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Fractal Music

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

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	A Fractal in Bach's Cello Suite - http://www.maa.org/mathtourist/mathtourist_9_3_08.html An article by Ivars Peterson at the Mathematical Association of America on research appearing in the journal Fractals.
	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.
	The Music of José Oscar Marques - http://midiworld.com/c/jmarques.htm Fractal-based compositions in general MIDI file format.
	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.
	Music from Fractal Noise - http://www.maths.uq.edu.au/~mrb/qamt/fractalmusic.pdf An introduction to 1/f scaling in music by Michael Bulmer. Includes demonstrations and exercises.

	Fractal Music - http://bowerbird-studios.com/aicaramba/page2.html A recursive approach to composition by Dmitry Kormann, including detailed examples of structural scaling.
	PubMed Central (PMC): Fractal geometry of music - http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=53384 Kenneth and Andrew Hsu found evidence of melodic interval scaling in the works of Bach, Mozart, and a collection of Swiss folk songs.
	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.
	Multifractal Analyses of Music Sequences - http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVK-4KSVFV4-1&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=ae882d7846ec508e02013442a9a35cdc 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 - http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVG-4N5CXCT-Y&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=cf5cbff449ed22d40c24423449f33dc0 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.

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