Summary

Chapter VI synthesizes the preceding rhythmic chapters, demonstrating how added values, augmentation/diminution, nonretrogradable structures, and canonic imitation combine to create complex polyrhythmic textures. By systematically exploring superposition of rhythms of unequal length, rhythms at different time-scales, rhythms and their retrogrades, and various canonic structures, Messiaen constructs a comprehensive polyrhythmic practice. The introduction of rhythmic pedal—patterns repeating ostinato-fashion independent of surrounding rhythmic activity—establishes the concept that will find harmonic parallel in polymodality (Chapter XIX), demonstrating the parametric analogies governing his entire system.

The chapter's examples progress from simple two-layer polyrhythms through increasingly complex multi-dimensional structures where rhythm, melody, and harmony operate with independent periodicities, creating temporal stratification characteristic of Messiaen's mature style. The acknowledgment of notational tension—that complex polyrhythms often require "gathering into meter" despite their ametric conception—reveals practical compromises between theoretical innovation and performative reality.

For contemporary readers, this chapter illustrates how systematic combination of relatively simple techniques (adding values, scaling proportions, palindromic construction, canonic imitation) can generate extraordinary rhythmic complexity, and how parametric independence (each musical dimension operating according to its own logic) creates rich, multi-layered textures. The rhythmic pedal concept, with its disproportion between melodic, rhythmic, and harmonic periodicity, represents a distinctively modern approach to musical texture—stratified, non-hierarchical, and resistant to unified metric reduction. Together with the preceding five chapters, Chapter VI completes Messiaen's rhythmic system: a comprehensive toolkit for generating precise, complex, ametric temporal organization through systematic procedures rather than intuitive improvisation.