4172edo: Difference between revisions
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{{EDO intro|4172}} | {{EDO intro|4172}} | ||
==Theory== | ==Theory== | ||
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 | 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. | ||
4172's divisors are {{EDOs|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 | === Subsets and supersets === | ||
4172's divisors are {{EDOs|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, although its approximations have long been diluted by edo of this size. | |||
=== Odd harmonics === | === Odd harmonics === | ||
Revision as of 12:03, 15 June 2023
| ← 4171edo | 4172edo | 4173edo → |
Theory
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.
Subsets and supersets
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, although its approximations have long been diluted by edo of this size.
Odd harmonics
| 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) | |