# 17ed4

Jump to navigation
Jump to search
Prime factorization
17 (prime)
Step size
141.176¢
Octave
9\17ed4 (1270.59¢)
Twelfth
13\17ed4 (1835.29¢)
Consistency limit
1
Distinct consistency limit
1

← 15ed4 | 17ed4 | 19ed4 → |

**17ed4** is the equal division of the double octave into 17 parts of 141.18 cents each, corresponding to 8.5edo or every second step of 17edo.

## Theory

17ed4 is the smallest ED4 to contain a diatonic fifth, in this case 17edo's sharp fifth, and it can be used to generate heptatonic (3L 4s<4/1>) and decatonic (7L 3s<4/1>) MOS scales with a period of 4/1. The decatonic scale is the more usable of these two scales, corresponding to an octave-repeating pentatonic scale in terms of step sizes, while the heptatonic scale has too large step sizes, corresponding to an octave-repeating tritonic or tetratonic scale in terms of step sizes.

## Intervals

# | Cents | Approximate ratios | 17edo notation | Diaquadic notation (J = 1/1) |
---|---|---|---|---|

0 | 0.00 | 1/1 | C | J |

1 | 141.18 | 13/12, 12/11, 14/13, 25/23 | C# | J#, Kb |

2 | 282.36 | 13/11, 7/6 | Eb | K |

3 | 423.54 | 32/25, 9/7, 14/11, 33/26, 23/18 | E | K#, Lb |

4 | 564.72 | 11/8, 18/13, 32/23 | ^F | L |

5 | 705.90 | 3/2, 32/21 | G | M |

6 | 847.08 | 13/8, 18/11, 23/14 | G#, vA | M#, Nb |

7 | 988.26 | 16/9, 7/4, 25/14, 44/25, 23/13 | Bb | N |

8 | 1129.44 | 25/13, 48/25, 27/14, 64/33, 23/12 | B | N#, Ob |

9 | 1270.62 | 15/7 | ^C | O |

10 | 1411.80 | 9/4, 16/7 | D | O#, Pb |

11 | 1552.98 | 12/5, 5/2 | vE | P |

12 | 1694.16 | 8/3 | F | Q |

13 | 1835.34 | 3/1 | F# | Q#, Rb |

14 | 1976.52 | 16/5 | ^G, Ab | R |

15 | 2117.70 | 10/3 | A | R#, Sb |

16 | 2258.88 | 11/3 | vB | S |

17 | 2400.00 | 4/1 | C | J |