A Projection-Oriented Mathematical Model for Second-Species Counterpoint

TL;DR

This paper introduces a new mathematical model for second-species counterpoint, extending classical symmetry-based approaches to handle two notes against one note, inspired by traditional music theory methods.

Contribution

It presents a novel projection-oriented mathematical framework specifically designed for second-species counterpoint, expanding existing models for first-species counterpoint.

Findings

Develops a formal mathematical model for second-species counterpoint

Extends classical symmetry-based models to more complex counterpoint

Provides a theoretical foundation for analyzing second-species counterpoint

Abstract

Drawing inspiration from both the classical Guerino Mazzola's symmetry-based model for first-species counterpoint (one note against one note) and Johann Joseph Fux's "Gradus ad Parnassum", we propose an extension for second-species (two notes against one note).