243edo: Difference between revisions

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The ''243 equal division'' divides the octave into 243 equal parts of 4.938 cents each. It tempers out the semicomma (5-limit orwell comma) 2109375/2097152 in the 5-limit, and 2401/2400 and 4375/4374 in the 7-limit. In the 11-limit it tempers out 243/242 and 441/440, and provides the [[~~Optimal_patent_val|~~optimal patent val]] for [[~~Ragismic_microtemperaments~~#Ennealimmal|ennealimnic temperament]]. In the 13-limit it tempers out 364/363 and 625/624, and provides the optimal temperament for 13-limit ennealimnic and the rank ~~three~~ [[~~Breed_family~~|jovial temperament]], and in the 17-limit it tempers out 375/374 and 595/594 and provides the optimal patent val for 17-limit ennealimnic.

The '''243 equal division''' divides the octave into 243 equal parts of 4.938 cents each. It tempers out the [[semicomma]] (5-limit orwell comma) 2109375/2097152 in the 5-limit, and [[2401/2400]] and [[4375/4374]] in the 7-limit. In the 11-limit it tempers out [[243/242]] and [[441/440]], and provides the [[optimal patent val]] for the [[Ragismic microtemperaments #Ennealimmal|ennealimnic temperament]]. In the 13-limit it tempers out [[364/363]] and [[625/624]], and provides the optimal temperament for 13-limit ennealimnic and the rank-3 [[Breed family #Jovial|jovial temperament]], and in the 17-limit it tempers out 375/374 and 595/594 and provides the optimal patent val for 17-limit ennealimnic.

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

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-The ''243 equal division'' divides the octave into 243 equal parts of 4.938 cents each. It tempers out the semicomma (5-limit orwell comma) 2109375/2097152 in the 5-limit, and 2401/2400 and 4375/4374 in the 7-limit. In the 11-limit it tempers out 243/242 and 441/440, and provides the [[Optimal_patent_val|optimal patent val]] for [[Ragismic_microtemperaments#Ennealimmal|ennealimnic temperament]]. In the 13-limit it tempers out 364/363 and 625/624, and provides the optimal temperament for 13-limit ennealimnic and the rank three [[Breed_family|jovial temperament]], and in the 17-limit it tempers out 375/374 and 595/594 and provides the optimal patent val for 17-limit ennealimnic.
+The '''243 equal division''' divides the octave into 243 equal parts of 4.938 cents each. It tempers out the [[semicomma]] (5-limit orwell comma) 2109375/2097152 in the 5-limit, and [[2401/2400]] and [[4375/4374]] in the 7-limit. In the 11-limit it tempers out [[243/242]] and [[441/440]], and provides the [[optimal patent val]] for the [[Ragismic microtemperaments #Ennealimmal|ennealimnic temperament]]. In the 13-limit it tempers out [[364/363]] and [[625/624]], and provides the optimal temperament for 13-limit ennealimnic and the rank-3 [[Breed family #Jovial|jovial temperament]], and in the 17-limit it tempers out 375/374 and 595/594 and provides the optimal patent val for 17-limit ennealimnic.
+=== Prime harmonics ===
+{{Harmonics in equal|243}}
+[[Category:Equal divisions of the octave]]