FuxCP : A validated constraint programming formalization of fux four-voice counterpoint

Details

Supervisors

Van Roy, Peter

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] en sciences informatiques, à finalité spécialisée

Abstract

enThis thesis takes over the constraint-programming formalization of Fux’s musical theory developed in prior work and consolidates, clarifies, and validates the rule system for Fuxian counterpoint. The model distinguishes hard rules (stylistic necessities) from soft preferences (graded tendencies) and adopts a figure-driven validation methodology based on Minimal Unsatisfiable Subsets (MUS) to diagnose and resolve tensions between the formalism, Fux’s examples, and auxiliary sources. Validation proceeds along four complementary axes: (i) consistency with implicit theoretical knowledge and practical pedagogy; (ii) verification against worked examples from Gradus ad Parnassum using MUS to isolate minimal conflicts; (iii) cross-checking with the explicit formulations in the Trait´e de Contrepoint by No¨el Gallon and Marcel Bitsch; and (iv) systematic correction of formulation inconsistencies and implementation errors inherited from previous iterations. On the engineering side, the thesis extends and corrects the Gecode-based solver, introduces a modular activation/deactivation mechanism that enables controlled experimentation with subsets of rules, and integrates MUS diagnostics directly into the testing pipeline. Several rules are re-cast as soft constraints to encode stylistic latitude without sacrificing correctness. A unified, documented constraint library and reproducible test harness (including species/voice-count figure tests) provide a coherent, maintainable framework for future research and extensions. Together, these contributions deliver a clearer and more faithful executable theory of species counterpoint: a consolidated catalogue of general and speciesspecific constraints with explicit domains of application; an implementation that explains failures at rule level via MUS; and a validated workflow that reproduces Fux’s figures where supported and pinpoints precisely where the model must be refined or extended.