3422edo
| ← 3421edo | 3422edo | 3423edo → |
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
| 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.