Both modern mathematical music theory and computer science are strongly
influenced by the theory of categories and functors. One outcome of this
research is the data format of denotators, which is based on set-valued
presheaves over the category of modules and diaffine homomorphisms. The
functorial approach of denotators deals with generalized points in the
form of arrows and allows the construction of a universal concept
architecture. This architecture is ideal for handling all aspects of
music, especially for the analysis and composition of highly abstract
musical works.
This book presents an introduction to the theory of module categories
and the theory of denotators, as well as the design of a software
system, called Rubato Composer, which is an implementation of the
category-theoretic concept framework. The application is written in
portable Java and relies on plug-in components, so-called rubettes,
which may be combined in data flow networks for the generation and
manipulation of denotators.
The Rubato Composer system is open to arbitrary extension and is freely
available under the GPL license. It allows the developer to build
specialized rubettes for tasks that are of interest to composers, who in
turn combine them to create music. It equally serves music theorists,
who use them to extract information from and manipulate musical
structures. They may even develop new theories by experimenting with the
many parameters that are at their disposal thanks to the increased
flexibility of the functorial concept architecture.
Two contributed chapters by Guerino Mazzola and Florian Thalmann
illustrate the application of the theory as well as the software in the
development of compositional tools and the creation of a musical work
with the help of the Rubato framework.
