Interactive Composition Using Markov Chain and Boundary Functions

Jônatas Manzolli

Interdisciplinary Nucleus for Sound Studies (NICS)
University of Campinas (UNICAMP)
13081-970 Campinas - SP - Brasil

Adolfo Maia Jr.

Applied Mathematcs Department (IMEEC)
University of Campinas (UNICAMP)
13081-970 Campinas - SP - Brasil

Abstract:

The research presented here reviews the use of stochastic process on composition; Markov chains were studied as a tool for developing musical structures in the 70s. This paper presents a model based on Probability Vectors and Boundary Functions which are used on interactive process to generate further sequences of vectors. The resultant nimerical structure are mapped to different classes of musical parameters. The text presents this new approach - the musical ideas behind the method as well as the mathematical model. Finally, it describes a graphic-based compositional system for a MS-Windows Environment.