Literature DB >> 11607061

Fractal geometry of music.

K J Hsü1, A J Hsü.   

Abstract

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.

Entities:  

Year:  1990        PMID： 11607061      PMCID： PMC53384          DOI： 10.1073/pnas.87.3.938

Source DB:  PubMed          Journal:  Proc Natl Acad Sci U S A        ISSN： 0027-8424            Impact factor:   11.205


  1 in total

1.  Characterizing irregularity.

Authors:  F Dyson
Journal:  Science       Date:  1978-05-12       Impact factor: 47.728
  1 in total
  13 in total

1.  Self-similarity of the "1/f noise" called music.

Authors:  K J Hsü; A Hsü
Journal:  Proc Natl Acad Sci U S A       Date:  1991-04-15       Impact factor: 11.205

2.  Musical rhythm spectra from Bach to Joplin obey a 1/f power law.

Authors:  Daniel J Levitin; Parag Chordia; Vinod Menon
Journal:  Proc Natl Acad Sci U S A       Date:  2012-02-21       Impact factor: 11.205

3.  Locating protein-coding regions in human DNA sequences by a multiple sensor-neural network approach.

Authors:  E C Uberbacher; R J Mural
Journal:  Proc Natl Acad Sci U S A       Date:  1991-12-15       Impact factor: 11.205

4.  Universality and diversity in human song.

Authors:  Samuel A Mehr; Manvir Singh; Dean Knox; Daniel M Ketter; Daniel Pickens-Jones; S Atwood; Christopher Lucas; Nori Jacoby; Alena A Egner; Erin J Hopkins; Rhea M Howard; Joshua K Hartshorne; Mariela V Jennings; Jan Simson; Constance M Bainbridge; Steven Pinker; Timothy J O'Donnell; Max M Krasnow; Luke Glowacki
Journal:  Science       Date:  2019-11-22       Impact factor: 47.728

5.  Music of brain and music on brain: a novel EEG sonification approach.

Authors:  Shankha Sanyal; Sayan Nag; Archi Banerjee; Ranjan Sengupta; Dipak Ghosh
Journal:  Cogn Neurodyn       Date:  2018-08-28       Impact factor: 5.082

6.  Fine-structured multi-scaling long-range correlations in completely sequenced genomes--features, origin, and classification.

Authors:  Tobias A Knoch; Markus Göker; Rudolf Lohner; Anis Abuseiris; Frank G Grosveld
Journal:  Eur Biophys J       Date:  2009-06-17       Impact factor: 1.733

7.  Zipf's law in short-time timbral codings of speech, music, and environmental sound signals.

Authors:  Martín Haro; Joan Serrà; Perfecto Herrera; Alvaro Corral
Journal:  PLoS One       Date:  2012-03-29       Impact factor: 3.240

8.  Scale-free brain quartet: artistic filtering of multi-channel brainwave music.

Authors:  Dan Wu; Chaoyi Li; Dezhong Yao
Journal:  PLoS One       Date:  2013-05-22       Impact factor: 3.240

9.  Fractality of sensations and the brain health: the theory linking neurodegenerative disorder with distortion of spatial and temporal scale-invariance and fractal complexity of the visible world.

Authors:  Marina V Zueva
Journal:  Front Aging Neurosci       Date:  2015-07-15       Impact factor: 5.750

10.  Bach Is the Father of Harmony: Revealed by a 1/f Fluctuation Analysis across Musical Genres.

Authors:  Dan Wu; Keith M Kendrick; Daniel J Levitin; Chaoyi Li; Dezhong Yao
Journal:  PLoS One       Date:  2015-11-06       Impact factor: 3.240
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