421edo
| ← 420edo | 421edo | 422edo → |
Theory
421et is only consistent to the 3-odd-limit, with its harmonic 5 being way too sharp. It is suitable for the 2.3.7.11.13.29.37 subgroup, tempering out 638/637, 53361/53248, 88209/87808, 5292/5291, 24192/24167 and 85293/85184.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.77 | +1.33 | +0.30 | +1.32 | -1.20 | +0.33 | +0.57 | +0.51 | -1.08 | -0.47 | -1.20 |
| Relative (%) | -26.9 | +46.8 | +10.4 | +46.2 | -42.1 | +11.5 | +19.9 | +17.8 | -37.7 | -16.6 | -42.0 | |
| Steps (reduced) |
667 (246) |
978 (136) |
1182 (340) |
1335 (72) |
1456 (193) |
1558 (295) |
1645 (382) |
1721 (37) |
1788 (104) |
1849 (165) |
1904 (220) | |
Subsets and supersets
421edo is the 82nd prime edo. 1263edo, which triples 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 | [-667 421⟩ | [⟨421 667]] | 0.2421 | 0.2421 | 8.49 |
| 2.3.7 | [-44 26 1⟩, [37 5 -16⟩ | [⟨421 667 1182]] | 0.1263 | 0.2567 | 9.01 |
| 2.3.7.11 | 88209/87808, 2893401/2883584, 208971104256/208422380089 | [⟨421 667 1182 1456]] | 0.1814 | 0.2419 | 8.49 |
| 2.3.7.11.13 | 53361/53248, 88209/87808, 24192/24167, 85293/85184 | [⟨421 667 1182 1456 1558]] | 0.1274 | 0.2418 | 8.48 |