# 131edo

← 130edo | 131edo | 132edo → |

**131 equal divisions of the octave** (abbreviated **131edo**), or **131-tone equal temperament** (**131tet**), **131 equal temperament** (**131et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 131 equal parts of about 9.16 ¢ each. Each step of 131edo represents a frequency ratio of 2^{1/131}, or the 131st root of 2.

## Theory

131edo is the next EDO, after 81edo, on the "Golden Tone System" (Das Goldene Tonsystem) of Thorvald Kornerup, using the 131b val. The patent val has a fifth sharp by 3.389 cents rather than flat like the meantone fifth; rather than tempering out 81/80 it tempers out the immunity comma, 1638400/1594323. In the 7-limit it tempers out 3125/3087 and 245/243, so that it supports bophier temperament.

131edo is the 32nd prime EDO.

Harmonic | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +3.39 | -1.58 | +2.17 | -1.70 | +2.22 | -4.19 | -4.38 | +3.79 | -3.62 | +0.00 | -4.02 |

relative (%) | +37 | -17 | +24 | -19 | +24 | -46 | -48 | +41 | -40 | +0 | -44 | |

Steps (reduced) |
208 (77) |
304 (42) |
368 (106) |
453 (60) |
485 (92) |
535 (11) |
556 (32) |
593 (69) |
636 (112) |
649 (125) |
682 (27) |

**Some MOS Scales in 131-EDO:**

33 16 33 33 16 | Pentatonic (comparable with 8edo and 99edo) |

23 23 8 23 23 23 8 | Pythagorean tuning (comparable with 17edo) |

21 21 13 21 21 21 13 | Meantone tuning (comparable with 50edo) |

19 12 19 19 12 19 19 12 | Father Tuning (comparable with 55edo) |

18 18 18 18 18 18 18 5 | Porcupine Tuning (comparable with 29edo and 80edo) |

17 17 17 6 17 17 17 17 6 | Superdiatonic tuning (comparable with 23edo) |

16 16 16 16 16 16 16 16 3 | Bohpier tuning (comparable with 41edo) |

13 13 9 13 13 13 9 13 13 13 9 | Sensi-11 Tuning |

11 11 11 11 11 5 11 11 11 11 11 11 5 | De Vries 13-tone Tuning |

10 10 10 7 10 10 10 10 7 10 10 10 10 7 | Ketradektriatoh Tuning |

21 17 21 17 17 21 17 | mohaha7 |

4 17 17 17 4 17 17 4 17 17 | mohaha10 |