Studying Structural Regularities through Abstraction Trees

Abstract. “Structure” is a somewhat elusive concept in music, despite being of extreme importance in a variety of applications. Being inherently a hidden feature, it is not always explicitly considered in algorithms and representations of music. We propose a hierarchical approach to the study of musical structures, that builds upon tree representations of music like Schenkerian analysis, and adds additional layers of abstraction introducing pairwise comparisons between these trees. Finally, these representations can be joined into probabilistic representations of a music corpus. The probability distributions contained in these representation allow us to use concepts from Information Theory to show how the structures we introduce can be applied to musicological and music information retrieval applications.