Quantifying the generalization capacity of Markov models for melody prediction

We analyze melodies of classical music by stochastic modeling and prediction, analogous to symbolic time series from a nonlinear dynamical system. The performance in a one-step prediction task indicates the capabilities of the models, given by Markov chains of different orders, to preserve prominent patterns of the compositions. We use cross-prediction between songs within a style, and between songs of different styles, to quantify how well the models can capture similarities between underlying dynamical rules. With this framework, the complexity and individuality of dynamical processes generating classical melodies can be systematically addressed.