Fractal Geometry of Music

Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geom...

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Bibliographic Details
Published in:	Proceedings of the National Academy of Sciences - PNAS Vol. 87; no. 3; pp. 938 - 941
Main Authors:	Hsu, Kenneth J., Hsu, Andreas J.
Format:	Journal Article
Language:	English
Published:	Washington, DC National Academy of Sciences of the United States of America 01-02-1990 National Acad Sciences
Subjects:	Acoustics Art music Audio frequencies Childrens songs Diminished intervals Exact sciences and technology Fractals Fundamental areas of phenomenology (including applications) Integers Melody Music and musical intruments Music composition Musical intervals Physics Ratios Fractal system Musical acoustics
Online Access:	Get full text
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Summary:	Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0027-8424 1091-6490
DOI:	10.1073/pnas.87.3.938