  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.

Physics and Society;Computers and Society