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

TL;DR

This paper introduces multi-patterns as an algebraic operad-based framework for the random generation of polyphonic musical phrases, enabling structured composition and style emulation in generative music.

Contribution

It develops a novel operad-based formalism for encoding and composing musical phrases, with algorithms for random generation using operad grammars.

Findings

Operad structure effectively models polyphonic musical phrases.

Algorithms successfully generate new phrases emulating input styles.

Framework facilitates algebraic manipulation of musical patterns.

Abstract

We introduce the notion of multi-patterns, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach in encoding musical phrases lies in the fact that it becomes possible to compose multi-patterns in order to produce new ones. This composition is parameterized by a monoid structure on the scale degrees. This embeds 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 types of grammars working with operads and colored operads, known as bud generating systems.