Connection to Added Notes

Definition: The parametric analogy between rhythmic added values and harmonic added notes—both techniques involve augmentation through addition rather than substitution or multiplication.

Messiaen's Treatment: Messiaen explicitly recalls Chapter I's promise to relate values added to rhythms with notes added to chords, stating this relationship will receive fuller treatment in Chapter XIII. The analogy operates at multiple levels:

• Operational parallel: Just as a simple rhythm receives additional durational values, a simple chord receives additional pitch-classes
• Perceptual parallel: Just as added values create metric imbalance, added notes create harmonic ambiguity or enrichment
• Aesthetic parallel: Both techniques produce complexity through augmentation rather than through fundamental alteration of basic structures

The added note technique (developed fully in Chapter XIII on Debussy's harmony) involves taking triadic or seventh-chord structures and adding foreign tones that become integral coloristic elements rather than dissonances requiring resolution. Similarly, added values augment rhythmic structures without functioning as embellishments to be eliminated—they are constitutive of the rhythm's identity.

Modern Context: This parametric analogy represents Messiaen's systematic approach to musical language—conceiving rhythm, melody, and harmony as domains governed by parallel principles rather than as independent parameters requiring separate theoretical frameworks.

Contemporary music theory recognizes such analogies through concepts of:

• Transformational isomorphism: Operations in different domains sharing mathematical structure
• Cross-domain mapping: Systematic relationships between parametric spaces
• Unified compositional systems: Theoretical frameworks applying consistent operations across multiple musical dimensions (serial technique, spectralism, etc.)

Messiaen's added value/added note analogy anticipates integral serialism's application of serial operations to rhythm, dynamics, articulation, and other parameters beyond pitch. However, Messiaen's approach remains less systematic—he identifies suggestive parallels rather than enforcing strict isomorphisms.

Examples: Harmonic examples appear in Chapter XIII; rhythmic examples throughout Chapter III suggest the analogy.