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.
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