Functors for Music: The Rubato Composer System

Abstract

In abstract mathematical music theory, the data format of denotators is associated with set-valued presheaves over module categories. In this paper, we present an implementation of this concept framework in the Rubato Composer system, a Java application comprising a GUI for manipulation and combination of rubettes. These are plug-ins that can be added and connected for communication of denotator data. Rubato Composer is a GPL software and is accessible to the computer music community for download and collaboration. In this paper, the functionality, architecture, concept framework, and the implemented mathematical operators are presented and illustrated with a "functorial composition".

Music in the pedagogy of mathematics

“…However, as it is necessary to work with set constructions to, say, represent musical embellishments that are seen as sets of sets of notes, the theoretical and implementational designers opted for working in the functor category, which consists of presheaves on the category of modules (whose objects are the functors). The development of this theory and its relation to Rubato Composer can be found in Mazzola (2002), Thalmann and Mazzola (2008), Mazzola et al (2008), andMilmeister (2009).…”