The counterpoint game: Rules, constraints and computational spaces

We envision first species counterpoint as a fundamental step in defining rules in a game-theoretical approach to algorithmic composition. While previous literature focuses on producing counterpoints that are aesthetically pleasing, our work formalizes the space where cantus firmi and counterpoints can be considered valid. A set of common rules is extracted from a comparative analysis of treatises from the 18th to the 20th century, and a generative algorithm is implemented to explore the validity space. The results highlight the existence of a subset of cantus firmi that do not admit valid counterpoint. Human experts in a qualitative assessment perform similarly to our validation algorithm; at the same time, the systematic omission of single and pairs of rules does not eliminate such a subset. It follows either that unwritten musical knowledge must be rendered explicit to modify the proposed rule set, or that, in general, admitting valid counterpoint is not a necessary property of cantus firmus.