232edo: Difference between revisions

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The ''232 equal division'' divides the octave into 232 equal parts of 5.172 cents each. It provides the [[Optimal_patent_val|optimal patent val]] for [[13-limit|13-limit]] [[Hemifamity_temperaments#Mystery|mystery temperament]], the rank three [[Hemifamity_family#Pele|pele temperament]] and the rank three [[Trimyna_family#Trimyna-13-limit|trimyna temperament]] and other temperaments tempering out 196/195, for which it gives the optimal patent val for the corresponding rank five temperament. Aside from its patent val, the 232d val is worth considering. Both temper out the wuerschmidt comma, 393216/390625, in the 5-limit. In the 7-limit, the patent val tempers out hemifamity, 5120/5103 and the trimyna comma, 50421/50000; and 232d 3125/3097 and 245/243, [[support|supporting]] [[Sensamagic_clan#Bohpier|bohpier temperament]]. In the 11-limit, the patent val tempers out 441/440 and 896/891, and 232d 540/539, 1375/1372 and 4000/3993, supporting octoid. In the 13-limit, the patent val tempers out 196/195, 352/351, 364/363, 441/440 and 676/675, which leads to 13-limit mystery, for which it provides the optimal patent val. 232d also tempers out 352/351 and 676/675, which supports variants of octoid.

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			{{Infobox ET}}
	The ''232 equal division'' divides the octave into 232 equal parts of 5.172 cents each. It provides the [[Optimal_patent_val\|optimal patent val]] for [[13-limit\|13-limit]] [[Hemifamity_temperaments#Mystery\|mystery temperament]], the rank three [[Hemifamity_family#Pele\|pele temperament]] and the rank three [[Trimyna_family#Trimyna-13-limit\|trimyna temperament]] and other temperaments tempering out 196/195, for which it gives the optimal patent val for the corresponding rank five temperament. Aside from its patent val, the 232d val is worth considering. Both temper out the wuerschmidt comma, 393216/390625, in the 5-limit. In the 7-limit, the patent val tempers out hemifamity, 5120/5103 and the trimyna comma, 50421/50000; and 232d 3125/3097 and 245/243, [[support\|supporting]] [[Sensamagic_clan#Bohpier\|bohpier temperament]]. In the 11-limit, the patent val tempers out 441/440 and 896/891, and 232d 540/539, 1375/1372 and 4000/3993, supporting octoid. In the 13-limit, the patent val tempers out 196/195, 352/351, 364/363, 441/440 and 676/675, which leads to 13-limit mystery, for which it provides the optimal patent val. 232d also tempers out 352/351 and 676/675, which supports variants of octoid.		The ''232 equal division'' divides the octave into 232 equal parts of 5.172 cents each. It provides the [[Optimal_patent_val\|optimal patent val]] for [[13-limit\|13-limit]] [[Hemifamity_temperaments#Mystery\|mystery temperament]], the rank three [[Hemifamity_family#Pele\|pele temperament]] and the rank three [[Trimyna_family#Trimyna-13-limit\|trimyna temperament]] and other temperaments tempering out 196/195, for which it gives the optimal patent val for the corresponding rank five temperament. Aside from its patent val, the 232d val is worth considering. Both temper out the wuerschmidt comma, 393216/390625, in the 5-limit. In the 7-limit, the patent val tempers out hemifamity, 5120/5103 and the trimyna comma, 50421/50000; and 232d 3125/3097 and 245/243, [[support\|supporting]] [[Sensamagic_clan#Bohpier\|bohpier temperament]]. In the 11-limit, the patent val tempers out 441/440 and 896/891, and 232d 540/539, 1375/1372 and 4000/3993, supporting octoid. In the 13-limit, the patent val tempers out 196/195, 352/351, 364/363, 441/440 and 676/675, which leads to 13-limit mystery, for which it provides the optimal patent val. 232d also tempers out 352/351 and 676/675, which supports variants of octoid.