Inversion of Intervals


An earlier tutorial showed how the distance between two notes (called an interval) can be named depending on its size (i.e. the number of semitones between the notes). For example, an interval of 7 semitones can be called a "perfect fifth", such as the interval between C and G:

Perfect 5th

However, it is not totally correct to say that the interval between C and G will always be 7 semitones, a perfect fifth. This is only true where C is the lower of the two notes. The interval may be inverted by moving C up by an octave (or, conversely, moving G down by an octave):

Perfect 4th

This interval is a perfect fourth, 5 semitones.

Bear in mind here that we are talking only about moving pairs of notes around within the octave, not extending an interval beyond an octave by moving the higher note up by 12 semiones, or the lower note down by 12 semitones. Such extended intervals will be the subject of a future tutorial.

The following table shows the intervals within an octave, with their inversions. Note that when the size of the first interval increases, the size of the inverted interval decreases. NB, the interval of a diminished fifth contains the same number of semitones as its inversion, an augmented fourth.

0 / 12 semitones Unison / Perfect Octave
1 / 11 semitones Minor 2nd / Major 7th
2 / 10 semitones Major 2nd / Minor 7th
3 / 9 semitones Minor 3rd / Major 6th
4 / 8 semitones Major 3rd / Minor 6th
5 / 7 semitones Perfect 4th / Perfect 5th
6 / 6 semitones Diminished 5th / Augmented 4th
7 / 5 semitones Perfect 5th / Perfect 4th
8 / 4 semitones Minor 6th / Major 3rd
9 / 3 semitones Major 6th / Minor 3rd
10 / 2 semitones Minor 7th / Major 2nd
11 / 1 semitones Major 7th / Minor 2nd


It really is worth taking some time to get comfortable with the concepts discussed here. In particular, it will make life a lot easier for you when you come to consider chord construction.

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