This document is for strictly personal use only. No public use may be made, including in the course of teaching, without the prior consent of the author.
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.
Be careful not to confuse the interval inversion with the change in direction of the interval (ascending to descending, for example).
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 |
Note that this table is symmetrical. The first 4 lines are enough to find the last 4 lines, since the intervals are complementary two by two. An inverted second gives a seventh, which inverted itself, gives back a second.
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).
It is sometimes more complicated to go through the inversion than to look directly for the initial interval. However, it is always useful to know how to do this gymnastics. This method allows you to check the result from another method. This method is also useful in the construction of chord inversions.
Last update on 2021/05/07
Printing for premium user only !
Print this course with a high quality layout by subscribing at www.musiclever.com