2711edo
Theory
2711edo is distinctly consistent to the 15-odd-limit, or the no-11 19-odd-limit. The equal temperament tempers out 78125000/78121827 in the 7-limit; 35156250/35153041, 14348907/14348180, 21437500/21434787, 151263/151250, 2359296/2358125, 5767168/5764801 and 199297406/199290375 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.074 | +0.112 | +0.115 | +0.213 | +0.048 | -0.049 | -0.058 | -0.167 | +0.006 | +0.077 |
| Relative (%) | +0.0 | +16.7 | +25.3 | +26.1 | +48.1 | +10.8 | -11.2 | -13.1 | -37.6 | +1.4 | +17.4 | |
| Steps (reduced) |
2711 (0) |
4297 (1586) |
6295 (873) |
7611 (2189) |
9379 (1246) |
10032 (1899) |
11081 (237) |
11516 (672) |
12263 (1419) |
13170 (2326) |
13431 (2587) | |
Subsets and supersets
2711edo is the 395th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [4297 -2711⟩ | [⟨2711 4297]] | -0.0233 | 0.0233 | 5.26 |
| 2.3.5 | [77 -31 -12⟩, [18 -89 53⟩ | [⟨2711 4297 6295]] | -0.0316 | 0.0223 | 5.04 |
| 2.3.5.7 | [3 -13 10 -2⟩, [37 -9 -11 1⟩, [0 -11 -7 12⟩ | [⟨2711 4297 6295 7611]] | -0.0340 | 0.0198 | 4.47 |
| 2.3.5.7.11 | 151263/151250, 14348907/14348180, 2359296/2358125, 21437500/21434787 | [⟨2711 4297 6295 7611 9379]] | -0.0395 | 0.0209 | 4.72 |
| 2.3.5.7.11.13 | 4096/4095, 43940/43923, 67392/67375, 151263/151250, 4429568/4428675 | [⟨2711 4297 6295 7611 9379 10032]] | -0.0351 | 0.0215 | 4.86 |