227edo: Difference between revisions

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~~'''227EDO''' is the [[~~EDO|~~equal division of the octave]] into~~ 227 ~~parts of 5.2863 [[cent]]s each.~~

It tempers out 15625/15552 (kleisma) and |61 -37 -1~~>~~ in the 5-limit; 5120/5103, 65625/65536, and 117649/116640 in the 7-limit, so that it [[support]]s [[~~Kleismic_family#Countercata|~~countercata ~~temperament~~]]. In the 11-limit, it tempers out 385/384, 2200/2187, 3388/3375, and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out 325/324, 352/351, 625/624, and 847/845.

The equal temperament tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], 2200/2187, 3388/3375, and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], and [[847/845]].

~~227EDO~~ is accurate for the 13th harmonic, as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]].

227edo is accurate for the 13th harmonic, as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]].

~~227EDO~~ is the 49th prime ~~EDO~~.

=== Prime harmonics ===

=== Subsets and supersets ===

227edo is the 49th [[prime edo]].

~~{{Harmonics in equal|227}}~~

~~[[Category:Equal divisions of the octave|###]] ~~

[[Category:Countercata]]

~~[[Category:Prime EDO]]~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''227EDO''' is the [[EDO|equal division of the octave]] into 227 parts of 5.2863 [[cent]]s each.
+{{EDO intro|227}}
-It tempers out 15625/15552 (kleisma) and |61 -37 -1&gt; in the 5-limit; 5120/5103, 65625/65536, and 117649/116640 in the 7-limit, so that it [[support]]s [[Kleismic_family#Countercata|countercata temperament]]. In the 11-limit, it tempers out 385/384, 2200/2187, 3388/3375, and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out 325/324, 352/351, 625/624, and 847/845.
+The equal temperament tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], 2200/2187, 3388/3375, and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], and [[847/845]].
-EDO is accurate for the 13th harmonic, as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]].
+edo is accurate for the 13th harmonic, as the denominator of a convergent to log<sub>2</sub>13, after [[10edo|10]] and before [[5231edo|5231]].
-EDO is the 49th prime EDO.
+=== Prime harmonics ===
+{{Harmonics in equal|227}}
+=== Subsets and supersets ===
+edo is the 49th [[prime edo]].
-{{Harmonics in equal|227}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Countercata]]
-[[Category:Prime EDO]]