• Guerino Mazzola
Part of the Computational Music Science book series (CMS)


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 \(\mathbb{Z}\)-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.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Guerino Mazzola
    • 1
  1. 1.School of MusicUniversity of MinnesotaMinneapolisUSA

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