1015edo
| ← 1014edo | 1015edo | 1016edo → |
1015 equal divisions of the octave (abbreviated 1015edo or 1015ed2), also called 1015-tone equal temperament (1015tet) or 1015 equal temperament (1015et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1015 equal parts of about 1.18 ¢ each. Each step represents a frequency ratio of 21/1015, or the 1015th root of 2.
1015edo is consistent in the 5-odd-limit, where it tunes quintosec. It also tunes the 2.3.5.11 subgroup natural extension for quintosec tempering out 5632/5625 and 26214400/26198073, despite not being consistent. The patent val also tempers out 3025/3024 and tunes the ganesha temperament in the 11-limit.
Aside from the patent val, there is a number of other mappings to be considered. For example, 1015edo is an excellent 2.5/3.9/7.13 subgroup tuning. 1015d val tunes supermajor.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.311 | +0.287 | -0.550 | -0.560 | -0.382 | +0.063 | -0.584 | +0.266 | +0.418 | -0.239 | -0.491 |
| Relative (%) | +26.3 | +24.3 | -46.5 | -47.4 | -32.3 | +5.4 | -49.4 | +22.5 | +35.4 | -20.2 | -41.5 | |
| Steps (reduced) |
1609 (594) |
2357 (327) |
2849 (819) |
3217 (172) |
3511 (466) |
3756 (711) |
3965 (920) |
4149 (89) |
4312 (252) |
4458 (398) |
4591 (531) | |
Subsets and supersets
Since 1015 factors as 5 × 7 × 29, 1015edo has subset edos 1, 5, 7, 29, 35, 145, 203.