PMID: 11607061Feb 1, 1990Paper

Fractal geometry of music

Proceedings of the National Academy of Sciences of the United States of America
K J Hsü, 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.

References

May 12, 1978·Science·F Dyson

❮ Previous
Next ❯

Citations

Aug 31, 1999·Biophysical Journal·R MeléndezE I Canela
May 14, 1999·Trends in Ecology & Evolution·R V SoléP Bak
Feb 23, 2012·Proceedings of the National Academy of Sciences of the United States of America·Daniel J LevitinVinod Menon
Dec 15, 1991·Proceedings of the National Academy of Sciences of the United States of America·E C Uberbacher, R J Mural
Apr 15, 1991·Proceedings of the National Academy of Sciences of the United States of America·K J Hsü, A Hsü
Jan 26, 2005·Biomedical Engineering Online·Yan SunShankar Muthu Krishnan
Apr 11, 2013·Noise & Health·Robert W Sweetow
Jan 27, 2015·Bulletin of Mathematical Biology·Marcus R GarvieJeff Morgan
Jun 27, 2017·Physical Chemistry Chemical Physics : PCCP·Philippos Pomonis, Antigoni Margellou
Nov 23, 2019·Science·Samuel A MehrLuke Glowacki
Feb 12, 2020·Research : a Science Partner Journal·Paul Yaozhu ChanHaizhou Li
Nov 30, 2019·Scientific Reports·Ana Filipa Teixeira BorgesKlaus Linkenkaer-Hansen
Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R E MoctezumaF Donado
Feb 8, 2019·Cognitive Neurodynamics·Shankha SanyalDipak Ghosh
Sep 17, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V KotimäkiE J Heller
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R S MendesE K Lenzi

❮ Previous
Next ❯

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Proceedings of the National Academy of Sciences of the United States of America
K J Hsü, A J Hsü
© 2021 Meta ULC. All rights reserved