Article ID: CBB000774155

Musical Logarithms in the Seventeenth Century: Descartes, Mercator, Newton (2008)


This paper describes three previously little-studied sources from the 17th century, which reveal early uses of logarithms in the mathematical study of music. It describes the problem, which had existed since antiquity, of providing quantitative measures for the relationships between musical intervals when the latter were defined by identification with mathematical ratios; and it shows how this problem was solved by Descartes, Newton, and Nicolaus Mercator in the mid-17th century by using logarithms to provide measures of intervals, which could then be compared with one another. It discusses the composition and interrelationships of the manuscript sources for this work.


Description Explores “the early uses of logarithms in the mathematical study of music.” (from the abstract)

Citation URI

Similar Citations

Book Rommevaux, S.; Vendrix, P.; Zara, V.; (2011)
Proportions. Science, musique, peinture et architecture (/isis/citation/CBB001211955/)

Thesis Abram Kaplan; (2018)
The Myth of Greek Algebra: Progress and Community in Early-Modern Mathematics (/isis/citation/CBB202265617/)

Chapter Roux, Sophie; (2006)
Découvrir le principe d'inertie (/isis/citation/CBB001024285/)

Article Whiteside, D. T.; (2014)
“And John Napier created logarithms...” (/isis/citation/CBB001451419/)

Article Burn, R. P.; (2001)
Alphonse Antonio de Sarasa and Logarithms (/isis/citation/CBB000100596/)

Article Navarro-Loidi, Juan; Llombart, José; (2008)
The Introduction of Logarithms into Spain (/isis/citation/CBB000774619/)

Article Clark, Kathleen M.; Montelle, Clemency; (2012)
Priority, Parallel Discovery, and Pre-eminence: Napier, Bürgi and the Early History of the Logarithm Relation (/isis/citation/CBB001211450/)

Book Havil, Julian; (2014)
John Napier: Life, Logarithms, and Legacy (/isis/citation/CBB001510061/)

Article Mishra, Vinod; (2005)
Invention of Logarithms (/isis/citation/CBB000741848/)

Book Gladstone-Millar, Lynne; (2003)
John Napier: Logarithm John (/isis/citation/CBB000320403/)

Article Fischer, Joachim; Ruess, Bärbel; (2014)
Napier Revisited or a New Look at the Computation of His Logarithms (/isis/citation/CBB001451420/)

Book Assayag, Gérard; Feichtinger, Hans Georg; Rodrigues, José Francisco; (2002)
Mathematics and Music: A Diderot Mathematical Forum (/isis/citation/CBB000330004/)

Book Cerrai, Paola; Freguglia, Paolo; Pellegrini, Claudio; (2002)
The Application of Mathematics to the Sciences of Nature: Critical Moments and Aspects (/isis/citation/CBB000201259/)

Book Wolff, Christoph; (2000)
Johann Sebastian Bach: The Learned Musician (/isis/citation/CBB000320288/)

Article Guicciardini, Niccolò; (2013)
The Role of Musical Analogies in Newton's Optical and Cosmological Work (/isis/citation/CBB001211204/)

Book David S. Richeson; (2019)
Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity (/isis/citation/CBB243851906/)

Authors & Contributors
Kaplan, Abram
Zara, V.
Wolff, Christoph
Whiteside, D. T.
Vendrix, Philippe
Ruess, Bärbel
Historia Mathematica
British Society for the History of Mathematics Bulletin
Archive for History of Exact Sciences
Studies in History of Medicine and Science
Revue d'Histoire des Mathématiques
Journal of the History of Ideas
Princeton University Press
W. W. Norton & Co.
National Museums of Scotland Publishing
Kluwer Academic
El Colegio de Mexico
Ratio and proportion
Science and music
Newton, Isaac
Napier, John
Leibniz, Gottfried Wilhelm von
Descartes, René
Viète, François de la Bigotière
Galilei, Galileo
Time Periods
17th century
16th century
18th century
21st century

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment