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Music is a complex socio-cultural construct, which fascinates researchers indiverse fields, as well as the general public. Understanding the historicaldevelopment of music may help us understand perceptual and cognition, whilealso yielding insight in the processes of cultural transmission, creativity,and innovation. Here, we present a study of musical features related toharmony, and we document how they evolved over 400 years in western classicalmusic. We developed a variant of the center of effect algorithm to call themost likely for a given set of notes, to represent a musical piece as asequence of local keys computed measure by measure. We develop measures toquantify key uncertainty, and diversity and novelty in key transitions. Weprovide specific examples to demonstrate the features represented by theseconcepts, and we argue how they are related to harmonic complexity and can beused to study the evolution of harmony. We confirm several observations andtrends previously reported by musicologists and scientists, with somediscrepancies during the Classical period. We report a decline in innovation inharmonic transitions in the early classical period followed by a steep increasein the late classical; and we give an explanation for this finding that isconsistent with accounts by music theorists. Finally, we discuss thelimitations of this approach for cross-cultural studies and the need for moreexpressive but still tractable representations of musical scores, as well as alarge and reliable musical corpus, for future study.

Quantifying the evolution of harmony and novelty in western classical music