# 1880edo

← 1879edo | 1880edo | 1881edo → |

^{3}× 5 × 47**1880 equal divisions of the octave** (abbreviated **1880edo** or **1880ed2**), also called **1880-tone equal temperament** (**1880tet**) or **1880 equal temperament** (**1880et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1880 equal parts of about 0.638 ¢ each. Each step represents a frequency ratio of 2^{1/1880}, or the 1880th root of 2.

1880 = 20 × 94, and 1880edo shares its harmonic 3 with 94edo. It is consistent in the 7-odd-limit, and is overall a decent 13-limit system, although its 9/8 is off the stack of two 3/2's by one step, which prevents consistency in the 9-odd-limit.

In the 13-limit, it tempers out 6656/6655 and supports the 2.5.7.11.13 subgroup eternal revolutionary temperament.

### Odd harmonics

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

Error | Absolute (¢) | +0.173 | -0.144 | +0.110 | -0.293 | +0.171 | +0.111 | +0.029 | -0.275 | -0.066 | +0.283 | -0.189 |

Relative (%) | +27.0 | -22.5 | +17.3 | -45.9 | +26.9 | +17.3 | +4.6 | -43.0 | -10.4 | +44.3 | -29.6 | |

Steps (reduced) |
2980 (1100) |
4365 (605) |
5278 (1518) |
5959 (319) |
6504 (864) |
6957 (1317) |
7345 (1705) |
7684 (164) |
7986 (466) |
8258 (738) |
8504 (984) |

### Subsets and supersets

Since 1880 factors into 2^{3} × 5 × 47, 1880edo has subset edos 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, and 940.