Before revision:  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 .
After revision:  This 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 .