The Music Box Operad: Random Generation of Musical Phrases from Patterns

Abstract

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 composition is parametrized by a monoid structure on the scale degrees. This dives the set of the musical phrases into an algebraic framework since the set of the multi-patterns is endowed with the structure of an operad. Operads are algebraic structures offering a formalization and an abstraction 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 initial multi-patterns, we propose various algorithms to randomly generate a new and longer phrase emulating the style suggested by the inputted multi-patterns. The designed algorithms use sorts of grammars working with operads and colored operads, known as bud generating systems.

Keywords

• generative music
• formal grammars
• random generation
• combinatorics
• operads