Directory of Fractal Music Resources

Home > Arts > Music > Styles > E > Experimental > Fractal Music

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

• Conlon Nancarrow

Resources in This Category

• A Fractal in Bach's Cello Suite

  http://mathtourist.blogspot.com/2008/09/fractal-in-bachs-cello-suite.html
  An article by Ivars Peterson at the Mathematical Association of America on research by Harlan Brothers appearing in the journal Fractals.

• Applications of Fractal Geometry to the Player Piano Music of Conlon Nancarrow

  http://homepages.wmich.edu/~jscriven/bridges.2000.pdf
  By Julie Scrivener, from the proceedings of the Bridges 2000 Math/Art conference.

• Audio Fractals

  http://halfcadence.net/audio-fractals/
  Samples of audio structures programmed by Terran Olson using recursive algorithms.

• Brothers Technology: Fractal Music

  http://www.brotherstechnology.com/math/fractal-music.html
  Research, publications, and compositions by Harlan Brothers. A mathematically rigorous treatment of the subject of fractal music including background information and sound files.

• Dmitry's Research

  http://bowerbird-studios.com/aicaramba/page2#gold.html
  A recursive approach to composition by Dmitry Kormann, illustrated using the golden ratio.

• Fractal Dimension and Classification of Music

  https://www.researchgate.net/publication/223535440_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.)

• Fractal Tempo Fluctuation

  http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4151502/
  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.

• Modelling Complexity in Musical Rhythm

  http://arxiv.org/abs/cs/0703124
  Application of L-systems to the analysis of musical rhythm. Research by Cheng-Yuan Liou, Tai-Hei Wu, and Chia-Ying Lee.

• Multifractal Analyses of Music Sequences

  http://www.sciencedirect.com/science/article/pii/S0167278906003010
  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.

• Music from Fractal Noise

  http://www.maths.uq.edu.au/~mrb/research/papers/fractalmusic.pdf
  An introduction to 1/f scaling in music by Michael Bulmer. Includes demonstrations and exercises.

• Music Walk, Fractal Geometry in Music

  http://www.sciencedirect.com/science/article/pii/S0378437107002014
  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.

• Musical rhythm spectra from Bach to Joplin obey a 1/f power law

  http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3309746/
  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.

• PubMed Central (PMC): Fractal geometry of music

  http://www.ncbi.nlm.nih.gov/pmc/articles/PMC53384/
  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 José Oscar Marques

  http://midiworld.com/c/jmarques.htm
  Fractal-based compositions in general MIDI file format. (Not necessarily fractal from a mathematical perspective.)

• The Music of Phil Jackson

  http://www.midiworld.com/c/pj.htm
  A sample of fractal-based and generative compositions by Phil Jackson. (Not necessarily fractal from a mathematical perspective.)

• Voss & Clarke

  http://classes.yale.edu/Fractals/Panorama/Music/VossClarke/VossClarke.html
  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

  http://www.cs.cofc.edu/~manaris/ZipfMIDI/
  Bill Manaris uses stochastic techniques to computationally identify and emphasize aesthetic aspects of music.

Related Categories

• Home > Computers > Multimedia > Music and Audio > Software > Composition > Fractal and Generative
• Home > Science > Math > Chaos and Fractals
• Home > Science > Math > Chaos and Fractals > Fractal Art

 

Home > Arts > Music > Styles > E > Experimental > Fractal Music

 

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