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About this paper
John McDonough, Andrzej Herczyński
Physicists John McDonough and Andrzej Herczyński developed a mathematical framework to identify and quantify fractal patterns in musical compositions, focusing on self-similarity in melodic motifs across temporal scales. Their approach defines musical fractal dimension based on both temporal scaling and tonal complexity, which was then applied to works spanning five centuries to reveal and measure the presence of such structures.
Key insights
- Musical fractals are often 'quasi-fractal,' meaning composers adapt mathematical structures for artistic expression rather than strict adherence.
- The proposed framework offers a quantifiable and musically sensitive method for identifying fractal patterns that respects compositional intent and listener perception.
- Analysis across centuries reveals distinct historical patterns in the use and sophistication of musical fractal techniques, from Renaissance prolation canons to Baroque nested sequences and their revival in contemporary works.
Summary by alphaXiv.
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