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| (optimal 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. Using the 223b 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. 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.

223edo is the 48th prime EDO.