# 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 21/888, 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 (%) -44.7 +12.8 +6.9 +10.7 +2.5 +1.0 -31.9 +33.3 -16.0 -37.8 +7.7
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.