682edo
| ← 681edo | 682edo | 683edo → |
682 equal divisions of the octave (abbreviated 682edo or 682ed2), also called 682-tone equal temperament (682tet) or 682 equal temperament (682et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 682 equal parts of about 1.76 ¢ each. Each step represents a frequency ratio of 21/682, or the 682nd root of 2.
682edo is consistent in the 9-odd-limit, with a sharp tendency for 3, 5, and 7. In the 7-limit, 682edo supports the septisemitonic temperament, described as the 128 & 142 temperament. It is a tuning for the major arcana temperament in the 7-limit. It also shares the mapping for 5 with 31edo, tempering out the [72 0 -31⟩ comma.
Beyond that, 682edo is a strong 2.3.19.23 subgroup tuning.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.098 | +0.783 | +0.676 | +0.196 | -0.585 | +0.528 | -0.879 | +0.616 | -0.152 | +0.773 | -0.122 |
| Relative (%) | +5.6 | +44.5 | +38.4 | +11.1 | -33.2 | +30.0 | -49.9 | +35.0 | -8.7 | +44.0 | -6.9 | |
| Steps (reduced) |
1081 (399) |
1584 (220) |
1915 (551) |
2162 (116) |
2359 (313) |
2524 (478) |
2664 (618) |
2788 (60) |
2897 (169) |
2996 (268) |
3085 (357) | |
Subsets and supersets
682edo factors as 2 × 11 × 31, so it notably contains 22edo and 31edo.