Synthetic Harmonies: An Approach to Musical Semiosis by Means of Cellular Automata

Abstract

The authors explore the creation of artificial universes that are expressible through music and internally comprehensible as complex systems. The semiotic approach this paper presents could also allow the development of new tools of investigation into the complexity of artificial-life systems. Through codification systems using musical language, it is possible to understand the patterns that the global ynamics of cellular automata produce and to use the results in the musical domain. In the authors' approach, music can be considered the semantics of complexity. The authors identify analogies between elements of cellular automata and elements of musical form, creating a narrative musical framework that has allowed them to develop a productive, computational and semantic methodology. Music fosters an increased capability for analyzing and reconstructing complexity, providing unexpected insight into its organization.

Music is the arithmetic of soul, that uses numbers without realising it.

—Leibniz

This article discusses music, mathematics and artificial-life (A-Life) models, linking them together through a semiotic approach. Music and mathematics, as expressions of creative thought, can be studied through their reciprocal relationship (as has been previously noted by both ancient and modern philosophers). Music and mathematics can be analyzed using models of the auditory perception used by the human mind during listening. They can also be studied in relation to the emotions they evoke, creating that "arithmetic of the soul" to which Leibniz referred. They can be analyzed from the formal point of view as well, which entails investigating the structures of the models that artists use for musical composition. We have chosen to use cellular automata (CA) (dynamic structures in which space, time and states of the system are discrete; mathematical models able to simulate the complex behavior of some physical and/or biological systems) to study complexity and then to translate this complexity into music. The relative simplicity of CA and their extraordinary capacity to mimic both evolution and growth in biological life seem to have some basic peculiarities in common with natural human languages (and thus with music) and with semiotics. Like languages, CA exhibit dynamic behavior. An important aspect of most complex systems is that they are massively parallel in operation, with all their parts working simultaneously. This allows their features to change in many ways, exhibiting emergent and self-organizing qualities. In order to understand complexity, we need to identify the laws in this behavior, the properties that remain unchanged (invariant).

The link between mathematics and music, combined with certain models taken from modern science, allows music to be reproduced, synthesized and made to evolve through many theoretical-conceptual instruments offered by the A-Life field. As Christopher Langton has said, "Artificial Life is a field of study devoted to understanding life by attempting to abstract the fundamental dynamical principles underlying biological phenomena, and recreating these dynamics in other physical media—such as computers—making them accessible to new kinds of experimental manipulation and testing" [1].

In fact, one of the most promising sectors of contemporary art is the application of A-Life models to art, design and entertainment [2] as well as music [3]. Some characteristics of such forms of art are related to the complexity of their production: starting from simple and repeatedly applied rules, and slightly modifying certain elements, the artist has the ability to generate ever-differing artifacts. The perspective provided by A-Life approaches raises the question of the ontological status of the artwork: the concept of the unique and immutable artifact is giving way to that of creations that can be replicated in ever-differing ways, applying the same fruitful rule. Nevertheless, the issue of what an artwork might be like, how it is possible to manage its overall organization and its detailed content, according to its deep structural models of production, is not well defined; there is no common grammar of creativity in art. Besides, the artwork evolves in time: a given structural configuration might receive many instantiations, each unique in its local details but all changing by means of evolutionary processes.

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