Summary

Chapter XVI presents Messiaen's modes of limited transpositions as mathematically closed systems of symmetrical pitch collections that can only be transposed a limited number of times before reproducing their original content. Seven such modes exist within twelve-tone equal temperament: the whole-tone scale (Mode 1, transposable twice), the octatonic collection (Mode 2, transposable three times), a nine-note collection (Mode 3, transposable four times), and four hexachordal modes (Modes 4–7, each transposable six times). Messiaen demonstrates comprehensive melodic and harmonic applications of these modes, showing how they generate characteristic sonorities while existing "in the atmosphere of several tonalities" without committing to any single tonal center. The profound connection established between these modes and the nonretrogradable rhythms of Chapter V reveals symmetry as the fundamental organizational principle unifying all dimensions of Messiaen's musical language, creating what he describes as a "theological rainbow"—a compositional system reflecting divine order and eternal truth. The modes provide Messiaen with a distinctive harmonic vocabulary that avoids both traditional tonality and what he perceives as the excessive transposability of other contemporary approaches, establishing the foundation for all subsequent harmonic discussions in the treatise.