390edo
| ← 389edo | 390edo | 391edo → |
Theory
390et is only consistent to the 3-odd-limit. It can be used in the 2.3.7.11.13.17.23.31.41 subgroup. Using the patent val, it tempers out 32805/32768 in the 5-limit; 283115520/282475249, 184528125/184473632, 589824/588245, 2460375/2458624, 67108864/66976875, 6144/6125, 102760448/102515625, 3136/3125, 2401/2400 and 5250987/5242880 in the 7-limit. It supports trilobite.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.42 | +1.38 | +0.40 | -0.55 | -0.53 | -0.34 | +0.95 | -0.58 | +1.19 | -0.42 |
| Relative (%) | +0.0 | -13.5 | +44.8 | +13.2 | -17.8 | -17.1 | -11.1 | +30.8 | -18.9 | +38.7 | -13.7 | |
| Steps (reduced) |
390 (0) |
618 (228) |
906 (126) |
1095 (315) |
1349 (179) |
1443 (273) |
1594 (34) |
1657 (97) |
1764 (204) |
1895 (335) |
1932 (372) | |
Subsets and supersets
390 factors into 2 × 3 × 5 × 13 with subset edos 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, and 195. 780edo, 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 | [-103 65⟩ | [⟨390 618]] | 0.1314 | 0.1314 | 4.27 |
| 2.3.7 | 118098/117649, 34451725707/34359738368 | [⟨390 618 1095]] | 0.0395 | 0.1685 | 5.48 |
| 2.3.7.11 | 118098/117649, 1362944/1361367, 235782657/234881024 | [⟨390 618 1095 1349]] | 0.0693 | 0.1548 | 5.03 |
| 2.3.7.11.13 | 729/728, 16848/16807, 10648/10647, 1574573/1572864 | [⟨390 618 1095 1349 1443]] | 0.0839 | 0.1415 | 4.60 |
| 2.3.7.11.13.17 | 729/728, 1089/1088, 16848/16807, 95823/95744, 65637/65536 | [⟨390 618 1095 1349 1443 1594]] | 0.0838 | 0.1292 | 4.20 |