188edo

← 187edo

188edo

189edo →

Prime factorization	22 × 47
Step size	6.38298 ¢
Fifth	110\188 (702.128 ¢) (→ 55\94)
Semitones (A1:m2)	18:14 (114.9 ¢ : 89.36 ¢)
Consistency limit	9
Distinct consistency limit	9

188 equal divisions of the octave (abbreviated 188edo or 188ed2), also called 188-tone equal temperament (188tet) or 188 equal temperament (188et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 188 equal parts of about 6.38 ¢ each. Each step represents a frequency ratio of 2^1/188, or the 188th root of 2.

188edo is closely related to 94edo, but the patent vals differ on the mapping for 5. The equal temperament tempers out 129140163/128000000 (graviton) and 268435456/263671875 (mabila comma) in the 5-limit; 2401/2400, 19683/19600, and 110592/109375 in the 7-limit. It supports harry and newt, and provides the optimal patent val for tuskaloosa, the 77 & 111 temperament.

Using the patent val, it tempers out 176/175, 1331/1323, 3773/3750, and 16896/16807 in the 11-limit; 351/350, 352/351, 676/675, 1573/1568, and 16848/16807 in the 13-limit; supporting 13-limit tuskaloosa. Using the alternative 188e val, 243/242, 441/440, 540/539, 8019/8000, and 9801/9800 in the 11-limit; 351/350, 1716/1715, and 2080/2079 in the 13-limit; supporting 13-limit harry.

The 188cef val is a tuning for the hemigari temperament in the 11- and 13-limit.

Odd harmonics

Approximation of odd harmonics in 188edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.17	+3.05	+1.39	+0.35	-2.38	+2.03	-3.16	-2.83	+2.49	+1.56	-2.74
	Relative (%)	+2.7	+47.8	+21.7	+5.4	-37.3	+31.7	-49.5	-44.3	+39.0	+24.4	-43.0
Steps (reduced)		298 (110)	437 (61)	528 (152)	596 (32)	650 (86)	696 (132)	734 (170)	768 (16)	799 (47)	826 (74)	850 (98)

Subsets and supersets

Since 188 factors into 2² × 47, 188edo contains subset edos 2, 4, 47, and 94.