Procedural Generation of Several Instrument Music Pieces with Hierarchical Wave Function Collapse

Abstract

Wave Function Collapse (WFC) can be described as a family of algorithms, meant for content generation through constraint solving. One variant is Hierarchical WFC, where a hierarchical structure is given to the tileset used in WFC. This variant has seen use in a mixed-initiative procedural music generation model, where pieces of music simulating a single instrument playing chords and a melody are generated. In this paper, we explore how this model can be adapted to generate (coherent) pieces of music simulating several instruments playing in parallel. To achieve this, three model properties had to be defined: a new canvas structure, a set of constraints that instruments impose on each other, and the manner in which cells of all canvasses are collapsed. A hierarchical structure has been defined of a single section canvas, of which every cell has an inheriting chord canvas, of which every cell has an inheriting melody canvas for each instrument. The section cells impose constraints on inheriting chord and melody cells, and the chord cells impose constraints on inheriting melody cells. Besides this, melody cells impose constraints on cells belonging to other melody canvases (i.e. other instruments). With this canvas structure and these sets of constraints, the cells could be collapsed, such that coherent pieces of music simulating several instruments playing in parallel were generated.