Quantifying the evolution of harmony and novelty in western classical music.

Music is a complex socio-cultural construct that fascinates researchers across many fields. Understanding its historical development may inform questions of perception and cognition, and offer insight into cultural transmission, creativity, and innovation. Here we study musical features related to harmony and document how they evolved over 400 years in western classical music. We develop a variant of the center of effect algorithm to assign the most likely key to a given set of notes, representing a piece as a sequence of local keys computed bar by bar, and we define information-theoretic measures of key uncertainty, key diversity, and novelty in key transitions. We illustrate these measures with specific examples and give them a musical interpretation, showing how they can be used to study the evolution of harmony. Applying them across the corpus, we confirm several trends previously reported by musicologists and scientists, with some discrepancies during the Classical period: in particular, we find a decline in harmonic innovation during the Early Classical period followed by a steep increase in the Late Classical, for which we offer an explanation consistent with accounts by music theorists. Comparing composers directly by their key-transition vocabularies, we further find that they group by historical period, and that both the overall arrangement and the individual nearest-neighbor relations recover connections consistent with the documented historical record. Finally, we discuss the limitations of this approach for cross-cultural studies and the need for more expressive yet tractable score representations, and a large and reliable corpus, for future study.