The music box operad: Random generation of musical phrases from patterns
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We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach to encode musical phrases lies in the fact that it becomes possible to compose multi-patterns in order to produce new ones. This dives the set of musical phrases into an algebraic framework since the set of multi-patterns has the structure of an operad. Operads are algebraic 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. Indeed, given a set of short patterns, we propose various algorithms to randomly generate a new and longer phrase inspired by the inputted patterns.
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