189edo

← 188edo

189edo

190edo →

Prime factorization	33 × 7
Step size	6.34921 ¢
Fifth	111\189 (704.762 ¢) (→ 37\63)
Semitones (A1:m2)	21:12 (133.3 ¢ : 76.19 ¢)
Dual sharp fifth	111\189 (704.762 ¢) (→ 37\63)
Dual flat fifth	110\189 (698.413 ¢)
Dual major 2nd	32\189 (203.175 ¢)
Consistency limit	7
Distinct consistency limit	7

The equal temperament tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the hemikleismic temperament. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 189edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+2.81	+0.99	+2.60	-0.74	+1.06	-2.43	-2.55	+2.98	+0.90	-0.94	+0.30
	Relative (%)	+44.2	+15.6	+41.0	-11.6	+16.7	-38.3	-40.2	+47.0	+14.2	-14.8	+4.7
Steps (reduced)		300 (111)	439 (61)	531 (153)	599 (32)	654 (87)	699 (132)	738 (171)	773 (17)	803 (47)	830 (74)	855 (99)

Subsets and supersets

Since 189 factors into 3³ × 7, 189edo contains 3, 7, 9, 21, 27, and 63 as its subsets.