# 590edo

← 589edo | 590edo | 591edo → |

**590 equal divisions of the octave** (abbreviated **590edo** or **590ed2**), also called **590-tone equal temperament** (**590tet**) or **590 equal temperament** (**590et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 590 equal parts of about 2.03 ¢ each. Each step represents a frequency ratio of 2^{1/590}, or the 590th root of 2.

590edo has the same tuning as the 118edo in the 5-limit and provides a good correction for the harmonics 7, 11, and 13, altogether being consistent in the 15-odd-limit. Among the 118th-octave temperaments, it by definition tunes parakleischis as well as centenniamajor in the 590ee val.

Besides that, it is a tuning for the quintaschis temperament in the 7-limit.

### Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +0.000 | -0.260 | +0.127 | -0.690 | -0.132 | -0.528 | +0.807 | -0.564 | +0.200 | -0.425 | +0.049 |

Relative (%) | +0.0 | -12.8 | +6.2 | -33.9 | -6.5 | -25.9 | +39.7 | -27.7 | +9.8 | -20.9 | +2.4 | |

Steps (reduced) |
590 (0) |
935 (345) |
1370 (190) |
1656 (476) |
2041 (271) |
2183 (413) |
2412 (52) |
2506 (146) |
2669 (309) |
2866 (506) |
2923 (563) |

### Subsets and supersets

Since 590 factors into 2 × 5 × 59, 590edo has subset edos 2, 5, 10, 59, 118, and 295.