539edo
| ← 538edo | 539edo | 540edo → |
539 equal divisions of the octave (abbreviated 539edo or 539ed2), also called 539-tone equal temperament (539tet) or 539 equal temperament (539et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 539 equal parts of about 2.23 ¢ each. Each step represents a frequency ratio of 21/539, or the 539th root of 2.
539edo is inconsistent to the 5-odd-limit. If harmonic 5 is used at all, the 539c val has better overall accuracy than the patent val. Meanwhile, the patent val tempers out the sensipent comma, 78732/78125, and provides the optimal patent val for the 5-limit sensipent temperament, tuning it more accurate than 65et by a tiny margin.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.656 | +1.070 | -0.366 | +0.914 | +0.816 | +1.031 | +0.414 | -0.317 | +0.817 | -1.022 | -0.445 |
| relative (%) | -29 | +48 | -16 | +41 | +37 | +46 | +19 | -14 | +37 | -46 | -20 | |
| Steps (reduced) |
854 (315) |
1252 (174) |
1513 (435) |
1709 (92) |
1865 (248) |
1995 (378) |
2106 (489) |
2203 (47) |
2290 (134) |
2367 (211) |
2438 (282) | |
Subsets and supersets
Since 539 factors into 72 × 11, 539edo has subset edos 7, 11, 49, and 77.