Relationship to Other Chapters

Chapter III occupies a central position in Messiaen's rhythmic theory and extends its influence into harmonic domains:

• Chapter I (Charm of Impossibilities): The preview of the relationship between added rhythmic values and added harmonic notes is fulfilled here and in Chapter XIII.

• Chapter II (Rāgavardhana): The added dot observed in rāgavardhana's retrograde (Example 4 of Chapter II) provides the conceptual seed for the entire added value technique.

• Chapter IV (Augmented or Diminished Rhythms): Added values represent one type of rhythmic transformation; Chapter IV explores proportional augmentation/diminution, creating complementary approaches to rhythmic modification.

• Chapter V (Nonretrogradable Rhythms): Added values can be incorporated into palindromic structures, affecting their symmetrical properties.

• Chapter VI (Polyrhythm): Added values create temporal complexity within single rhythmic layers; polyrhythm creates complexity through simultaneous independent layers—complementary approaches to rhythmic density.

• Chapter XIII (Harmony, Debussy, Added Notes): The parametric analogy established here receives full harmonic development—added values find their vertical counterpart in added sixth, ninth, eleventh, and thirteenth chords.

• Chapter XV (Enlargement of Foreign Notes, Upbeats, Terminations): The discussion of rhythmic preparations and descents in this chapter connects to melodic upbeats and terminations in Chapter XV, demonstrating Messiaen's cross-parametric thinking.

The added value technique also influences Messiaen's actual compositional practice extensively. Many of his most characteristic rhythmic gestures employ added values, and the technique becomes central to his mature rhythmic language in works like Vingt regards sur l'enfant-Jésus, Turangalîla-Symphonie, and the late organ works.