In music, the inversion means placing the lower note of a group one octave higher or the higher note an octave lower.

## Inversion of Intervals

Inversion of an interval means placing the lower note of an interval one octave higher or the higher note an octave lower. When we invert the intervals, we also change their quality (except perfect intervals) and quantity of them. For example, let’s say we have a major second interval between C and D.

If we place the lower note C, one octave higher, we invert this interval. The new interval between D and C is a minor seventh. Let’s see another example.

In this example, we have a perfect fourth interval between G and C. This time, let’s invert this interval by placing the higher note C an octave lower. The new interval between C and G is a perfect fifth. Notice that when we invert a perfect interval, we don’t change its quality. The inverted interval is still a perfect interval.

### Quantity Change

As you may notice from the previous examples, the interval number and the number of its inversion always add up to nine. For example, a perfect fourth interval becomes a perfect fifth interval when we invert it. 4+5=9. For example, a minor third interval becomes a major sixth interval when we invert it. 3+6=9.

You may wonder why it adds up to nine instead of eight. Because we count the note we don’t move twice. Let’s look at this example again.

There are two notes between C-D major second and those are C and D. When we invert it by placing C an octave higher, the new interval will be the D-C minor seventh. There are seven notes between D and C and those are D, E, F, G, A, B, and C. So these two intervals have nine notes in total. D is the note that we haven’t moved and notice that both intervals have D. So we count it twice.

Let’s see what happens the quantity of all intervals when we invert them in a table.

INTERVAL BEFORE INVERSION | INTERVAL AFTER INVERSION |
---|---|

Unison | Octave |

2nd | 7th |

3rd | 6th |

4th | 5th |

5th | 4th |

6th | 3rd |

7th | 2nd |

Octave | Unison |

### Quality Change

When we invert an interval, we also change the quality of that interval except for perfect intervals. When we invert a perfect interval, the new interval will be a perfect interval too. The inversion of a major interval is a minor interval and vice versa. The inversion of an augmented interval is a diminished interval and vice versa. Let’s see this in a table.

INTERVAL BEFORE INVERSION | INTERVAL AFTER INVERSION |
---|---|

Perfect | Perfect |

Major | Minor |

Minor | Major |

Augmented | Diminished |

Diminished | Augmented |

### Inversion of Compound Intervals

Since compound intervals are larger than an octave, the inversion of any compound interval is always the same as the inversion of the simple interval from which it is compounded. For example, let’s say we have a major ninth interval between C and D.

If we invert this interval by placing the lower note C an octave higher, the new interval will be a minor seventh between D and C. Notice that inverting a major ninth between C and D is basically same as inverting a major second between C and D. Because a major ninth is compounded from a major second.

Notice that here we moved C two octaves higher. Because when we invert an interval lower notes should be higher and vice versa.

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