The music box operad: Random generation of musical phrases from patterns

Abstract

A. 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. C 2.1. A primer on operads 2.2. Music box operads 2.3. Operations on musical phrases 3. Generation and random generation 3.1. Colored operads and bud operads 3.2. Bud generating systems 3.3. Random generation 4. Applications: exploring variations of patterns 4.1. Patterns to patterns 4.2. Patterns to multi-patterns Conclusion and perspectives References