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# Interval inversion

To invert an interval consists to put an octave higher the interval lowest note. This gives a new interval, complementary to the first one.

## Principles

To invert an interval consists to put an octave higher the interval lowest note. **An interval and its inversion are complementary and always form an octave.**

## Name of an inverted interval

To find the name of the inverted interval, simply perform the following operation:
9 - *interval* = *inverted interval*.

For example, the inversion of a third is a sixth (9 - 3 = 6).

The following table summarizes the equivalences between interval and inversion.

Interval | Inversion |
---|---|

Unison | Octave |

Second | Seventh |

Third | Sixth |

Fourth | Fifth |

Fifth | Fourth |

Sixth | Third |

Seventh | Second |

Octave | Unison |

## Qualification of a inverted interval

The qualification of an inverted interval is always the opposite of the qualification of the original interval.

Qualification | Inversion qualification |
---|---|

Diminished | Augmented |

Minor | Major |

Perfect | Perfect |

Major | Minor |

Augmented | Diminished |

The interval D-C becomes C-D when inversed. The latter is a major second. The interval D-C is therefore a minor seventh (9 - 2 = 7, minor opposite to major).

The interval F-D becomes D-F when inversed. The latter is a major third. The interval F-D is therefore a minor sixth (9 - 3 = 6, minor opposite to major).

The interval C-G becomes G-C when inversed. The latter is a diminished fourth. The interval C-G is therefore an augmented fifth (9 - 4 = 5, augmented opposite to diminished).

Last update on 2021/05/07

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