Chapter V: Nonretrogradable Rhythms
Original: Pages 20–21 in Satterfield translation
Musical Examples:
Overview
This chapter develops the first of Messiaen's two central "impossibilities" announced in Chapter I—rhythmic structures that cannot be retrograded because they are palindromic, reading identically forwards and backwards. Building from the nonretrogradable fragment discovered within rāgavardhana (Chapter II), Messiaen systematizes the construction of temporal palindromes and establishes their crucial relationship to the modes of limited transposition. The chapter articulates the fundamental analogy undergirding his entire system: nonretrogradable rhythms realize in the horizontal (temporal) direction what modes of limited transposition realize in the vertical (pitch) direction—both are symmetrical structures whose internal organization prevents certain transformations, creating the "charm of impossibilities." This chapter also reveals Messiaen's theological aesthetic, arguing that these mathematical impossibilities produce perceptual effects of tonal ubiquity, temporal unity, and ultimately spiritual transcendence.