What is Retrograde Inversion?

Retrograde inversion is a contrapuntal technique in which a melody or musical theme is both inverted and reversed in order. This means that the intervals of the original melody are flipped in direction, and the resulting inverted melody is then played backward.

First, the melody undergoes inversion, where upward intervals become downward intervals of the same size and downward intervals become upward. After this inversion is created, the sequence of notes is then reversed, so the last note of the inverted melody becomes the first, and the first becomes the last.

Retrograde inversion is commonly used in fugue development, serial music, and twelve-tone composition, especially in the works of composers like Arnold Schoenberg and Anton Webern. The technique allows composers to create complex variations of a theme while maintaining a clear structural relationship to the original musical idea.