682edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
682edo is [[consistent]] in the [[9-odd-limit]]. In the 7-limit, 682edo [[support]]s the [[septisemitonic]] temperament, described as the 128 & 142 temperament. It is a tuning for the [[major arcana]] temperament in the | 682edo is [[consistent]] in the [[9-odd-limit]], with a sharp tendency for [[3/1|3]], [[5/1|5]], and [[7/1|7]]. In the 7-limit, 682edo [[support]]s 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 [[5/1|5]] with [[31edo]], tempering out the {{monzo|72 0 -31}} comma. | ||
Beyond that, 682edo is a strong 2.3.19.23 subgroup tuning. | Beyond that, 682edo is a strong 2.3.19.23 subgroup tuning. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{harmonics in equal|682}} | {{harmonics in equal|682}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
682edo factors as {{Factorization|682}}, so it notably contains [[22edo]] and [[31edo]]. | 682edo factors as {{Factorization|682}}, so it notably contains [[22edo]] and [[31edo]]. | ||
Latest revision as of 13:12, 21 February 2025
| ← 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.