  We introduce a Maximum Entropy model able to capture the statistics of
melodies in music. The model can be used to generate new melodies that emulate
the style of the musical corpus which was used to train it. Instead of using
the $n-$body interactions of $(n-1)-$order Markov models, traditionally used in
automatic music generation, we use a $k-$nearest neighbour model with pairwise
interactions only. In that way, we keep the number of parameters low and avoid
over-fitting problems typical of Markov models. We show that long-range musical
phrases don't need to be explicitly enforced using high-order Markov
interactions, but can instead emerge from multiple, competing, pairwise
interactions. We validate our Maximum Entropy model by contrasting how much the
generated sequences capture the style of the original corpus without
plagiarizing it. To this end we use a data-compression approach to discriminate
the levels of borrowing and innovation featured by the artificial sequences.
The results show that our modelling scheme outperforms both fixed-order and
variable-order Markov models. This shows that, despite being based only on
pairwise interactions, this Maximum Entropy scheme opens the possibility to
generate musically sensible alterations of the original phrases, providing a
way to generate innovation.
