682edo

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← 681edo682edo683edo →
Prime factorization 2 × 11 × 31
Step size 1.75953¢
Fifth 399\682 (702.053¢)
Semitones (A1:m2) 65:51 (114.4¢ : 89.74¢)
Consistency limit 9
Distinct consistency limit 9

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 1.760 ¢ 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

Approximation of odd harmonics in 682edo
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 (%) +6 +45 +38 +11 -33 +30 -50 +35 -9 +44 -7
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.