# 8edt

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Prime factorization
2
Step size
237.744¢
Octave
5\8edt (1188.72¢)

(convergent)
Consistency limit
10
Distinct consistency limit
4

← 7edt | 8edt | 9edt → |

^{3}(convergent)

**8 equal divisions of the tritave** (**8edt**) is the nonoctave tuning system derived by dividing the tritave (3/1) into 13 equal steps of 237.744 cents each, or the eighth root of 3. As the double of 4edt, harmonically, it is the analog of 10edo for Lambda-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in 5edo.

What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically.

## Interval table

Steps | Cents | Approximate ratios |
---|---|---|

0 | 0 | 1/1, 49/48, 55/54, 56/55, 64/63, 81/80 |

1 | 237.744 | 7/6, 8/7, 9/8, 15/13, 52/45, 55/48, 55/49, 63/55, 64/55, 81/70 |

2 | 475.489 | 4/3, 13/10, 21/16, 35/26, 35/27, 55/42, 64/49, 72/55 |

3 | 713.233 | 3/2, 20/13, 32/21, 40/27, 49/32, 49/33, 52/35, 54/35, 55/36 |

4 | 950.978 | 7/4, 12/7, 26/15, 45/26, 55/32, 56/33 |

5 | 1188.72 | 2/1, 35/18, 39/20, 55/28, 63/32, 81/40 |

6 | 1426.47 | 9/4, 16/7, 30/13, 55/24, 78/35, 81/35 |

7 | 1664.21 | 8/3, 13/5, 18/7, 21/8, 55/21, 70/27 |

8 | 1901.96 | 3/1, 49/16, 55/18, 64/21, 80/27 |

## Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | -11 | +0 | +67 | -40 | -110 | +77 | +88 | -105 | +40 | +114 | -1 |

relative (%) | -5 | +0 | +28 | -17 | -46 | +32 | +37 | -44 | +17 | +48 | -1 | |

Steps (reduced) |
5 (5) |
8 (0) |
12 (4) |
14 (6) |
17 (1) |
19 (3) |
21 (5) |
21 (5) |
23 (7) |
25 (1) |
25 (1) |