1517edo
| ← 1516edo | 1517edo | 1518edo → |
1517 equal divisions of the octave (abbreviated 1517edo or 1517ed2), also called 1517-tone equal temperament (1517tet) or 1517 equal temperament (1517et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1517 equal parts of about 0.791 ¢ each. Each step represents a frequency ratio of 21/1517, or the 1517th root of 2.
1517edo is only consistent to the 5-odd-limit and the errors of both harmonics 3 and 5 are quite large. To start with, we may consider the patent val and 1517d val up to the 11-limit. Otherwise, it has a reasonable approximation to the 2.9.15.7.11.17 subgroup with optional additions of either 13 or 19.
For higher harmonics, the first 5 prime harmonics which are approximated below 25% are: 7, 11, 19, 23, 59. In the 2.7.11.19.23.59 subgroup, 1517edo has a comma basis {52877/52864, 157757/157696, 194672/194579, [18 -12 2 1 1 0⟩, [44 -4 -9 1 0 -1⟩}.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.307 | -0.289 | +0.192 | +0.177 | +0.033 | +0.342 | +0.195 | +0.252 | -0.084 | -0.115 | -0.193 |
| Relative (%) | -38.8 | -36.5 | +24.3 | +22.4 | +4.2 | +43.3 | +24.7 | +31.9 | -10.6 | -14.6 | -24.3 | |
| Steps (reduced) |
2404 (887) |
3522 (488) |
4259 (1225) |
4809 (258) |
5248 (697) |
5614 (1063) |
5927 (1376) |
6201 (133) |
6444 (376) |
6663 (595) |
6862 (794) | |
Subsets and supersets
Since 1517 factors into 37 × 41, 1517edo contains 37edo and 41edo as subsets.