# 578edo

← 577edo | 578edo | 579edo → |

^{2}**578 equal divisions of the octave** (abbreviated **578edo** or **578ed2**), also called **578-tone equal temperament** (**578tet**) or **578 equal temperament** (**578et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 578 equal parts of about 2.08 ¢ each. Each step represents a frequency ratio of 2^{1/578}, or the 578th root of 2.

578edo is enfactored in the 5-limit, tempering out 32805/32768 (schisma) with the same tuning as 289edo. It tempers out 118098/117649 (stearnsma) which together with the schisma gives 7-limit pogo temperament, the 224 & 354 temperament. In the 11-limit it tempers out 540/539 and 4000/3993 and provides the optimal patent val for 11-limit pogo and the planar temperament hades, as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079, and provides the optimal patent val for 13-limit pogo.

### Prime harmonics

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

Error | Absolute (¢) | +0.000 | -0.225 | -0.155 | +0.724 | +0.931 | +0.303 | +0.927 | -0.627 | +0.791 | +0.181 | +0.985 |

Relative (%) | +0.0 | -10.8 | -7.4 | +34.9 | +44.9 | +14.6 | +44.6 | -30.2 | +38.1 | +8.7 | +47.5 | |

Steps (reduced) |
578 (0) |
916 (338) |
1342 (186) |
1623 (467) |
2000 (266) |
2139 (405) |
2363 (51) |
2455 (143) |
2615 (303) |
2808 (496) |
2864 (552) |

### Subsets and supersets

578 factors as 2 × 17^{2}, with divisors 2, 17, 34, and 289.