# 19ed11/5

← 18ed11/5 | 19ed11/5 | 20ed11/5 → |

**19 equal divisions of 11/5** (abbreviated **19ed11/5**) is a nonoctave tuning system that divides the interval of 11/5 into 19 equal parts of about 71.8 ¢ each. Each step represents a frequency ratio of (11/5)^{1/19}, or the 19th root of 11/5.

19ed11/5 fails to produce acceptable approximations of any small harmonics. However, it does approximate harmonics 7, 8 and 9 very well.

19ed11/5 tempers out the septimal comma, 64/63.

Using 3 steps of 19ed11/5 (215.527 cents) as a generator, and 47 steps of 19ed11/5 (3376.589) as a period, you get the 7.8.9 regular temperament with the lowest badness using x31eq's default parameters, Sixscared.

You could, then, approach 19ed11/5 as a Sixscared[47] scale.

Sixscared doesn't have any useful small MOS scales, so a more viable approach to composing with 19ed11/5 may be to use a MODMOS of Sixscared[5], [6], [7] or [8]. Another approach might be to use a small subset of tones from Sixscared[15] or [16].

## Intervals

Steps | Cents | Approximate Ratios |
---|---|---|

0 | 0 | 1/1 |

1 | 71.842 | 23/22, 24/23 |

2 | 143.685 | 12/11, 13/12, 14/13 |

3 | 215.527 | 17/15 |

4 | 287.369 | 13/11 |

5 | 359.212 | 21/17 |

6 | 431.054 | 14/11 |

7 | 502.896 | |

8 | 574.739 | 7/5 |

9 | 646.581 | 19/13 |

10 | 718.423 | |

11 | 790.266 | 11/7, 19/12 |

12 | 862.108 | 23/14 |

13 | 933.95 | 12/7, 19/11 |

14 | 1005.793 | |

15 | 1077.635 | 13/7, 24/13 |

16 | 1149.477 | |

17 | 1221.32 | |

18 | 1293.162 | 23/11 |

19 | 1365.004 | 11/5, 24/11 |

## Harmonics

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

Error | Absolute (¢) | +21.3 | -34.1 | -29.2 | +15.5 | -12.7 | +7.8 | -7.9 | +3.7 | -35.0 | +15.5 | +8.6 |

Relative (%) | +29.7 | -47.4 | -40.6 | +21.6 | -17.7 | +10.8 | -11.0 | +5.2 | -48.7 | +21.6 | +11.9 | |

Steps (reduced) |
17 (17) |
26 (7) |
33 (14) |
39 (1) |
43 (5) |
47 (9) |
50 (12) |
53 (15) |
55 (17) |
58 (1) |
60 (3) |

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

Error | Absolute (¢) | +13.7 | +29.1 | -18.5 | +13.4 | -19.7 | +25.1 | +3.3 | -13.7 | -26.3 | -35.0 | +31.7 |

Relative (%) | +19.1 | +40.5 | -25.8 | +18.7 | -27.4 | +34.9 | +4.6 | -19.0 | -36.6 | -48.7 | +44.2 | |

Steps (reduced) |
62 (5) |
64 (7) |
65 (8) |
67 (10) |
68 (11) |
70 (13) |
71 (14) |
72 (15) |
73 (16) |
74 (17) |
76 (0) |