Quantum game-theoretic interpretation of harmonic dynamics in contrapuntal structures

We present a time-dependent quantum game-theoretic framework to analyze general two-voice contrapuntal structures. Utilizing the polyphony of J.S. Bach as a representative proof of concept, we model the functional interdependence of independent voices using a multi-contextual binary abstraction of tonal harmony. By incorporating an entanglement parameter and a payoff penalty reflecting asymmetric musical roles, we extract underlying quantum strategies from symbolic musical data. Our optimization demonstrates that the game-theoretic model assuming quantum entanglement reproduces empirical probability distributions with significantly higher accuracy than the corresponding unentangled baseline model. Furthermore, applying the payoff penalty drives the system beyond classical limits, revealing that the structural demands of counterpoint actively exploit nonlocal quantum correlations. Finally, we show that the resulting payoff-induced probabilistic deviations can be mathematically mapped to temporal timing fluctuations. This exploratory study provides a physics-based foundation for interpreting structurally driven deviations from a musical score as emergent temporal dynamics in creative performance.