# 3422edo

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 ← 3421edo 3422edo 3423edo →
Prime factorization 2 × 29 × 59
Step size 0.350672¢
Fifth 2002\3422 (702.046¢) (→1001\1711)
Semitones (A1:m2) 326:256 (114.3¢ : 89.77¢)
Consistency limit 7
Distinct consistency limit 7

3422 equal divisions of the octave (abbreviated 3422edo or 3422ed2), also called 3422-tone equal temperament (3422tet) or 3422 equal temperament (3422et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3422 equal parts of about 0.351 ¢ each. Each step represents a frequency ratio of 21/3422, or the 3422nd root of 2.

3422edo is consistent in the 7-odd-limit, where it tempers out the euzenius comma and [-2 -25 1 14. It is enfactored in the 5-limit, with the same tuning as 1711edo. Despite large errors and inconsistency, it is a strong tuning for the oganesson temperament in the 19-limit patent val.

### Odd harmonics

Approximation of odd harmonics in 3422edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.091 +0.127 +0.081 -0.169 -0.061 +0.033 -0.133 -0.104 -0.143 +0.172 +0.130
Relative (%) +25.8 +36.2 +23.1 -48.3 -17.5 +9.5 -38.0 -29.8 -40.8 +49.0 +37.1
Steps
(reduced)
5424
(2002)
7946
(1102)
9607
(2763)
10847
(581)
11838
(1572)
12663
(2397)
13369
(3103)
13987
(299)
14536
(848)
15031
(1343)
15480
(1792)

### Subsets and supersets

Since 3422 factors as 2 × 29 × 59, 3422edo has subset edos 1, 2, 29, 58, 59, 118, 1711, notably containing 29edo, 58edo, and 118edo.