You are currently viewing the abstract.
View Full TextLog in to view the full text
AAAS login provides access to Science for AAAS members, and access to other journals in the Science family to users who have purchased individual subscriptions.
Register for free to read this article
As a service to the community, this article is available for free. Existing users log in.
More options
Download and print this article for your personal scholarly, research, and educational use.
Buy a single issue of Science for just $15 USD.
Abstract
Western musicians traditionally classify pitch sequences by disregarding the effects of five musical transformations: octave shift, permutation, transposition, inversion, and cardinality change. We model this process mathematically, showing that it produces 32 equivalence relations on chords, 243 equivalence relations on chord sequences, and 32 families of geometrical quotient spaces, in which both chords and chord sequences are represented. This model reveals connections between music-theoretical concepts, yields new analytical tools, unifies existing geometrical representations, and suggests a way to understand similarity between chord types.
