# 6edt

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Prime factorization
2 × 3
Step size
316.993¢
Octave
4\6edt (1267.97¢) (→2\3edt)
Consistency limit
7
Distinct consistency limit
2
Special properties

← 5edt | 6edt | 7edt → |

**6 equal divisions of the tritave**, **perfect twelfth**, or **3rd harmonic** (abbreviated **6edt** or **6ed3**), is a nonoctave tuning system that divides the interval of 3/1 into 6 equal parts of about 317 ¢ each. Each step represents a frequency ratio of 3^{1/6}, or the 6th root of 3.

## Theory

Since 6edt contains one interval of 2edt and two intervals of 3edt, it introduces 2 new notes unseen in previous edts. These new notes happen to approximate 6/5 and 5/2 very well, the former being only 1.351 cents sharp. 6edt is therefore the smallest edt other than 5edt to accurately approximate 5-limit harmony, as well as some elements from the 13-limit inherited from 3edt. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54...

### Harmonics

Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | -59 | +0 | -118 | -124 | -59 | +55 | -176 | +0 | -182 | +33 | -118 |

relative (%) | -15 | +0 | -31 | -32 | -15 | +14 | -46 | +0 | -48 | +9 | -31 | |

Steps (reduced) |
3 (3) |
5 (0) |
6 (1) |
7 (2) |
8 (3) |
9 (4) |
9 (4) |
10 (0) |
10 (0) |
11 (1) |
11 (1) |

## Intervals

Degrees | Cents | hekts | ApproximateRatios |
---|---|---|---|

0 | 1/1 | ||

1 | 316.993 | 216.667 | 6/5, 65/54 |

2 | 633.985 | 433.333 | 13/9 |

3 | 950.978 | 650 | 19/11, 26/15 |

4 | 1267.97 | 866.667 | 27/13 |

5 | 1584.963 | 1093.333 | 5/2 (5/4 plus an octave) |

6 | 1901.955 | 1300 | 3/1 |