We introduce a model for music generation where melodies are seen as a network of interacting notes. Starting from the principle of maximum entropy we assign to this network a probability distribution, which is learned from an existing musical corpus. We use this model to generate novel musical sequences that mimic the style of the corpus. Our main result is that this model can reproduce high-order patterns despite having a polynomial sample complexity. This is in contrast with the more traditionally used Markov models that have an exponential sample complexity.
