165edo

← 164edo

165edo

166edo →

Prime factorization	3 × 5 × 11
Step size	7.27273¢
Fifth	97\165 (705.455¢)
Semitones (A1:m2)	19:10 (138.2¢ : 72.73¢)
Dual sharp fifth	97\165 (705.455¢)
Dual flat fifth	96\165 (698.182¢) (→32\55)
Dual major 2nd	28\165 (203.636¢)
Consistency limit	3
Distinct consistency limit	3

165edo is the equal division of the octave into 165 parts of 7.2727 cents each.

It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383| (patent val) and <165 261 383| (165b).

Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit.

Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

Approximation of odd harmonics in 165edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	+3.50	-0.86	-1.55	-0.27	+1.41	+3.11	+2.64	-3.14	+0.67	+1.95	-2.82
	relative (%)	+48	-12	-21	-4	+19	+43	+36	-43	+9	+27	-39
Steps (reduced)		262 (97)	383 (53)	463 (133)	523 (28)	571 (76)	611 (116)	645 (150)	674 (14)	701 (41)	725 (65)	746 (86)