Summary

Chapter V develops the first of Messiaen's two central "impossibilities"—nonretrogradable rhythms—and establishes the fundamental analogy between temporal and pitch-class symmetries that structures his entire compositional system. By demonstrating that rhythmic palindromes cannot be retrograded (because they already contain their own retrograde within their structure) and connecting this temporal impossibility to the transpositional limitations of symmetrical pitch-class collections, Messiaen reveals the deep unity of his musical thinking. The chapter moves beyond technical instruction to articulate aesthetic and theological significance: these mathematical impossibilities produce perceptual effects of temporal unity and tonal ubiquity that, Messiaen argues, can lead listeners toward spiritual transcendence.

For contemporary readers, the chapter illustrates how symmetry can function as a primary compositional principle, how operations in different musical domains can be governed by parallel mathematical structures, and how technical innovation and spiritual expression can be integrated rather than opposed. The nonretrogradable rhythm becomes not merely a compositional technique but an embodiment of Messiaen's vision of music as existing outside normal temporal flow, suggesting the eternal through structures that possess no inherent temporal direction—music that begins and ends at the same moment, pointing beyond time toward the timeless.