  Analogy-making is a key method for computer algorithms to generate both
natural and creative music pieces. In general, an analogy is made by partially
transferring the music abstractions, i.e., high-level representations and their
relationships, from one piece to another; however, this procedure requires
disentangling music representations, which usually takes little effort for
musicians but is non-trivial for computers. Three sub-problems arise:
extracting latent representations from the observation, disentangling the
representations so that each part has a unique semantic interpretation, and
mapping the latent representations back to actual music. In this paper, we
contribute an explicitly-constrained variational autoencoder (EC$^2$-VAE) as a
unified solution to all three sub-problems. We focus on disentangling the pitch
and rhythm representations of 8-beat music clips conditioned on chords. In
producing music analogies, this model helps us to realize the imaginary
situation of "what if" a piece is composed using a different pitch contour,
rhythm pattern, or chord progression by borrowing the representations from
other pieces. Finally, we validate the proposed disentanglement method using
objective measurements and evaluate the analogy examples by a subjective study.
