223edo

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223 equal divisions per octave

223edo is the equal division of the octave into 223 parts of 5.38117 cents each. It contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <223 353 518| (patent val), <223 354 518| (223b), and <223 353 517| (223c). Using the patent val, it tempers out the würschmidt comma, 393216/390625 and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the 223be val, it tempers out the kleisma, 15625/15552 and |58 -38 1> in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit. Using the 223c val, it tempers out the gravity comma, 129140163/128000000 and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit. Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

223edo is the 48th prime EDO.