246edo
Theory
246 = 6 × 41, and 246edo shares its fifth with 41edo. It is only consistent to the 5-odd-limit, but the patent val offers excellent approximations (within half a cent) of prime harmonics 11, 19, and 29, and quite good approximations (within one cent) of 5 and 23. It provides the optimal patent val for cata, the 2.3.5.13 subgroup temperament tempering out 325/324 and 625/624.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.48 | -0.95 | +1.91 | -0.10 | -1.50 | +2.36 | +0.05 | +0.99 | -0.31 | +1.31 |
| Relative (%) | +0.0 | +9.9 | -19.4 | +39.1 | -2.0 | -30.8 | +48.4 | +1.0 | +20.4 | -6.3 | +26.8 | |
| Steps (reduced) |
246 (0) |
390 (144) |
571 (79) |
691 (199) |
851 (113) |
910 (172) |
1006 (22) |
1045 (61) |
1113 (129) |
1195 (211) |
1219 (235) | |
Subsets and supersets
Since 246 factors into 2 × 3 × 41, 246edo has subset edos 2, 3, 6, 41, 82, and 123.
Scales
