220edo
Theory
Using the patent val, it tempers out 131072000/129140163 (rodan comma) and 6115295232/6103515625 (vishnuzma) in the 5-limit; 6144/6125, 10976/10935, and 390625/388962 in the 7-limit; 1331/1323, 1375/1372, 2200/2187, and 16384/16335 in the 11-limit; 325/324, 352/351, 1001/1000, 1573/1568, and 2704/2695 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.68 | +0.96 | +2.08 | -2.09 | -0.41 | -0.53 | +2.64 | -1.32 | +2.49 | -1.69 | -1.00 |
| Relative (%) | +30.8 | +17.6 | +38.2 | -38.4 | -7.5 | -9.7 | +48.4 | -24.2 | +45.6 | -31.0 | -18.4 | |
| Steps (reduced) |
349 (129) |
511 (71) |
618 (178) |
697 (37) |
761 (101) |
814 (154) |
860 (200) |
899 (19) |
935 (55) |
966 (86) |
995 (115) | |
Subsets and supersets
220 factors into 22 × 5 × 11, with subset edos 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [349 -220⟩ | ⟨220 349] | -0.5304 | 0.5302 | 9.72 |
| 2.3.5 | [20 -17 3⟩, [23 6 -14⟩ | ⟨220 349 511] | -0.4912 | 0.4364 | 8.00 |
| 2.3.5.7 | 6144/6125, 10976/10935, 390625/388962 | ⟨220 349 511 618] | -0.5538 | 0.3932 | 7.21 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 43\220 | 234.55 | 8/7 | Rodan |
| 1 | 83\220 | 452.73 | 125/81 | Maja |
| 2 | 13\220 | 70.91 | 25/24 | Vishnu |
| 11 | 91\220 (9\220) |
496.36 (49.09) |
4/3 (36/35) |
Hendecatonic |