  Connectionist sequence models (e.g., RNNs) applied to musical sequences
suffer from two known problems: First, they have strictly "absolute pitch
perception". Therefore, they fail to generalize over musical concepts which are
commonly perceived in terms of relative distances between pitches (e.g.,
melodies, scale types, modes, cadences, or chord types). Second, they fall
short of capturing the concepts of repetition and musical form. In this paper
we introduce the recurrent gated autoencoder (RGAE), a recurrent neural network
which learns and operates on interval representations of musical sequences. The
relative pitch modeling increases generalization and reduces sparsity in the
input data. Furthermore, it can learn sequences of copy-and-shift operations
(i.e. chromatically transposed copies of musical fragments)---a promising
capability for learning musical repetition structure. We show that the RGAE
improves the state of the art for general connectionist sequence models in
learning to predict monophonic melodies, and that ensembles of relative and
absolute music processing models improve the results appreciably. Furthermore,
we show that the relative pitch processing of the RGAE naturally facilitates
the learning and the generation of sequences of copy-and-shift operations,
wherefore the RGAE greatly outperforms a common absolute pitch recurrent neural
network on this task.
