# 777edo

← 776edo | 777edo | 778edo → |

**777 equal divisions of the octave** (abbreviated **777edo** or **777ed2**), also called **777-tone equal temperament** (**777tet**) or **777 equal temperament** (**777et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 777 equal parts of about 1.54 ¢ each. Each step represents a frequency ratio of 2^{1/777}, or the 777th root of 2.

777edo is inconsistent to 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise it is excellent in approximating harmonics 5, 7, 9, 11, 13, and 17, making it suitable for a 2.9.5.7.11.13.17 subgroup interpretation. A comma basis for the 2.9.5.7.11.13 subgroup is {4459/4455, 41503/41472, 496125/495616, 105644/105625, 123201/123200}. In addition, it tempers out the landscape comma in the 2.9.5.7 subgroup.

### Odd harmonics

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +0.748 | -0.213 | -0.486 | -0.049 | +0.033 | -0.373 | +0.534 | +0.064 | +0.556 | +0.262 | +0.297 |

Relative (%) | +48.4 | -13.8 | -31.5 | -3.2 | +2.2 | -24.2 | +34.6 | +4.1 | +36.0 | +16.9 | +19.2 | |

Steps (reduced) |
1232 (455) |
1804 (250) |
2181 (627) |
2463 (132) |
2688 (357) |
2875 (544) |
3036 (705) |
3176 (68) |
3301 (193) |
3413 (305) |
3515 (407) |

### Subsets and supersets

Since 777 factors into 3 × 7 × 37, 777edo has subset edos 3, 7, 21, 37, 111, and 333.