Fractals and music. A reconnaissance

• Authors: Iwona Lindstedt
• Languages of publication: PL

Abstracts

PL

Among the many definitions of the fractal employed by mathematicians, one of the most suggestive holds that ‘the fractal is a self-similar figure displaying an invariability in respect to the transformations of scaling’. This article is an effort to present the overview of fractals in mathematics and nature and then to describe the current state of research on fractal nature of music. It is shown that self-similarity and scaling are properties of many canonic works of Western music (e.g. Johann Sebastian Bach, Ludwig van Beethoven), appearing in various forms in all historical periods. It is found in binary and ternary divisions of form and in melodic structures. It is also noted that a frequent point of reference in fractal studies of the properties of music is twentieth-century repertoire (e.g. Per Norgárd, Conlon Nancarrow, Gyórgy Ligeti, Charles Wuorinen). The case of l/f noise in which frequency (pitch) scaling naturally occurs is also discussed. Such ‘scaling noise’ is typical of many natural phenomena; it is observed, for example, in the variable tension of nerve cells and in heartbeats. It was also discovered in music. The article summarizes the results of the research made by Voss and Clarke (1975, 1978), Hsü and Hsü (1990,1991), Henze and Cooper (1997) who analyzed stylistically diverse works - classical, jazz, blues, rock and non-European music - and found in them l/f relationships referring to Fourier spectra, notes or intervals. The article reports also the psychological experiments raising the statements about a close relationship between fractal structure and the human sense of beauty. It is stressed that the fractal orientation of modern mathematics provides interesting cognitive tools allowing us to discover hitherto unexplored links between nature and art, both in the area of listeners’ aesthetic preferences and also in the fascinating realm of artistic creation.

Keywords

PL

fractals; fractal nature of music; music analysis; l/ f noise; scaling; selfsimilarity

• Publisher: Uniwersytet im. Adama Mickiewicza w Poznaniu
• Journal: Interdisciplinary Studies in Musicology
• Year: 2009
• Issue: 8
• Pages: 151-172

Dates

published

2018-10-17

Contributors

author

Iwona Lindstedt

• Ph.D., lecturer in the Institute of Musicology at the University of Warsaw. Her research interests center on the history, theoiy and analysis of 20th and 21th century music. She has published on the work of Józef Koffler, Bogusław Schaeffer, Krzysztof Penderecki, Witold Lutosławski, as well as articles on methods for the analysis of the musical work. Her most recent research interests include the topic of the so-called ‘sonoristic music’ of Polish 20th century composers. She is the author o f Dodekafonia i serializm w twórczości kompozytorów polskich XX wieku [Dodecaphony and serialism in the output of 20th century polish composers] (Lublin, 2001) and articles on Fryderyk Chopin's music and sonoristic music.