We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score can always be interpreted as a dynamical network where every chord is a node and each progression links successive chords. We demonstrate that in a tonal harmony context this network displays scale-free properties, and optimal (most economical) chord progressions can be found by solving a path optimization like the Chinese postman problem. Moreover, the dynamical network can be viewed as a time series of a non-stationary signal  and as such  can be partitioned for the automatic identification of key regions using well-established techniques for time series analysis and change point detection . Based on this interpretation we introduce a key-finding algorithm that does not rely on comparisons with pre-determined reference sets , as in the Krumhansl-Schmuckler model, or extensive corpora , as in machine-learning approaches . Finally, we show how the principles discussed in this work can be used to design a generative model of tonal compositional design.
We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This network can be viewed as a time series of a non-stationary signal , and as such , it can be partitioned for the automatic identification of tonal regions using time series analysis and change point detection without relying on comparisons with pre-determined reference sets or extensive corpora . We demonstrate that the essential features of tonal harmony, centricity, referentiality, directedness and hierarchy, emerge naturally from the network topology and its scale-free properties . Finally, solving for the minimal length path through a route optimization algorithm on these graphs provides an abstraction of harmonic sequences that can be generalized for the conception of generative models of tonal compositional design.
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