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.
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.
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 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
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
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
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 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.
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.
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 José Oscar Marques
Fractal-based compositions in general MIDI file format. (Not necessarily fractal from a mathematical perspective.)
The Music of Phil Jackson
A sample of fractal-based and generative compositions by Phil Jackson. (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.