Retrograde Rhythms

Definition: The temporal reversal of a rhythmic pattern, reading from right to left what would normally be read from left to right, creating an inversion in the temporal domain analogous to horizontal reflection.

Messiaen's Treatment: Messiaen begins by establishing retrograde as a standard contrapuntal procedure that, when applied to rhythm alone, produces curious value reversals. Example 28 presents a complex rhythmic formula combining augmented rhythms, added values, inexact augmentations and diminutions, and interpretation of rāgavardhana—a typical instance of his rhythmic practice incorporating multiple techniques simultaneously. The total duration spans thirteen quarter-notes (a prime number). Within this formula, all fragment B elements represent diminution or augmentation of fragment A elements, and added values appear at cross markings.

Example 29 demonstrates the formula's retrograde: the order of values completely reverses, with diminutions becoming augmentations and vice versa. This transformation illustrates that retrograde operation on complex rhythms produces substantial reorganization—what was initially a diminution of some element becomes an augmentation in retrograde form, creating a new rhythmic character while preserving (in reverse) the original's durational sequence.

Messiaen notes that Chapter VI will explore superposition of a rhythm upon its retrograde, creating a particular species of polyrhythmic texture where forward and backward versions of the same material sound simultaneously.

Modern Context: Retrograde represents one of the classical contrapuntal transformations, historically applied primarily to pitch sequences (cancrizans or crab canon) but applicable to any ordered sequence. Contemporary music theory recognizes retrograde as a member of the standard transformational set: transposition (T), inversion (I), retrograde (R), and retrograde-inversion (RI).

In twelve-tone technique, retrograde forms are systematically catalogued in the tone row matrix alongside prime, inversion, and retrograde-inversion forms. Messiaen's application of retrograde to rhythm alone—independent of pitch retrograde—represents a parametric separation characteristic of his approach: each musical dimension (rhythm, pitch, harmony) can undergo independent transformations.

The observation that retrograde operation reverses augmentation/diminution relationships has implications for rhythmic perception: retrograded rhythms may sound qualitatively different even when their durational sequences are preserved (in reverse order), since the temporal trajectory—whether values are expanding or contracting—affects perception of phrase shape and direction.

Examples: Examples 28–29 demonstrate a complex rhythmic formula and its retrograde.