# Intervals of Negri-9

This is one possible naming system, suggested by Ray Perlner, for intervals of negri temperament based on the negri[9] scale. The names of intervals are chosen to give intuition for those used to diatonic interval naming conventions, even when this results in a slight abuse of notation. For example, 3 step intervals are called "ditones", not because the true ditone of 81/64 would be rendered as such (this system would refer to the interval mapping to 81/64 as a doubly augmented semifourth), but because the "ditones" which appear naturally in the negri[9] MOS scale are either a little larger (major) or a little smaller (minor) than a true ditone. 3-limit intervals, and intervals that divide 3-limit intervals exactly in half are referred to as "perfect" regardless of how commonly they occur in the MOS scale.

Name | Size* | Ratio | No. of Negri Generators(~125.6¢) | Comments |
---|---|---|---|---|

Unisons | ||||

Perfect unison (P1) | 0 | 1/1 | 0 | |

Augmented unison (A1) | 69.9 | 36/35~21/20~27/26 | -9 | |

Seconds | ||||

Diminished second (d2) | 55.7 | 25/24~28/27~50/49~64/63 | 10 | "Negri[10] Chroma" |

Minor second (m2) | 125.6 | 16/15~15/14~14/13~13/12 | 1 | |

Major second (M2) | 195.5 | 9/8 | -8 | Also "major wholetone" |

Semifourths | ||||

Diminished semifourth (d2.5) | 181.2 | 10/9 | 11 | Also "minor wholetone" |

Perfect semifourth (P2.5) | 251.1 | 8/7~7/6~15/13 | 2 | |

Augmented semifourth (A2.5) | 321.0 | 6/5 | -7 | Also "minor third" |

Ditones | ||||

Minor ditone (m3.3) | 376.7 | 5/4~16/13 | 3 | Also "major third" |

Major ditone (M3.3) | 446.6 | 9/7~13/10 | -6 | Also "supermajor third" |

Fourths | ||||

Perfect fourth (P4) | 502.3 | 4/3 | 4 | |

Augmented fourth (A4) | 572.2 | 7/5~18/13 | -5 | |

Fifths | ||||

Diminished fifth (d5) | 628.8 | 10/7~13/9 | 5 | Also "supermajor fourth" |

Perfect fifth (P5) | 697.7 | 3/2 | -4 | |

Tetratones | ||||

Minor tetratone (m5.7) | 753.4 | 14/9~20/13 | 6 | Also "subminor sixth" |

Major tetratone (M5.7) | 813.5 | 8/5 | -3 | Also "minor sixth" |

Semitwelfths | ||||

diminished semitwelfth (d6.5) | 879.0 | 5/3 | 7 | Also "major sixth" |

Perfect semitwelfth (P6.5) | 948.9 | 7/4~12/7~26/15 | -2 | Also "supermajor sixth" |

Augmented semitwelfth (A6.5) | 1017.8 | 9/5 | -11 | Also "just minor seventh" |

Sevenths | ||||

Minor seventh (m7) | 1004.5 | 16/9 | 8 | Also "Pythagorean minor 7th" |

Major seventh (M7) | 1074.4 | 15/8~13/7~28/15~24/13 | -1 | |

Augmented seventh (A7) | 1144.3 | 48/25~27/14~49/25~63/32 | -10 | |

Octaves | ||||

Diminished octave (d8) | 1130.1 | 35/18~40/21~52/27 | 9 | |

Perfect octave (P8) | 1200 | 2/1 | 0 | |

Augmented octave (A8) | 1269.9 | 72/35~21/10~27/13 | -9 |

- In POTE 11-limit porcupine