  Graphs can be leveraged to model polyphonic multitrack symbolic music, where
notes, chords and entire sections may be linked at different levels of the
musical hierarchy by tonal and rhythmic relationships. Nonetheless, there is a
lack of works that consider graph representations in the context of deep
learning systems for music generation. This paper bridges this gap by
introducing a novel graph representation for music and a deep Variational
Autoencoder that generates the structure and the content of musical graphs
separately, one after the other, with a hierarchical architecture that matches
the structural priors of music. By separating the structure and content of
musical graphs, it is possible to condition generation by specifying which
instruments are played at certain times. This opens the door to a new form of
human-computer interaction in the context of music co-creation. After training
the model on existing MIDI datasets, the experiments show that the model is
able to generate appealing short and long musical sequences and to
realistically interpolate between them, producing music that is tonally and
rhythmically consistent. Finally, the visualization of the embeddings shows
that the model is able to organize its latent space in accordance with known
musical concepts.
