Fractal Music Websites

Fractal-based compositions in general MIDI file format. (Not necessarily fractal from a mathematical perspective.)

Research, publications, and compositions by Harlan Brothers. A mathematically rigorous treatment of the subject of fractal music including background information and sound files.

A sample of fractal-based and generative compositions by Phil Jackson. (Not necessarily fractal from a mathematical perspective.)

Samples of audio structures programmed by Terran Olson using recursive algorithms.

Application of L-systems to the analysis of musical rhythm. Research by Cheng-Yuan Liou, Tai-Hei Wu, and Chia-Ying Lee.

By Julie Scrivener, from the proceedings of the Bridges 2000 Math/Art conference.

An introduction to 1/f scaling in music by Michael Bulmer. Includes demonstrations and exercises.

Across 16 subgenres and 40 composers, researchers Daniel Levitin, Parag Chordia, and Vinod Menonc found that an overwhelming majority of rhythms sampled obeyed a 1/f^β power law with β ranging from ~0.5 to 1.

Article by Zhi-Yuan Su and Tzuyin Wu in "Physica D: Nonlinear Phenomena" on a multifractal technique for analysis of melodic lines. Abstract available, but subscription required for full text.

Research by Maxence Bigerelle and Alain Iost appearing in: Chaos, Solitons and Fractals 11 (2000) 2179-2192. "The fractal aspect of different kinds of music was analyzed in keeping with the time domain." (From Research Gate - membership not required for access.)

Kenneth and Andrew Hsu found evidence of melodic interval scaling in the works of Bach, Mozart, and a collection of Swiss folk songs.

Article by Zhi-Yuan Su and Tzuyin Wu in "Physica D: Nonlinear Phenomena." Hurst exponent and Fourier spectral analyses are performed on single variable random musical walk sequences. Abstract available, but subscription or fee required for full text.

Summer Rankin, Edward Large, and Philip Fink investigated temporal fluctuations in piano performance and the prediction of these fluctuations by listeners. Their findings indicated that not only did the sample performances show fractal structure with respect to tempo fluctuation, but also that listeners appeared capable of predicting the variations, consistent with 1/f correlation.