Audio: invert (0:08)
An invert melody is a melody turned upside down.
Inverting a melody means making two decisions:
Choosing an axis about which to invert is a simple decision if you have already decided the key: invert about the tonic of the key.
You may have an original melodic idea which could be in a number of keys. This makes the choice more interesting. The original melodic idea is in the key of G mixolydian. As usual, the key signature is no help, because the writer has to decide the key. Since there are only 5 notes in the original idea, there are a lot of possible keys, not just G mixolydian but any of its 6 related modes including C major, or G major and any of its six related modes, or even G major pentatonic. The inverted melody will differ depending on which key is chosen, which all goes to show how tricky some things in music are.
The second issue is whether to invert diatonically or chromatically. Diatonic inversion means using the notes of a scale and inverting the degree. Chromatic inversion means inverting by interval which may, and usually does, change the key.
invert is diatonic inversion. The tonic note G, the first degree of the scale, remains unchanged. To invert a note diatonically, you determine which degree it is, and count that number down from the tonic. For example, B is the third degree in G mixolydian. The third degree below the tonic is the note E. The diatonic invert of note B is note E.
Chromatic inversion is the same as inversion by interval. To invert a note chromatically, you determine its interval above the tonic and invert it. For example, the note B in G mixolydian is a major third above the tonic. The inversion of a major third is a minor sixth. Eb is a minor sixth above G. The chromatic invert of B is Eb. You can also do this another way: the note B is four semitones above the tonic, the note Eb is four semitones below the tonic.
Invert melody is simple in principle, subtle in practice. It provides hours of harmless fun and, who knows, you might find something pleasing along the way.