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.
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Related categories 3
Sites 23
By Julie Scrivener, from the proceedings of the Bridges 2000 Math/Art conference. (Page contains abstract, citation, and link to full PDF)
[PDF]
Samples of audio structures programmed by Terran Olson using recursive algorithms.
Research, publications, and compositions by Harlan Brothers. A mathematically rigorous treatment of the subject of fractal music including background information and sound files.
Article on an early example of a mensuration canon composed by Josquin des Prez.
Amplitude and temporal fluctuations in Jeff Porcaro’s hi-hat patterns in the track “I Keep Forgettin’” show fractal scaling.
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.)
An article by Ivars Peterson at the Mathematical Association of America on research by Harlan Brothers appearing in the journal Fractals.
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]
The distribution of interval-related data in Coltrane’s famous solo is an example of a musical power-law. (Free access with free account)
The cello suites of Johann Sebastian Bach exhibit several types of power-law scaling, the best examples of which can be considered fractal in nature. This article examines scaling with respect to the characteristics of melodic interval and its derivative, melodic moment. A new and effective method for pitch-related analysis is described and then applied to a selection of the 36 pieces that comprise the six cello suites.
An examination of Bach’s Contrapunctus IX from the perspective of fractal geometry. Conference paper by Harlan Brothers.
Application of L-systems to the analysis of musical rhythm. Research by Cheng-Yuan Liou, Tai-Hei Wu, and Chia-Ying Lee.
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.
An introduction to 1/f scaling in music by Michael Bulmer. Includes demonstrations and exercises.
[PDF]
A sample of fractal-based and generative compositions. (Not necessarily fractal from a mathematical perspective.)
Fractal-based compositions in general MIDI file format. (Not necessarily fractal from a mathematical perspective.)
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.
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.
Kenneth and Andrew Hsu found evidence of melodic interval scaling in the works of Bach, Mozart, and a collection of Swiss folk songs.
Article by Stephen Ornes in Proceedings of the National Academy of Sciences.
The Bourrée Part I from Johann Sebastian Bach's Cello Suite No. 3 provides a clear example of structural scaling. The recursive form of this structure can be visualized in the manner of a well known fractal construction — the Cantor set.
Michael Frame's entry at the Yale Fractal Geometry site on the work of Richard Voss and John Clarke on 1/f scaling.
Bill Manaris uses stochastic techniques to computationally identify and emphasize aesthetic aspects of music.
The distribution of interval-related data in Coltrane’s famous solo is an example of a musical power-law. (Free access with free account)
A sample of fractal-based and generative compositions. (Not necessarily fractal from a mathematical perspective.)
Amplitude and temporal fluctuations in Jeff Porcaro’s hi-hat patterns in the track “I Keep Forgettin’” show fractal scaling.
Article on an early example of a mensuration canon composed by Josquin des Prez.
The cello suites of Johann Sebastian Bach exhibit several types of power-law scaling, the best examples of which can be considered fractal in nature. This article examines scaling with respect to the characteristics of melodic interval and its derivative, melodic moment. A new and effective method for pitch-related analysis is described and then applied to a selection of the 36 pieces that comprise the six cello suites.
The Bourrée Part I from Johann Sebastian Bach's Cello Suite No. 3 provides a clear example of structural scaling. The recursive form of this structure can be visualized in the manner of a well known fractal construction — the Cantor set.
Michael Frame's entry at the Yale Fractal Geometry site on the work of Richard Voss and John Clarke on 1/f scaling.
Bill Manaris uses stochastic techniques to computationally identify and emphasize aesthetic aspects of music.
Article by Stephen Ornes in Proceedings of the National Academy of Sciences.
An examination of Bach’s Contrapunctus IX from the perspective of fractal geometry. Conference paper by Harlan Brothers.
Samples of audio structures programmed by Terran Olson using recursive algorithms.
By Julie Scrivener, from the proceedings of the Bridges 2000 Math/Art conference. (Page contains abstract, citation, and link to full PDF)
[PDF]
An introduction to 1/f scaling in music by Michael Bulmer. Includes demonstrations and exercises.
[PDF]
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]
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.
Kenneth and Andrew Hsu found evidence of melodic interval scaling in the works of Bach, Mozart, and a collection of Swiss folk songs.
Application of L-systems to the analysis of musical rhythm. Research by Cheng-Yuan Liou, Tai-Hei Wu, and Chia-Ying Lee.
An article by Ivars Peterson at the Mathematical Association of America on research by Harlan Brothers appearing in the journal Fractals.
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.
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.)
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.
Fractal-based compositions in general MIDI file format. (Not necessarily fractal from a mathematical perspective.)
Research, publications, and compositions by Harlan Brothers. A mathematically rigorous treatment of the subject of fractal music including background information and sound files.
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November 30, 2023 at 20:01:53 UTC
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