16218edo
| ← 16217edo | 16218edo | 16219edo → |
16218edo is a strong 5-limit system, is consistent in the 15-odd-limit, and it is a satisfactory 2.3.5.11.19.23.31.37.43 subgroup system in the higher limits.
While it may not be useful as a system in its own right, it contains many notable xenharmonic systems as subsets, which opens potential for a step of 16218edo being used as an interval size measure.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0058 | -0.0022 | +0.0235 | -0.0046 | +0.0199 | -0.0350 | +0.0083 | -0.0095 | +0.0196 | -0.0115 | +0.0063 | +0.0164 | -0.0120 |
| Relative (%) | +0.0 | +7.8 | -3.0 | +31.8 | -6.2 | +26.9 | -47.2 | +11.2 | -12.8 | +26.4 | -15.6 | +8.5 | +22.2 | -16.2 | |
| Steps (reduced) |
16218 (0) |
25705 (9487) |
37657 (5221) |
45530 (13094) |
56105 (7451) |
60014 (11360) |
66290 (1418) |
68893 (4021) |
73363 (8491) |
78787 (13915) |
80347 (15475) |
84487 (3397) |
86889 (5799) |
88003 (6913) | |
Subsets and supersets
Since 16218 factors as 2 × 32 × 17 × 53, 16218edo has subset edos 1, 2, 3, 6, 9, 17, 18, 34, 51, 53, 102, 106, 153, 159, 306, 318, 477, 901, 954, 1802, 2703, 5406, 8109.
Particularly notable subsets are 17 53, 159, 306, 901, and 954.
32436edo, while not as consistent or impressive harmonically, may offer additional possibilites due to inclusion of 612edo in subset edos.