16218edo
| ← 16217edo | 16218edo | 16219edo → |
16218 equal divisions of the octave (abbreviated 16218edo or 16218ed2), also called 16218-tone equal temperament (16218tet) or 16218 equal temperament (16218et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 16218 equal parts of about 0.074 ¢ each. Each step represents a frequency ratio of 21/16218, or the 16218th root of 2.
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.