482edo
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.12 | -0.42 | -0.36 | -1.11 | +0.97 | -0.39 | +1.24 | -0.89 | +1.13 | +0.19 |
| Relative (%) | +0.0 | +4.8 | -16.9 | -14.5 | -44.6 | +38.8 | -15.7 | +49.9 | -35.7 | +45.3 | +7.7 | |
| Steps (reduced) |
482 (0) |
764 (282) |
1119 (155) |
1353 (389) |
1667 (221) |
1784 (338) |
1970 (42) |
2048 (120) |
2180 (252) |
2342 (414) |
2388 (460) | |
Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have rather large errors, but they are reasonable to work with.
In the 7-limit, 482edo provides excellent tuning for the tertiaseptal temperament.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5 | [24, -21, 4⟩, [-59, 5, 22⟩ | [⟨482 764 1119]] | 0.035344 | 0.058672 | |
| 2.3.5.7 | [-6, 3, 9, -7⟩, [-26, -1, 1, 9⟩, [8, -20, 9, 1⟩ | [⟨482 764 1119 1353]] | 0.058672 | 0.101802 | 4.089 |
| 2.3.5.7.11 | 2401/2400, 9801/9800, 19712/19683, 65625/65536 | [⟨482 764 1119 1353 1667]] | 0.111136 | 0.138937 | |
| 2.3.5.7.11.13 | 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721 | [⟨482 764 1119 1353 1667 1784]] | 0.049077 | 0.187961 | |