Modeling musical expectancy via reinforcement learning and directed graphs

Abstract

Algorithms strive to capture the intricacies of our complex world, but translating qualitative aspects into quantifiable data poses a significant challenge. In our paper, we embark on a journey to unveil the hidden structure of music by exploring the interplay between our predictions and the sequence of musical events. Our ultimate goal is to gain insights into how certainty fluctuates throughout a musical piece using a three-fold approach: a listening test, reinforcement learning (RL), and graph construction. Through this approach, we seek to understand how musical expectancy affects physiological measurements, visualize the graphical structure of a composition, and analyze the accuracy of prediction accuracy across 15 musical pieces. We conducted a listening test using western classical music on 50 subjects, monitoring changes in blood pressure, heart rate, and oxygen saturation in response to different segments of the music. We also assessed the accuracy of the RL agent in predicting notes and pitches individually and simultaneously. Our findings reveal that the average accuracy of the RL agent in note and pitch prediction is 64.17% and 22.48%, respectively, while the accuracy for simultaneous prediction is 73.84%. These results give us a glimpse into the minimum level of certainty present across any composition. To further analyze the accuracy of the RL agent, we propose novel directed graphs in our paper. Our analysis shows that the variance of the edge distributions in the graph is inversely proportional to the accuracy of the RL agent. Through this comprehensive study, we hope to shed light on the enigmatic nature of music and pave the way for future research in this fascinating field.