all right-2"
+{| class="wikitable mw-collapsible mw-collapsed center-all right-2"
 |-
 ![[Degree|#]]