4327edo
Theory
4327edo is consistent to the 11-odd-limit, tempering out 117649/117612, 50014503/50000000, 234365481/234256000 and 369140625/369098752. It supports mikkolic.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.037 | +0.005 | -0.118 | -0.074 | +0.011 | +0.055 | -0.032 | -0.125 | +0.060 | +0.123 | -0.126 |
| Relative (%) | -13.3 | +1.7 | -42.5 | -26.5 | +3.9 | +19.7 | -11.6 | -45.2 | +21.8 | +44.3 | -45.3 | |
| Steps (reduced) |
6858 (2531) |
10047 (1393) |
12147 (3493) |
13716 (735) |
14969 (1988) |
16012 (3031) |
16905 (3924) |
17686 (378) |
18381 (1073) |
19006 (1698) |
19573 (2265) | |
Subsets and supersets
4327edo is the 591st prime EDO.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-6858 4327⟩ | [⟨4327 6858]] | 0.0116 | 0.0116 | 4.18 |
| 2.3.5 | [-69 45 -1⟩, [96 83 -98⟩ | [⟨4327 6858 10047]] | 0.0071 | 0.0115 | 4.15 |
| 2.3.5.7 | [-9 5 -8 7⟩, [3 -24 3 10⟩, [-57 16 10 3⟩ | [⟨4327 6858 10047 12147]] | 0.0158 | 0.0181 | 6.53 |
| 2.3.5.7.11 | 117649/117612, 50014503/50000000, 234365481/234256000, 369140625/369098752 | [⟨4327 6858 10047 12147 14969]] | 0.0120 | 0.0179 | 6.45 |
| 2.3.5.7.11.13 | 123201/123200, 4100625/4100096, 1990656/1990625, 4917248/4915625, 3195731/3194880 | [⟨4327 6858 10047 12147 14969 16012]] | 0.0075 | 0.0191 | 6.89 |