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 -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.
CITATION STYLE
Mazzola, G. (2017). Orbits. In Computational Music Science (pp. 167–223). Springer Nature. https://doi.org/10.1007/978-3-319-64364-9_11
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