# 789edo

← 788edo | 789edo | 790edo → |

**789 equal divisions of the octave** (abbreviated **789edo** or **789ed2**), also called **789-tone equal temperament** (**789tet**) or **789 equal temperament** (**789et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 789 equal parts of about 1.52 ¢ each. Each step represents a frequency ratio of 2^{1/789}, or the 789th root of 2.

789edo is notable for an extremely good approximation of the 2.5.7 subgroup, unbeaten until 3945edo. It also has a very accurate representation of the 17th harmonic and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

1578edo, which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong 11-limit and higher-limit system.

### Odd harmonics

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

Error | Absolute (¢) | +0.707 | -0.002 | -0.005 | -0.108 | -0.748 | +0.537 | +0.705 | -0.012 | +0.586 | +0.702 | -0.137 |

Relative (%) | +46.5 | -0.1 | -0.3 | -7.1 | -49.2 | +35.3 | +46.3 | -0.8 | +38.5 | +46.2 | -9.0 | |

Steps (reduced) |
1251 (462) |
1832 (254) |
2215 (637) |
2501 (134) |
2729 (362) |
2920 (553) |
3083 (716) |
3225 (69) |
3352 (196) |
3466 (310) |
3569 (413) |

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