888edo

← 887edo

888edo

889edo →

Prime factorization	23 × 3 × 37
Step size	1.35135¢
Fifth	519\888 (701.351¢) (→173\296)
Semitones (A1:m2)	81:69 (109.5¢ : 93.24¢)
Dual sharp fifth	520\888 (702.703¢) (→65\111)
Dual flat fifth	519\888 (701.351¢) (→173\296)
Dual major 2nd	151\888 (204.054¢)
Consistency limit	3
Distinct consistency limit	3

888 equal divisions of the octave (abbreviated 888edo or 888ed2), also called 888-tone equal temperament (888tet) or 888 equal temperament (888et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 888 equal parts of about 1.35 ¢ each. Each step represents a frequency ratio of 2^1/888, or the 888th root of 2.

888edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise it is excellent in approximating harmonics 5, 7, 9, 11, and 13, making it suitable for a 2.9.5.7.11.13 subgroup interpretation. The equal temperament tempers out 4096/4095, 6656/6655, 9801/9800, 10648/10647, 105644/105625, 151263/151200, and 250047/250000 in the above subgroup.

Odd harmonics

Approximation of odd harmonics in 888edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	-0.604	+0.173	+0.093	+0.144	+0.033	+0.013	-0.431	+0.450	-0.216	-0.511	+0.104
	relative (%)	-45	+13	+7	+11	+2	+1	-32	+33	-16	-38	+8
Steps (reduced)		1407 (519)	2062 (286)	2493 (717)	2815 (151)	3072 (408)	3286 (622)	3469 (805)	3630 (78)	3772 (220)	3900 (348)	4017 (465)

Subsets and supersets

Since 888 factors into 2³ × 3 × 37, 888edo has subset edos 2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, and 444. 1776edo, which doubles it, provides a good correction for harmonic 3.