# 888edo

← 887edo | 888edo | 889edo → |

^{3}× 3 × 37**888 equal divisions of the octave** (abbreviated **888edo**), or **888-tone equal temperament** (**888tet**), **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 of 888edo 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

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 2^{3} × 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.