4172edo
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.133 | -0.024 | -0.082 | +0.021 | +0.072 | -0.067 | +0.130 | +0.030 | -0.102 | +0.072 | -0.086 |
| Relative (%) | -46.4 | -8.4 | -28.5 | +7.3 | +25.1 | -23.5 | +45.2 | +10.5 | -35.4 | +25.2 | -30.0 | |
| Steps (reduced) |
6612 (2440) |
9687 (1343) |
11712 (3368) |
13225 (709) |
14433 (1917) |
15438 (2922) |
16300 (3784) |
17053 (365) |
17722 (1034) |
18325 (1637) |
18872 (2184) | |
The first 8 prime harmonics below 25% in 4172edo are 2, 5, 13, 17, 31, 37, 53, 61. Therefore, 4172edo can be thought of as a 2.5.13.17.31.37.53.61 subgroup temperament, on which it is consistent. Other than that, it offers satisfactory representation of the 13-odd-limit (<28% error).
4172's divisors are 1, 2, 4, 7, 14, 28, 149, 298, 596, 1043, 2086. Notable member of the group is 149edo, which is the smallest edo uniquely consistent in the 17-odd limit. Therefore from a logarithmic pitch or highly composite EDO theory perspective, 4172edo can be thought of as a compound of 28 149edos interlocked together.