Stochastic processes and probability theory in music.

This dissertation examines the connections between music and mathematics with particular reference to Markov chains and generative grammars. The main purpose of this study is to investigate how mathematical concepts can help to control, create and analyse music material. The core part of this study is software that allows one to compose music with Markov Chains and generative grammars. The study will explore the on-going influence of such tools on composers and their relationship to musical sources and inspirations. An in-depth analysis of existing literature, music material and composition tools was conducted. Using comparative case studies, this research explored the significant role of mathematics in music in the twentieth and twenty-first centuries. The evolving role of stochastic concepts in music was presented. The next step was to develop a useful tool that would allow composers to apply Markov chains and generative grammars in their compositions. The web application that resulted was called Stochastic Composer. To evaluate this application five composers were invited to test it. The results include over one hundred samples of music material that were later analysed and used to improve the software. This dissertation offers insight into applications of various mathematical concepts in music. The Stochastic Composer software, available online, proved to be a useful tool in a compositional process.