482edo
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Prime factorization
2 × 241
Step size
2.48963¢
Fifth
282\482 (702.075¢) (→141\241)
Semitones (A1:m2)
46:36 (114.5¢ : 89.63¢)
Consistency limit
9
Distinct consistency limit
9
| ← 481edo | 482edo | 483edo → |
482 equal divisions of the octave (abbreviated 482edo or 482ed2), also called 482-tone equal temperament (482tet) or 482 equal temperament (482et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 482 equal parts of about 2.49 ¢ each. Each step represents a frequency ratio of 21/482, or the 482nd root of 2.
Theory
482edo has good approximations of harmonics 3, 5, 7, 17, 31, and 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 | +5 | -17 | -15 | -45 | +39 | -16 | +50 | -36 | +45 | +8 | |
| Steps (reduced) |
482 (0) |
764 (282) |
1119 (155) |
1353 (389) |
1667 (221) |
1784 (338) |
1970 (42) |
2048 (120) |
2180 (252) |
2342 (414) |
2388 (460) | |
Subsets and supersets
Since 482 factors into 2 × 241, 482edo contains 2edo and 241edo as subsets.
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 |