# 9edt

The **9 equal division of 3**, the tritave, divides it into 9 equal steps of size 211.328 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 interval for 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. On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. 9edt is the third no-twos zeta peak edt.

Following 4edt, this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to 7edo in diatonic music.

This scale is also related to 17edo by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1.

Steps | Size | Comparable intervals | |
---|---|---|---|

(in ¢) | in hekts | ||

0 | 1/1 | ||

1 | 211.328 | 144.444 | 9/8 (204) |

2 | 422.657 | 288.889 | 9/7 (435) |

3 | 633.985 | 433.333 | 13/9 (637) |

4 | 845.313 | 577.778 | 13/8 (841), 5/3 (884), 8/5 (814) |

5 | 1056.642 | 722.222 | 9/5 (1018), 11/6 (1049) |

6 | 1267.970 | 866.667 | 27/13 (1265) |

7 | 1479.298 | 1011.111 | 7/3 (1467) |

8 | 1690.627 | 1155.556 | 8/3 (1698) |

9 | 1901.955 | 1300 | 3/1 |