  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 $\mathbb{Z}_{12}$, generated by $3$ and $4$. Using $\mathbb{Z}_{12}$
as a model, we extend the above music concepts to a particular class of groups
$\mathbb{Z}_{n}$, which displays geometric and algebraic features similar to
$\mathbb{Z}_{12}$. We identify a weaker form of counterpoint which, in
particular leads to Fux's dichotomy in $\mathbb{Z}_{12}$, and to consonant sets
in $\mathbb{Z}_n$. Using Maple software, we implement these new constructions
and show how to experiment with them musically.
