# 15ed7/3

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Prime factorization
3 × 5
Step size
97.7914¢
Octave
12\15ed7/3 (1173.5¢) (→4\5ed7/3)
Twelfth
19\15ed7/3 (1858.04¢)
Consistency limit
3
Distinct consistency limit
3

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← 14ed7/3 | 15ed7/3 | 16ed7/3 → |

**15 equal divisions of 7/3** (abbreviated **15ed7/3**) is a nonoctave tuning system that divides the interval of 7/3 into 15 equal parts of about 97.8 ¢ each. Each step represents a frequency ratio of (7/3)^{1/15}, or the 15th root of 7/3.

## Intervals

Degrees | ed7/3 |
---|---|

1 | 97.7914 |

2 | 195.5828 |

3 | 293.3742 |

4 | 391.1656 |

5 | 488.957 |

6 | 586.7484 |

7 | 684.5398 |

8 | 782.33115 |

9 | 880.1225 |

10 | 977.9139 |

11 | 1075.7053 |

12 | 1173.4967 |

13 | 1271.2881 |

14 | 1369.0795 |

15 | 1466.8709 |

## Harmonics

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

Error | Absolute (¢) | -26.5 | -43.9 | +44.8 | -48.2 | +27.4 | -43.9 | +18.3 | +10.0 | +23.1 | -44.1 | +0.9 |

Relative (%) | -27.1 | -44.9 | +45.8 | -49.2 | +28.0 | -44.9 | +18.7 | +10.2 | +23.7 | -45.1 | +0.9 | |

Steps (reduced) |
12 (12) |
19 (4) |
25 (10) |
28 (13) |
32 (2) |
34 (4) |
37 (7) |
39 (9) |
41 (11) |
42 (12) |
44 (14) |

Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | -39.9 | +27.4 | +5.7 | -8.2 | -15.4 | -16.5 | -12.4 | -3.4 | +10.0 | +27.2 | +48.0 |

Relative (%) | -40.8 | +28.0 | +5.8 | -8.4 | -15.7 | -16.9 | -12.6 | -3.4 | +10.2 | +27.8 | +49.1 | |

Steps (reduced) |
45 (0) |
47 (2) |
48 (3) |
49 (4) |
50 (5) |
51 (6) |
52 (7) |
53 (8) |
54 (9) |
55 (10) |
56 (11) |