How Blue Can You Get? Learning Structural Relationships for Microtones via Continuous Stochastic Transduction Grammars
AbstractWe describe a new approach to probabilistic modeling of structural inter-part relationships between continuous-valued musical events such as microtones, through a novel class of continuous stochastic transduction grammars. Linguistic and grammar oriented models for music commonly approximate features like pitch using discrete symbols to represent ‘clean’ notes on scales. In many musical genres, however, contextual relationships between continuous values are essential to improvisational and accompaniment decisions—as with the ‘bent notes’ that blues rely heavily upon. In this paper, we study how stochastic transduction grammars or STGs, which have until now only been able to handle discrete symbols, can be generalized to model continuous valued features for such applications. STGs are interesting for modeling the learning of musical improvisation and accompaniment where parallel musical sequences interact hierarchically (compositionally) at many overlapping levels of granularity. Each part influences decisions made by other parts while at the same time satisfying contextual preferences across multiple dimensions; applications to flamenco and hip hop have recently been shown using discrete STGs. We propose to use a formulation of continuous STGs in which musical signals are finely represented as continuous values without crude quantization into discrete symbols, yet still retaining the ability to model probabilistic structural relations between multiple musical languages. We instantiate this approach for the specific class of stochastic inversion transduction grammars (SITGs), which has proven useful in many applications, via a polynomial time algorithm for expectation-maximization training of continuous SITGs.
Proceedings of the Seventh International Conference on Computational Creativity (ICCC 2016), 2016, p. 286-293, François Pachet, Amilcar Cardoso, Vincent Corruble, Fiammetta Ghedini (eds)