Retrograde inversion
Retrograde and inversion combined.
What it means
Retrograde inversion is a transformation of a theme in which two procedures are combined: the sequence of pitches is read backward — that is the retrograde — and at the same time all the intervals are mirrored — that is the inversion. What went upward at the end in the original now stands at the beginning and goes downward.
Musical use
From this a single pitch sequence yields four basic shapes: the original, the inversion, the retrograde, and the retrograde inversion. All four preserve the distances between the notes but arrange them in a different direction and order. The kinship is easier to recognize with the eye in the notation than with the ear; the retrograde and the retrograde inversion in particular are often hardly audible as derivations of the original, because melodic shape arises above all from forward motion.
In the contrapuntal art of the late Middle Ages, the Renaissance, and the Baroque, these transformations belong to the stock of artful procedures, some of them laid out as puzzles. The mirror and crab canons of this period are built so that voices are obtained from a single notated line through transformation.
In the twentieth century the four shapes received new significance in twelve-tone technique, which uses a basic row of all twelve tones in exactly these four forms and their transpositions.
Retrograde inversion is to be distinguished from inversion alone, in which only the direction of the intervals is mirrored, and from the retrograde alone, in which only the order is reversed.
Retrograde inversion is one of the four basic shapes of a twelve-tone row, alongside the prime form, the retrograde, and the inversion. Each can be transposed to twelve pitch levels, so that 48 row forms result. In older counterpoint teaching it appears as a display piece in canons and fugues, for instance in the riddle canons of the Renaissance.
Performance practice
If you want to recognize retrograde inversions in a piece, first check the interval sequence backward and mirrored — the notation is more reliable here than the ear. Shape such passages not as a curiosity but as a musical line with a course of its own.