# 539edo

← 538edo | 539edo | 540edo → |

^{2}× 11**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 2^{1/539}, 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 (%) | -29.5 | +48.1 | -16.4 | +41.0 | +36.6 | +46.3 | +18.6 | -14.2 | +36.7 | -45.9 | -20.0 | |

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 7^{2} × 11, 539edo has subset edos 7, 11, 49, and 77.