422edo
The 422 equal division of the octave divides the octave into 422 equal parts of 2.844 cents each.
422edo is a zeta peak edo, though not zeta integral nor zeta gap. It is distinctly consistent through the 27-odd-limit, with harmonics of 3 through 23 all tuned sharp. In the 5-limit it tempers out the vishnuzma, [23 6 -14⟩; and in the 7-limit 4375/4374 and 589824/588245 so that it supports the gamera temperament, and provides its optimal patent val, and also supports the vishnu temperament. A basis for the 11-limit is 3025/3024, 4375/4374, 5632/5625 and 825000/823543.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.41 | +0.42 | +0.84 | +0.34 | +1.18 | +0.26 | +1.07 | +0.16 | -0.19 | +0.94 |
| Relative (%) | +0.0 | +14.6 | +14.6 | +29.6 | +12.0 | +41.4 | +9.1 | +37.5 | +5.7 | -6.8 | +32.9 | |
| Steps (reduced) |
422 (0) |
669 (247) |
980 (136) |
1185 (341) |
1460 (194) |
1562 (296) |
1725 (37) |
1793 (105) |
1909 (221) |
2050 (362) |
2091 (403) | |