Musical composition based on skewed statistical distributions of stochastic processes

Abstract

The inclusion of skewed statistical distributions in the stochastic process for composing music contributes to clarify the effect of some pitch patterns for generating new pieces of music. The aim of this study was to compare and measure the effect of using skewed statistical distributions instead of using the common uniform distribution applied in Markov chains. We applied an explorative data analysis related to the Shannon entropy and the Monte Carlo approach, to generate and compare different stochastic realizations associated with a particular exponential and uniform distributions and two types of note selection based on intervals. Findings suggested that the presence of an exponential statistical distribution may generate a wide range of entropy values that could be associated with the diversity concept in complex systems. On the other hand, the presence of the uniform distribution may generate a narrow range of entropy values possibly associated with less diverse behaviors in simple systems. Therefore, the use of skewed statistical distributions, in particular the exponential, in the stochastic process for musical composition sets ground for the emergence of articulated musical patterns.

Keywords

• Nomusa Makhubu, University of Cape Town, South Africa
• Composition & Orchestration
• Elements of Music
• Music Technology
• Theory of Music
• Stochastic process