# 17-limit

In 17-limit Just Intonation, all ratios in the system will contain no primes higher than 17. The 17-limit adds to the 13-limit a "minor ninth" of about 105¢ -- 17/16 -- and several other intervals between the 17th overtone and the lower ones.

The 17-prime-limit can be modeled in a 6-dimensional lattice, with the primes 3, 5, 7, 11, 13, and 17 represented by each dimension. The prime 2 does not appear in the typical 17-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, a seventh dimension is need.

EDOs which provides an excellent tuning for 17-limit intervals are: 46, 58, 72, 80, 94, 111, 121, 149, 159, 183, 217, 253, 270, 282, 301, 311, 320, 354, 364, 383, 388, 400, 414, 422, 436, 441, 460, 494, 525, 535, 581, 597, 615, 624, 639, 643, 653, 684, 692, 718, 742, 764, 771, 776, 814, 860, 867, 882, 894, 908, 925, 935, 954, 981, 995, and 997 among others.

## 17-limit Intervals

Here are all the 21-odd-limit intervals of 17:

Ratio | Cents Value | Color Name | Name | |
---|---|---|---|---|

18/17 | 98.955 | 17u1 | su unison | small septendecimal semitone |

17/16 | 104.955 | 17o2 | so 2nd | large septendecimal semitone |

17/15 | 216.687 | 17og3 | sogu 3rd | septendecimal whole tone |

20/17 | 281.358 | 17uy2 | suyo 2nd | septendecimal minor third |

17/14 | 336.130 | 17or3 | soru 3rd | septendecimal supraminor third |

21/17 | 365.825 | 17uz3 | suzo 3rd | septendecimal submajor third |

22/17 | 446.363 | 17u1o3 | sulo 3rd | septendecimal supermajor third |

17/13 | 464.428 | 17o3u4 | sothu 4th | septendecimal sub-fourth |

24/17 | 597.000 | 17u4 | su 4th | lesser septendecimal tritone |

17/12 | 603.000 | 17o5 | so 5th | greater septendecimal tritone |

26/17 | 735.572 | 17u3o5 | sutho 5th | septendecimal super-fifth |

17/11 | 753.637 | 17o1u6 | solu 6th | septendecimal subminor sixth |

34/21 | 834.175 | 17uz6 | suzo 6th | septendecimal superminor sixth |

28/17 | 863.870 | 17uz6 | suzo 6th | septendecimal submajor sixth |

17/10 | 918.642 | 17og7 | sogu 7th | septendecimal major sixth |

30/17 | 983.313 | 17uy6 | suyo 6th | septendecimal minor seventh |

32/17 | 1095.045 | 17u7 | su 7th | small septendecimal major seventh |

17/9 | 1101.045 | 17o8 | so octave | large septendecimal major seventh |

To avoid confusion with the solfege syllable So, the so 2nd, 5th and 8ve are sometimes called the iso 2nd, 5th and 8ve.