Inversion and consonance · Music theory
Inverting intervals, compound intervals, consonances and dissonances, and enharmonic intervals.
Inversion
To invert an interval, move its lower note up an octave (or the upper note down an octave): C–E becomes E–C.
Three rules hold. An interval and its inversion add up to 9: a 3rd becomes a 6th, a 2nd becomes a 7th and a 4th, a 5th. Major becomes minor and minor, major. Augmented becomes diminished and diminished, augmented; perfect stays perfect.
It works as a shortcut: a 6th or a 7th is easy to classify by thinking of its inversion, the 3rd or the 2nd.
What it is for
Two intervals that invert into each other are complementary: together they complete an octave. That is why they share much of their sound: a major 3rd and a minor 6th have the same two notes in a different order. The idea also explains inverted chords, which keep their identity even when the bass note changes.
In calculation, it saves work with large intervals. To classify E–D, a 7th, you can think of D–E, a major 2nd: its inversion is a minor 7th.