# 18edt

18edt means the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.

As the double of 9edt, it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like 8edt, is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.

step | cents | hekts | approximated interval |
---|---|---|---|

0 | 1/1 | ||

1 | 105.664 | 72.222 | 16/15 |

2 | 211.328 | 144.444 | 9/8 |

3 | 316.993 | 216.667 | 6/5 |

4 | 422.657 | 288.889 | 9/7 |

5 | 528.321 | 361.111 | 27/20 |

6 | 633.985 | 433.333 | 13/9 |

7 | 739.649 | 505.556 | 17/13 |

8 | 845.313 | 577.778 | 5/3 |

9 | 950.978 | 650 | 19/11 |

10 | 1056.642 | 722.222 | 9/5 |

11 | 1162.306 | 794.444 | 49/25 |

12 | 1267.97 | 866.667 | 27/13 |

13 | 1373.634 | 938.889 | 20/9 |

14 | 1479.298 | 1011.111 | 7/3 |

15 | 1584.963 | 1083.333 | 5/2 |

16 | 1690.627 | 1155.556 | 8/3 |

17 | 1806.291 | 1227.778 | 45/16 |

18 | 1901.955 | 1300 | 3/1 |