Web Directory

» 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.
   http://www.maa.org/mathtourist/mathtourist_9_3_08.html

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

» 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.
   http://www.brotherstechnology.com/math/fractal-music.html

» Fractal Music
   A recursive approach to composition by Dmitry Kormann, including detailed examples of structural scaling.
   http://bowerbird-studios.com/aicaramba/page2.html

» Modelling Complexity in Musical Rhythm
   Application of L-systems to the analysis of musical rhythm.
   http://arxiv.org/abs/cs/0703124

» 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.
   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=ae882d7846ec508e02013442a9

» 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.
   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=cf5cbff449

» Music from Fractal Noise
   An introduction to 1/f scaling in music by Michael Bulmer. Includes demonstrations and exercises.
   http://www.maths.uq.edu.au/~mrb/qamt/fractalmusic.pdf

» 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.
   http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=53384

» The Music of José Oscar Marques
   Fractal-based compositions in general MIDI file format.
   http://midiworld.com/c/jmarques.htm

» The Music of Phil Jackson
   A sample of fractal-based and generative compositions by Phil Jackson.
   http://www.midiworld.com/c/pj.htm

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

» Zipf's Law in Music
   Bill Manaris uses stochastic techniques to computationally identify and emphasize aesthetic aspects of music.
   http://www.cs.cofc.edu/~manaris/ZipfMIDI/