1019edo
Theory
1019edo is consistent to the 17-odd-limit, tempering out 1275/1274, 3025/3024, 1716/1715, 4096/4095, 2500/2499 and 3536379/3536000. Using the 2.3.5.11.17.29.43 subgroup, it tempers out 17545/17544. It supports tritomere.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.090 | -0.053 | +0.360 | -0.189 | +0.297 | -0.147 | +0.426 | +0.577 | -0.333 | -0.384 |
| Relative (%) | +0.0 | -7.7 | -4.5 | +30.5 | -16.1 | +25.2 | -12.5 | +36.2 | +49.0 | -28.3 | -32.6 | |
| Steps (reduced) |
1019 (0) |
1615 (596) |
2366 (328) |
2861 (823) |
3525 (468) |
3771 (714) |
4165 (89) |
4329 (253) |
4610 (534) |
4950 (874) |
5048 (972) | |
Subsets and supersets
1019edo is the 171st prime EDO.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-1615 1019⟩ | [⟨1019 1615]] | +0.0285 | 0.0285 | 2.42 |
| 2.3.5 | [-31 43 -16⟩, [-68 18 17⟩ | [⟨1019 1615 2366]] | +0.0266 | 0.0235 | 2.00 |
| 2.3.5.7 | 703125/702464, 14348907/14336000, 283115520/282475249 | [⟨1019 1615 2366 2861]] | -0.0121 | 0.0700 | 5.94 |
| 2.3.5.7.11 | 3025/3024, 759375/758912, 180224/180075, 14348907/14336000 | [⟨1019 1615 2366 2861 3525]] | +0.0013 | 0.0681 | 5.78 |
| 2.3.5.7.11.13 | 3025/3024, 1716/1715, 4096/4095, 540000/539539, 216513/216320 | [⟨1019 1615 2366 2861 3525 3771]] | -0.0123 | 0.0692 | 5.88 |
| 2.3.5.7.11.13.17 | 1275/1274, 3025/3024, 1716/1715, 4096/4095, 2500/2499, 3536379/3536000 | [⟨1019 1615 2366 2861 3525 3771 4165]] | -0.0054 | 0.0662 | 5.62 |