Relationship to Other Chapters

Chapter IV complements and extends earlier rhythmic chapters while setting up later developments:

• Chapter II (Rāgavardhana): The asymmetrical augmentation/diminution observed in simhavikrîdita (Example 1 of Chapter II) prefigures inexact augmentation—one element scales while another remains invariant.

• Chapter III (Added Values): This chapter presents proportional transformation as a complement to Chapter III's non-proportional transformation. The two techniques combine in dot addition/withdrawal procedures and in examples incorporating both augmentation and added values (Example 27).

• Chapter V (Nonretrogradable Rhythms): Augmentation and diminution can apply to palindromic rhythms, preserving their retrograde invariance while changing their time-scale.

• Chapter VI (Polyrhythm): Inexact augmentation creates a specific type of polyrhythmic texture—simultaneous layers at different time-scales or rates of transformation.

• Chapter VII (Rhythmic Notations): Practical issues of notating extreme augmentations or diminutions, and representing inexact augmentations clearly, relate to notational concerns addressed in Chapter VII.

• Chapter XIII (Harmony, Debussy, Added Notes): Example 27 references the six-four chord with added sixth and augmented fourth, demonstrating interaction between rhythmic and harmonic transformation techniques. The analogy between rhythmic augmentation/diminution and harmonic expansion/contraction extends the parametric thinking established in Chapters I and III.

The table format itself becomes a model for systematic presentation—later chapters may employ similar cataloguing approaches for other techniques.