On first-species counterpoint theory

We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The generalization encompasses an alternative theory of contrapuntal intervals. We also propose several variations of the model that intend to deepen into its principles. The original motivations of the theory, as well as all technical passages, are carefully reviewed so as to provide a complete exposition.