# 7edf

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Prime factorization
7 (prime)
Step size
100.279¢
Octave
12\7edf (1203.35¢)

(convergent)
Twelfth
19\7edf (1905.31¢)

(convergent)
Consistency limit
10
Distinct consistency limit
4

← 6edf | 7edf | 8edf → |

(convergent)

(convergent)

**7 equal divisions of the perfect fifth** (abbreviated **7edf** or **7ed3/2**) is a nonoctave tuning system that divides the interval of 3/2 into 7 equal parts of about 100 ¢ each. Each step represents a frequency ratio of (3/2)^{1/7}, or the 7th root of 3/2.

## Theory

7edf is related to 12edo, but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

Lookalikes: 12edo, 19ed3, 31ed6, 43ed12.

### Harmonics

Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +3.35 | +3.35 | +6.70 | +21.51 | +6.70 | +40.67 | +10.05 | +6.70 | +24.86 | -39.87 | +10.05 | -28.24 | +44.02 | +24.86 | +13.41 |

Relative (%) | +3.3 | +3.3 | +6.7 | +21.4 | +6.7 | +40.6 | +10.0 | +6.7 | +24.8 | -39.8 | +10.0 | -28.2 | +43.9 | +24.8 | +13.4 | |

Steps (reduced) |
12 (5) |
19 (5) |
24 (3) |
28 (0) |
31 (3) |
34 (6) |
36 (1) |
38 (3) |
40 (5) |
41 (6) |
43 (1) |
44 (2) |
46 (4) |
47 (5) |
48 (6) |

## Intervals

# | Cents | 12edo Notation |
---|---|---|

1 | 100.3 | C#, Db |

2 | 200.6 | D |

3 | 300.8 | D#, Eb |

4 | 401.1 | E |

5 | 501.4 | F |

6 | 601.7 | F#, Gb |

7 | 702.0 | G |

8 | 802.2 | G#, Ab |

9 | 902.5 | A |

10 | 1002.8 | A#, Bb |

11 | 1103.1 | B |

12 | 1203.4 | C |

13 | 1303.6 | C#, Db |

14 | 1403.9 | D |