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|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 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|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]]. | ||
Revision as of 21:25, 4 October 2022
| ← 226edo | 227edo | 228edo → |
227EDO is the equal division of the octave into 227 parts of 5.2863 cents 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 supports 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. 227EDO is accurate for the 13th harmonic, as the denominator of a convergent to log213, after 10 and before 5231.
227EDO is the 49th prime EDO.