Modeling Counterpoint by Local Symmetries

Summary

This chapter presents the counterpoint model in form of a counterpoint theorem which guarantees the existence and exhibits an arsenal of admitted contrapuntal steps that come in extremely close to the rules of classical counterpoint. The theorem is based on the concept of a contrapuntal symmetry and follows the paradigm of local symmetries as a rationale for forces in physics. Because of its generic concept framework, the theorem, which in this general form1 was proved by Jens Hichert [466], is also valid for non-European scales. We discuss these extensions.

Der Rangunterschied zwischen den perfekten und den imperfekten Konsonanzen ermöglichte die Formulierung genereller Konsonanzfolgeregeln für eine indeterminata positio.

Klaus-Jürgen Sachs [924, p. 114]