# Meantone intervals

This table shows all the simple intervals of POTE septimal meantone, which includes the entire 7-limit tonality diamond. Other relevant tables of meantone intervals are the table of quarter-comma meantone intervals and the table of 31 edo intervals.

In 12edo the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.

In 19edo, in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.

More complex meantone tunings such as 31edo distinguish all intervals listed on this table.

See also Wikipedia: List of meantone intervals

Name | Size | Ratios |
---|---|---|

Unisons | ||

Perfect unison (P1) | 0.0 | 1/1 |

Augmented unison (A1) | 75.5 | 28/27~25/24~21/20 |

Seconds | ||

Diminished second (d2) | 42.0 | 128/125~64/63~50/49~36/35 |

Minor second (m2) | 117.5 | 16/15~15/14 |

Major second (M2) | 193.0 | 10/9~9/8~28/25 |

Augmented second (A2) | 268.5 | 7/6 |

Thirds | ||

Diminished third (d3) | 235.0 | 8/7 |

Minor third (m3) | 310.5 | 6/5 |

Major third (M3) | 386.0 | 5/4 |

Augmented third (A3) | 461.5 | 21/16 |

Fourths | ||

Double diminished fourth (dd4) | 352.5 | Close to 11/9 |

Diminished fourth (d4) | 428.0 | 9/7 (a bit 14/11-ish) |

Perfect fourth (P4) | 503.5 | 4/3 |

Augmented fourth (A4) | 579.0 | 7/5 |

Double augmented fourth (AA4) | 654.5 | Close to 16/11 |

Fifths | ||

Double diminished fifth (dd5) | 545.5 | Close to 11/8 |

Diminished fifth (d5) | 621.0 | 10/7 |

Perfect fifth (P5) | 696.5 | 3/2 |

Augmented fifth (A5) | 772.0 | 14/9 (a bit 11/7-ish) |

Double augmented fifth (AA5) | 847.5 | Close to 18/11 |

Sixths | ||

Diminished sixth (d6) | 738.5 | 32/21 |

Minor sixth (m6) | 814.0 | 8/5 |

Major sixth (M6) | 889.5 | 5/3 |

Augmented sixth (A6) | 965.0 | 7/4 |

Sevenths | ||

Diminished seventh (d7) | 931.5 | 12/7 |

Minor seventh (m7) | 1007.0 | 16/9~9/5~25/14 |

Major seventh (M7) | 1082.5 | 15/8~28/15 |

Augmented seventh (A7) | 1158.0 | 35/18~49/25~63/32 |

Octaves | ||

Diminished octave (d8) | 1124.5 | 27/14~48/25~40/21 |

Perfect octave (P8) | 1200.0 | 2/1 |

Augmented octave (A8) | 1275.5 | 25/12~21/10 |