333edo: Difference between revisions

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The ~~''333~~ equal temperament~~'' divides the octave into 333 equal parts of 3.604 cents each. It~~ tempers out 15625/15552 in the 5-limit and 5120/~~5013~~ in the 7-limit, so it ~~supports~~ [[~~Kleismic_family#Countercata|~~countercata ~~temperament~~]]. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the [[~~Optimal_patent_val|~~optimal patent val]] for the rank ~~two~~ temperament [[~~Kleismic_family#Novemkleismic|~~novemkleismic]], for the rank ~~three~~ temperament tempering out 325/324, 625/624 and 676/675, the rank ~~four~~ temperament tempering out 325/324 and 1375/1372, and the rank ~~five~~ temperament tempering out 325/324.

[[Category:~~countercata~~]]

[[Category:~~marveltwin~~]]

The equal temperament tempers out [[15625/15552]] in the 5-limit and [[5120/5103]] in the 7-limit, so it [[support]]s [[countercata]]. In the 11-limit it tempers out 1375/1372 and [[4000/3993]], and in the 13-limit [[325/324]], [[364/363]], [[625/624]] and [[676/675]], and provides the [[optimal patent val]] for the rank-2 temperament [[novemkleismic]], for the rank-3 temperament tempering out 325/324, 625/624 and 676/675, the rank-4 temperament tempering out 325/324 and 1375/1372, and the rank-5 temperament tempering out 325/324.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 333 factors into 3<sup>2</sup> × 37, 333edo has subset edos {{EDOs| 3, 9, 37, and 111 }}.

[[Category:Countercata]]

[[Category:Marveltwin]]

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-The ''333 equal temperament'' divides the octave into 333 equal parts of 3.604 cents each. It tempers out 15625/15552 in the 5-limit and 5120/5013 in the 7-limit, so it supports [[Kleismic_family#Countercata|countercata temperament]]. In the 11-limit it tempers out 1375/1372 and 4000/3993, and in the 13-limit 325/324, 364/363, 625/624 and 676/675, and provides the [[Optimal_patent_val|optimal patent val]] for the rank two temperament [[Kleismic_family#Novemkleismic|novemkleismic]], for the rank three temperament tempering out 325/324, 625/624 and 676/675, the rank four temperament tempering out 325/324 and 1375/1372, and the rank five temperament tempering out 325/324.
+{{Infobox ET}}
-[[Category:countercata]]
+{{ED intro}}
-[[Category:marveltwin]]
+The equal temperament tempers out [[15625/15552]] in the 5-limit and [[5120/5103]] in the 7-limit, so it [[support]]s [[countercata]]. In the 11-limit it tempers out 1375/1372 and [[4000/3993]], and in the 13-limit [[325/324]], [[364/363]], [[625/624]] and [[676/675]], and provides the [[optimal patent val]] for the rank-2 temperament [[novemkleismic]], for the rank-3 temperament tempering out 325/324, 625/624 and 676/675, the rank-4 temperament tempering out 325/324 and 1375/1372, and the rank-5 temperament tempering out 325/324.
+=== Prime harmonics ===
+{{Harmonics in equal|333}}
+=== Subsets and supersets ===
+Since 333 factors into 3<sup>2</sup> × 37, 333edo has subset edos {{EDOs| 3, 9, 37, and 111 }}.
+[[Category:Countercata]]
+[[Category:Marveltwin]]