Orbits

Summary

This chapter deals with groups of symmetries, their action and orbits as musicological and mathematical concepts. Elementary local compositions—chords, self-addressed chords, and motives are classified under group actions. Enumeration theory of orbits of local compositions in finite ℤ-modules including traditional pitch class sets and motives—is presented and discussed for its implications towards a “Big Science” in music. Follows a discussion of group-theoretical methods in composition and theory, including a review of the American tradition and recent developments.

2 230 741 522 540 743 033 415 296 821 609 381 912

The number of isomorphism classes (orbits) of

72-element motives in ℤ ²₁₂ .

Harald Fripertinger [169]

100 000 000 000 The average number of stars in a galaxis.

Hubert Reeves [436]