1879edo
| ← 1878edo | 1879edo | 1880edo → |
1879 equal divisions of the octave (abbreviated 1879edo or 1879ed2), also called 1879-tone equal temperament (1879tet) or 1879 equal temperament (1879et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1879 equal parts of about 0.639 ¢ each. Each step represents a frequency ratio of 21/1879, or the 1879th root of 2.
Theory
1879edo is consistent to the 21-odd-limit, tempering out 2376/2375, 12376/12375, 67392/67375, 20007/20000, 13377/13376, 11781/11776, 89376/89375 and 25025/25024 in the 23-limit. It is strong in the 2.3.5.7.13.19.29.31 subgroup, tempering out 20007/20000, 3969/3968, 28431/28420, 4901/4900, 1016064/1015625, 885735/885248 and 138240/138229. Using the 2.3.5.7.11.29.41 subgroup, it tempers out 2871/2870.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.092 | +0.062 | -0.013 | -0.174 | -0.081 | -0.219 | +0.092 | +0.145 | -0.093 | +0.042 |
| Relative (%) | +0.0 | -14.5 | +9.7 | -2.0 | -27.2 | -12.6 | -34.3 | +14.4 | +22.7 | -14.6 | +6.5 | |
| Steps (reduced) |
1879 (0) |
2978 (1099) |
4363 (605) |
5275 (1517) |
6500 (863) |
6953 (1316) |
7680 (164) |
7982 (466) |
8500 (984) |
9128 (1612) |
9309 (1793) | |
Subsets and supersets
1879edo is the 289th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2978 1879⟩ | [⟨1879 2978]] | 0.0291 | 0.0291 | 4.56 |
| 2.3.5 | [-8 49 -30⟩, [91 -12 -31⟩ | [⟨1879 2978 4363]] | 0.0105 | 0.0355 | 5.56 |
| 2.3.5.7 | 14348907/14336000, 200120949/200000000, 8796093022208/8792724609375 | [⟨1879 2978 4363 5275]] | 0.0090 | 0.0308 | 4.82 |
| 2.3.5.7.11 | 160083/160000, 151263/151250, 2657205/2656192, 262766592/262609375 | [⟨1879 2978 4363 5275 6500]] | 0.0173 | 0.0321 | 5.03 |
| 2.3.5.7.11.13 | 67392/67375, 160083/160000, 50193/50176, 557568/557375, 4100625/4100096 | [⟨1879 2978 4363 5275 6500 6953]] | 0.0180 | 0.0294 | 4.60 |
| 2.3.5.7.11.13.17 | 12376/12375, 67392/67375, 160083/160000, 75735/75712, 131648/131625, 194481/194480 | [⟨1879 2978 4363 5275 6500 6953 7680]] | 0.0231 | 0.0299 | 4.68 |
| 2.3.5.7.11.13.17.19 | 2376/2375, 12376/12375, 67392/67375, 10241/10240, 89376/89375, 28431/28424, 111537/111475 | [⟨1879 2978 4363 5275 6500 6953 7680 7982]] | 0.0175 | 0.0316 | 4.95 |