2819edo
| ← 2818edo | 2819edo | 2820edo → |
2819 equal divisions of the octave (abbreviated 2819edo or 2819ed2), also called 2819-tone equal temperament (2819tet) or 2819 equal temperament (2819et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2819 equal parts of about 0.426 ¢ each. Each step represents a frequency ratio of 21/2819, or the 2819th root of 2.
Theory
2819edo is consistent to the 7-odd-limit tempering out 645700815/645657712, [-18 21 -9 2⟩ and [28 7 -12 -4⟩. It is strong in the 2.3.7.11.19.23.31 subgroup, tempering out 247808/247779, 16929/16928, 214291/214272, 116964/116963, 531441/531392 and 4917561/4917248. Using the 2.3.7.11.23.31.41 subgroup, it tempers out 76384/76383.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.004 | +0.206 | +0.028 | -0.059 | +0.196 | +0.188 | +0.039 | +0.034 | +0.150 | +0.051 |
| Relative (%) | +0.0 | -0.9 | +48.5 | +6.6 | -13.8 | +46.0 | +44.2 | +9.2 | +7.9 | +35.2 | +12.1 | |
| Steps (reduced) |
2819 (0) |
4468 (1649) |
6546 (908) |
7914 (2276) |
9752 (1295) |
10432 (1975) |
11523 (247) |
11975 (699) |
12752 (1476) |
13695 (2419) |
13966 (2690) | |
Subsets and supersets
2819edo is the 410th prime edo. 5638edo, which doubles it, gives a good correction to the harmonic 5.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-4468 2819⟩ | [⟨2819 4468]] | +0.0012 | 0.0012 | 0.28 |