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.

Reviewing Editor:

• Nomusa Makhubu, University of Cape Town, South Africa

Subjects:

• Composition & Orchestration
• Elements of Music
• Music Technology
• Theory of Music

Keywords:

• Stochastic process
• skewed statistical distributions
• musical composition
• Monte Carlo simulation
• Shannon entropy
• complex systems
• Python language

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data and the code that support the findings of this study are openly available in [‘Music composition and statistical analysis’] at https://osf.io/nqg7u/?view only = 6d546bec469049b68fe08704ec97b6ad.

Additional information

Notes on contributors

Igor Lugo

Igor Lugo is interested in an interdisciplinary approach of science. He is interested in the fields of economic geography, complexity, transportation systems, system of cities, ancient civilizations, musical composition, computational modeling, and programming.

Martha G. Alatriste-Contreras

Martha G. Alatriste-Contreras is interested in the interdisciplinary scientific research on complex systems. In particular, she is interested in the study of the properties and dynamics of economic systems, network and statistical analyses, modeling, and programming.