Chapter XVI: Modes of Limited Transpositions
Original: Pages 58–63 in Satterfield translation
Musical Examples: Examples 312–357 (46 examples)
Overview
Chapter XVI presents the theoretical foundation and practical application of Messiaen's most distinctive contribution to twentieth-century harmonic practice: the modes of limited transpositions. These symmetrical pitch collections, formed from repeating intervallic groups, exhibit the remarkable property that they cannot be transposed beyond a certain number of times without duplicating their original pitch content. Messiaen identifies seven such modes within the twelve-tone equal-tempered system and demonstrates their comprehensive use for both melodic and harmonic purposes. The chapter establishes fundamental connections between these modal structures and the nonretrogradable rhythms discussed earlier, revealing deep symmetries operating across both pitch and temporal domains. This system provides Messiaen with a harmonic language that exists outside traditional tonality while avoiding what he perceives as the excessive transposability and lack of character in other contemporary approaches.