Reference

Inversion of Intervals

To invert an interval, place the lower note one octave higher or the highest note an octave lower:

In the following tables you can see how an interval is transformed when inverted:

Interval: after inversion
becomes:

2^nd 7^th

3^rd 6^th

4^th 5^th

5^th 4^th

6^th 3^rd

7^th 2^nd

Interval quality: after inversion becomes:

major minor

minor major

augmented diminished

diminished augmented

perfect perfect

The inversion of intervals is very useful in analyzing sixths and sevenths. See Identifying Intervals by Using Inversions.