# 90edo

← 89edo | 90edo | 91edo → |

^{2}× 5**90 equal divisions of the octave** (abbreviated **90edo**), or **90-tone equal temperament** (**90tet**), **90 equal temperament** (**90et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 90 equal parts of about 13.3 ¢ each. Each step of 90edo represents a frequency ratio of 2^{1/90}, or the 90th root of 2.
It tempers out 2048/2025 in the 5-limit, 3125/3087 and 245/243 in the 7-limit, 121/120 and 176/175 in the 11-limit, and 275/273 and 169/168 in the 13-limit. It provides the optimal patent val for the 31&90 temperament in the 7-, 11- and 13-limits. Notably, it is the second lowest in a series of four consecutive EDOs to temper out 117440512/117406179.

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +4.71 | +0.35 | +4.51 | -3.91 | -4.65 | -0.53 | +5.06 | +1.71 | -4.18 | -4.11 | -1.61 |

relative (%) | +35 | +3 | +34 | -29 | -35 | -4 | +38 | +13 | -31 | -31 | -12 | |

Steps (reduced) |
143 (53) |
209 (29) |
253 (73) |
285 (15) |
311 (41) |
333 (63) |
352 (82) |
368 (8) |
382 (22) |
395 (35) |
407 (47) |

## Interval table

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