Relationship to Other Chapters

Chapter XIX synthesizes concepts from throughout the treatise, particularly the entire harmonic section (Chapters XIII–XVIII). The modes of limited transpositions established in Chapter XVI provide the foundation, with their characteristic intervallic structures and limited transposability enabling polymodal combinations that maintain coherence rather than dissolving into chromaticism. The modulation techniques from Chapter XVII (modulation of modes to themselves or to other modes) extend to polymodal contexts, where multiple modal layers undergo transformation simultaneously or independently. The distinction from polytonality articulated in Chapter XVIII finds practical demonstration—the polymodal combinations create unified harmonic fields rather than conflicting tonal centers, the "modal force" absorbing potential polytonal implications.

The integration of polymodality with rhythmic techniques pervades the chapter: pedal groups from Chapter XV function polymodally (Examples 302, 371), rhythmic canons from Chapter VI appear in polymodal contexts (Example 49), added values and rhythmic preparation from Chapter III coordinate with polymodal modulation (Examples 14, 376, 379), and polyrhythm from Chapter VI combines with polymodality (Example 43). This demonstrates Messiaen's fundamental compositional principle: all musical parameters—rhythm, melody, harmony—operate according to parallel organizational principles, creating multi-dimensional structural coherence. The frequent references to actual compositions (Les sons impalpables du rêve, Action de grâces, l'Ange aux parfums, Cloches d'angoisse et larmes d'adieu) show how polymodality functions in practical compositional contexts rather than remaining merely theoretical possibility.