223edo

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 π (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),
• ⟨223 353 517] (223c).

← 222edo

223edo

224edo →

Prime factorization	223 (prime)
Step size	5.38117 ¢
Fifth	130\223 (699.552 ¢)
Semitones (A1:m2)	18:19 (96.86 ¢ : 102.2 ¢)
Dual sharp fifth	131\223 (704.933 ¢)
Dual flat fifth	130\223 (699.552 ¢)
Dual major 2nd	38\223 (204.484 ¢)
Consistency limit	3
Distinct consistency limit	3

Using the patent val, it tempers out 393216/390625 (würschmidt comma) 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 15625/15552 (kleisma) 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 129140163/128000000 (graviton) 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.

223 is also the number of lunar months in an astronomical concept known as saros.

Approximation of odd harmonics in 223edo

Harmonic		3	5	7	9	11	13	15	17	19	21
Error	Absolute (¢)	-2.40	+1.13	-0.22	+0.57	-2.44	-1.07	-1.27	+2.67	-1.55	-2.62
	Relative (%)	-44.7	+21.0	-4.0	+10.7	-45.3	-19.8	-23.7	+49.6	-28.8	-48.7
Steps (reduced)		353 (130)	518 (72)	626 (180)	707 (38)	771 (102)	825 (156)	871 (202)	912 (20)	947 (55)	979 (87)