This category contains sites relating to music that has demonstrably fractal characteristics, music that is derived from fractal graphics or algorithms, and research pertaining to the study or analysis of fractal music.
Subcategories 1
Related categories 3
Sites 17
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- The Music of José Oscar Marques Fractal-based compositions in general MIDI file format. (Not necessarily fractal from a mathematical perspective.)
- Brothers Technology: Fractal Music Research, publications, and compositions by Harlan Brothers. A mathematically rigorous treatment of the subject of fractal music including background information and sound files.
- Zipf's Law in Music Bill Manaris uses stochastic techniques to computationally identify and emphasize aesthetic aspects of music.
- Voss & Clarke Michael Frame's entry at the Yale Fractal Geometry site on the work of Richard Voss and John Clarke on 1/f scaling.
- The Music of Phil Jackson A sample of fractal-based and generative compositions by Phil Jackson. (Not necessarily fractal from a mathematical perspective.)
- Audio Fractals Samples of audio structures programmed by Terran Olson using recursive algorithms.
- Modelling Complexity in Musical Rhythm Application of L-systems to the analysis of musical rhythm. Research by Cheng-Yuan Liou, Tai-Hei Wu, and Chia-Ying Lee.
- Applications of Fractal Geometry to the Player Piano Music of Conlon Nancarrow By Julie Scrivener, from the proceedings of the Bridges 2000 Math/Art conference.
- Dmitry's Research A recursive approach to composition by Dmitry Kormann, illustrated using the golden ratio.
- Music from Fractal Noise An introduction to 1/f scaling in music by Michael Bulmer. Includes demonstrations and exercises.
- Musical rhythm spectra from Bach to Joplin obey a 1/f power law 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.
- Multifractal Analyses of Music Sequences 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.
- A Fractal in Bach's Cello Suite An article by Ivars Peterson at the Mathematical Association of America on research by Harlan Brothers appearing in the journal Fractals.
- Fractal Dimension and Classification of Music 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.)
- PubMed Central (PMC): Fractal geometry of music Kenneth and Andrew Hsu found evidence of melodic interval scaling in the works of Bach, Mozart, and a collection of Swiss folk songs.
- Music Walk, Fractal Geometry in Music 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.
- Fractal Tempo Fluctuation 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.