Quantifying the evolution of harmony and novelty in western classical music

Music is a complex socio-cultural construct, which fascinates researchers in diverse fields, as well as the general public. Understanding the historical development of music may help us understand perceptual and cognition, while also yielding insight in the processes of cultural transmission, creativity, and innovation. Here, we present a study of musical features related to harmony, and we document how they evolved over 400 years in western classical music. We developed a variant of the center of effect algorithm to call the most likely for a given set of notes, to represent a musical piece as a sequence of local keys computed measure by measure. We develop measures to quantify key uncertainty, and diversity and novelty in key transitions. We provide specific examples to demonstrate the features represented by these concepts, and we argue how they are related to harmonic complexity and can be used to study the evolution of harmony. We confirm several observations and trends previously reported by musicologists and scientists, with some discrepancies during the Classical period. We report a decline in innovation in harmonic transitions in the early classical period followed by a steep increase in the late classical; and we give an explanation for this finding that is consistent with accounts by music theorists. Finally, we discuss the limitations of this approach for cross-cultural studies and the need for more expressive but still tractable representations of musical scores, as well as a large and reliable musical corpus, for future study.