  In this paper, we consider the problem of probabilistically modelling
symbolic music data. We introduce a representation which reduces polyphonic
music to a univariate categorical sequence. In this way, we are able to apply
state of the art natural language processing techniques, namely the long
short-term memory sequence model. The representation we employ permits
arbitrary rhythmic structure, which we assume to be given. We show that our
model is effective on four out of four piano roll based benchmark datasets. We
further improve our model by augmenting our training data set with
transpositions of the original pieces through all musical keys, thereby
convincingly advancing the state of the art on these benchmark problems. We
also fit models to music which is unconstrained in its rhythmic structure,
discuss the properties of this model, and provide musical samples which are
more sophisticated than previously possible with this class of recurrent neural
network sequence models. We also provide our newly preprocessed data set of non
piano-roll music data.
