An inversion of a chord is the removal of the root from the bass to an upper part (an octave higher).

 

Consider the C major triad C-E-G. In a first inversion the third becomes the bass (E-G-C or E-C-G). In a second inversion the fifth becomes the bass (G-E-C or G-C-E). Because the three notes have the same key-center and tonality, they have the same name (C major, in this case) but a different sound and sense of motion.

 

A third inversion is when in a four-note chord the fourth note becomes the bass. (For example, in the G-B-D-F, third inversions would be F-G-B-D and F-B-G-D.)

 

The inversion of an interval involves moving the lower note to an octave higher. For example, the inversion of the perfect fifth C-G results in the perfect fourth G-C. The rules for inverting intervals are:

 

Perfect intervals always invert to other perfect intervals.

Fourths and fifths invert to each other.

Major intervals and minor intervals invert to each other.

Thirds and sevenths always invert to each other.

Diminished and augmented intervals invert to each other, e.g. C-F♯ (augmented 4th) inverts to F♯-C (diminished 5th)