482edo: Difference between revisions
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+data for an alternative 13-limit mapping that's actually better |
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[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 00:59, 4 July 2022
Theory
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.
Prime harmonics
| 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) | |
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]] | +0.0353 | 0.0587 | 4.33 |
| 2.3.5.7 | 2401/2400, 65625/65536, [8 -20 9 1⟩ | [⟨482 764 1119 1353]] | +0.0587 | 0.1018 | 4.09 |
| 2.3.5.7.11 | 2401/2400, 9801/9800, 19712/19683, 65625/65536 | [⟨482 764 1119 1353 1667]] | +0.1111 | 0.1389 | 5.58 |
| 2.3.5.7.11.13 | 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536 | [⟨482 764 1119 1353 1667 1783]] (482f) | +0.1612 | 0.1692 | 6.80 |
| 2.3.5.7.11.13 | 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721 | [⟨482 764 1119 1353 1667 1784]] (482) | +0.0491 | 0.1880 | 7.55 |