Chapter IV: Augmented or Diminished Rhythms and a Table of These Rhythms
Original: Pages 18–19 in Satterfield translation
Musical Examples:
Overview
This chapter complements Chapter III by exploring proportional rhythmic transformations—traditional augmentation and diminution—alongside their interaction with added values. Where Chapter III addressed non-proportional transformation through addition or subtraction of small durational increments, Chapter IV examines multiplicative scaling of rhythmic patterns. Messiaen develops a systematic taxonomy of augmentation and diminution procedures, presents them in tabular form for compositional reference, and introduces the concept of inexact augmentation where multiple rhythmic layers undergo different rates of transformation simultaneously. The chapter demonstrates that proportional and non-proportional transformations can combine to create complex rhythmic variants, and shows how extreme augmentation or diminution can generate either very long values (approaching stasis) or very short values (approaching perceptual limits).