Relationship to Other Chapters

Chapter VI represents a synthetic culmination of the rhythmic section, integrating all previous techniques:

• Chapter II (Rāgavardhana): The complex polyrhythmic formulas employ principles derived from Hindu rhythm, and Examples 51–52 explicitly reference the Chapter V formula that itself derives from rāgavardhana analysis.

• Chapter III (Added Values): Added values appear throughout (marked by crosses), demonstrating that polyrhythmic textures incorporate this non-proportional transformation.

• Chapter IV (Augmented or Diminished Rhythms): Examples 40–42 superpose different augmentation/diminution forms; Examples 56–57 systematically employ all transformations from the Chapter IV table in canonic structure.

• Chapter V (Nonretrogradable Rhythms): Examples 43–48 incorporate nonretrogradable bass rhythms; Examples 58–59 create canons of nonretrogradable rhythms; Examples 60–62 employ nonretrogradable structures within rhythmic pedals.

• Chapter VII (Rhythmic Notations): The gathering-into-meter issue introduced here receives fuller treatment in Chapter VII.

• Chapters XIII–XIV (Harmony, Added Notes, Special Chords): Examples 43 and 60–62 demonstrate integration of rhythmic techniques with harmonic innovations (modes of limited transposition, added notes, appoggiatura chords).

• Chapter XIX (Polymodality): The polymodal textures in Examples 43 and 60–62 preview the systematic treatment of simultaneous modes in Chapter XIX. The analogy between polyrhythm and polymodality—both involving simultaneous independent layers—extends the parametric thinking established throughout the treatise.

The chapter also marks a transition from purely technical exposition to integrated musical examples showing how techniques combine in actual compositional practice. Examples 43 and 60–62 present substantial musical passages rather than isolated demonstrations, revealing how Messiaen's systematic innovations generate rich musical surfaces.