Key Concepts

This chapter introduces six key concepts establishing the modes of limited transpositions:

1. Theory of the Modes of Limited Transpositions - Pitch collections formed from symmetrical intervallic groups that can only be transposed a limited number of times before reproducing the same pitch-class content

2. First Mode of Limited Transpositions (Whole-Tone Scale) - A six-note collection transposable only twice, equivalent to the whole-tone scale

3. Second Mode of Limited Transpositions (Octatonic Scale) - An eight-note collection consisting of four symmetrical groups, transposable three times, corresponding to the octatonic or diminished scale

4. Third Mode of Limited Transpositions - A nine-note collection transposable four times, consisting of three symmetrical groups of four notes each

5. Modes 4, 5, 6, and 7 - Four additional modes transposable six times, each divided into two symmetrical groups, offering distinctive harmonic colors

6. Relation of Modes of Limited Transpositions and Nonretrogradable Rhythms - A fundamental structural parallel between symmetrical properties of modes and nonretrogradable rhythms, creating a "theological rainbow"