Abstract: We apply geometric group theory to study and interpret known concepts from Western music. We show that chords, the circle of fifths, scales and certain aspects of the first species of counterpoint are encoded in the Cayley graph of the group ℤ_12, generated by 3 and 4. Using ℤ_12 as a model, we extend the above music concepts to a particular class of groups ℤ_n, which displays geometric and algebraic features similar to ℤ_12. We identify a weaker form of counterpoint which, in particular leads to Fux’s dichotomy in ℤ_12, and to consonant sets in ℤ_n. Using Maple software, we implement these new constructions and show how to experiment with them musically.

Keywords: Cayley graph, finitely generated group, chords, scales, circle of fifths, first species counterpoint.

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