# 15-odd-limit

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The **15-odd-limit** is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 15, once all powers of 2 are removed. To the 13-odd-limit, it adds 4 interval pairs involving 15.

Below is a list of all octave-reduced intervals in the 15-odd-limit. This collection of intervals has proven to be useful for illustrating certain characteristics of medium-sized EDOs (~15 to 41 steps).

- 1/1
**16/15, 15/8****15/14, 28/15**- 14/13, 13/7
- 13/12, 24/13
- 12/11, 11/6
- 11/10, 20/11
- 10/9, 9/5
- 9/8, 16/9
- 8/7, 7/4
**15/13, 26/15**- 7/6, 12/7
- 13/11, 22/13
- 6/5, 5/3
- 11/9, 18/11
- 16/13, 13/8
- 5/4, 8/5
- 14/11, 11/7
- 9/7, 14/9
- 13/10, 20/13
- 4/3, 3/2
**15/11, 22/15**- 11/8, 16/11
- 18/13, 13/9
- 7/5, 10/7

Ratio | Size (¢) | Color name | Name(s) | |
---|---|---|---|---|

16/15 | 111.731 | g2 | gu 2nd | classic diatonic semitone |

15/14 | 119.443 | ry1 | ruyo unison | septimal diatonic semitone |

15/13 | 247.741 | 3uy2 | thuyo 2nd | tridecimal supermajor second / tridecimal second-third |

15/11 | 536.951 | 1uy4 | luyo 4th | undecimal acute fourth |

22/15 | 663.049 | 1og5 | logu 5th | undecimal grave fifth |

26/15 | 952.259 | 3og7 | thogu 7th | tridecimal subminor seventh / tridecimal sixth-seventh |

28/15 | 1080.557 | zg8 | zogu octave | small septimal major seventh |

15/8 | 1088.269 | y7 | yo 7th | just major seventh |

The smallest EDO which is consistent in the 15-odd-limit is 29edo; that which is distinctly consistent in the same is 111edo.

## See also

- Arto and Tendo Theory
- Diamond15 – as a scale