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Open Directory - Arts: Music: Styles: E: Experimental: Fractal Music
Computers: Multimedia: Music and Audio: Software: Composition: Fractal and Generative
Science: Math: Chaos and Fractals
A Fractal in Bach's Cello Suite
- An article by Ivars Peterson at the Mathematical Association of America on research appearing in the journal Fractals.
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. [PDF]
- Samples of audio structures programmed by Terran Olson using recursive algorithms.
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.
- A recursive approach to composition by Dmitry Kormann, illustrated using the golden ratio.
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. [PDF]
Modelling Complexity in Musical Rhythm
- Application of L-systems to the analysis of musical rhythm.
Multifractal Analyses of Music Sequences
- Article in "Physica D: Nonlinear Phenomena" on a multifractal technique for analysis of melodic lines. Abstract available, but subscription required for full text.
Music Walk, Fractal Geometry in Music
- Article in "Physica D: Nonlinear Phenomena." Hurst exponent and Fourier spectral analyses are performed on single variable random musical walk sequences. Abstract available, but subscription required for full text.
Music from Fractal Noise
- An introduction to 1/f scaling in music by Michael Bulmer. Includes demonstrations and exercises. [pdf]
Musical rhythm spectra from Bach to Joplin obey a 1/f power law
- Authors found that an overwhelming majority of rhythms sampled obeyed a 1/fβ power law across 16 subgenres and 40 composers, with β ranging from ~0.5 to 1.
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.
The Music of Phil Jackson
- A sample of fractal-based and generative compositions by Phil Jackson. (Not necessarily fractal from a mathematical perspective.)
The Music of José Oscar Marques
- Fractal-based compositions in general MIDI file format. (Not necessarily fractal from a mathematical perspective.)
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.
Zipf's Law in Music
- Bill Manaris uses stochastic techniques to computationally identify and emphasize aesthetic aspects of music.
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