Generation of musical patterns through operads

We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach lies in the fact that this offers a way to compose two multi-patterns in order to produce a longer one. This dives musical phrases into an algebraic context since the set of multi-patterns has the structure of an operad; operads being structures offering a formalization of the notion of operators and their compositions. Seeing musical phrases as operators allows us to perform computations on phrases and admits applications in generative music: given a set of short patterns, we propose various algorithms to randomly generate a new and longer phrase inspired by the inputted patterns.