  Machine learning models of music typically break up the task of composition
into a chronological process, composing a piece of music in a single pass from
beginning to end. On the contrary, human composers write music in a nonlinear
fashion, scribbling motifs here and there, often revisiting choices previously
made. In order to better approximate this process, we train a convolutional
neural network to complete partial musical scores, and explore the use of
blocked Gibbs sampling as an analogue to rewriting. Neither the model nor the
generative procedure are tied to a particular causal direction of composition.
Our model is an instance of orderless NADE (Uria et al., 2014), which allows
more direct ancestral sampling. However, we find that Gibbs sampling greatly
improves sample quality, which we demonstrate to be due to some conditional
distributions being poorly modeled. Moreover, we show that even the cheap
approximate blocked Gibbs procedure from Yao et al. (2014) yields better
samples than ancestral sampling, based on both log-likelihood and human
evaluation.
