The applications of fractal geometry and self - similarity to art music

Abstract

The aim of this research study is to investigate different practical ways in which fractal geometry and self-similarity can be applied to art music, with reference to music composition and analysis. This specific topic was chosen because there are many misconceptions in the field of fractal and self-similar music. Analyses of previous research as well as the music analysis of several compositions from different composers in different genres were the main methods for conducting the research. Although the dissertation restates much of the existing research on the topic, it is (to the researcher‟s knowledge) one of the first academic works that summarises the many different facets of fractal geometry and music. Fractal and self-similar shapes are evident in nature and art dating back to the 16th century, despite the fact that the mathematics behind fractals was only defined in 1975 by the French mathematician, Benoit B. Mandelbrot. Mathematics has been a source of inspiration to composers and musicologists for many centuries and fractal geometry has also infiltrated the works of composers in the past 30 years. The search for fractal and self-similar structures in music composed prior to 1975 may lead to a different perspective on the way in which music is analysed. Basic concepts and prerequisites of fractals were deliberately simplified in this research in order to collect useful information that musicians can use in composition and analysis. These include subjects such as self-similarity, fractal dimensionality and scaling. Fractal shapes with their defining properties were also illustrated because their structures have been likened to those in some music compositions. This research may enable musicians to incorporate mathematical properties of fractal geometry and self-similarity into original compositions. It may also provide new ways to view the use of motifs and themes in the structural analysis of music.