Control Improvisation with Application to Music

Abstract : We introduce the concept of control improvisation, the process of generating a random sequence of control events guided by a reference sequence and satisfying a given specification. We propose a formal definition of the control improvisation problem and an empirical solution applied to the domain of music. More specifically, we consider the scenario of generating a monophonic Jazz melody (solo) on a given song harmonization. The music is encoded symbolically, with the improviser generating a sequence of note symbols consisting of pairs of pitches (frequencies) and discrete durations. Our approach has three phases. The first phase, generalization, learns from the given melody a nondeterministic automaton generating a set of melodies containing the original. We implement this phase using factor oracles. The second phase, safety supervision, enforces rules on the generalized automaton so that it plays in harmony with the accompaniment. The rules are analogous to safety properties that a control system must always obey. The third and final phase, divergence supervision, ensures that sequences produced by the improviser automaton lie, with high probability, within a specified similarity divergence from the original. This phase is implemented by replacing nondeterminism in the improviser automaton with probabilities, which are based on a given divergence measure. For music, several divergence measures have been proposed; amongst these, Normalized Compression Distances (NCDs) have been effectively used, and so we employ a variant of an NCD in this paper. An empirical evaluation is presented on a sample set of Jazz music.

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