1880edo
| ← 1879edo | 1880edo | 1881edo → |
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 21/1880, 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 | -22 | +17 | -46 | +27 | +17 | +5 | -43 | -10 | +44 | -30 | |
| 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 23 × 5 × 47, 1880edo has subset edos 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, and 940.