Jump to ContentJump to Main Navigation
Music and the Making of Modern Science$
Users without a subscription are not able to see the full content.

Peter Pesic

Print publication date: 2014

Print ISBN-13: 9780262027274

Published to MIT Press Scholarship Online: May 2017

DOI: 10.7551/mitpress/9780262027274.001.0001

Show Summary Details
Page of

PRINTED FROM MIT PRESS SCHOLARSHIP ONLINE (www.mitpress.universitypressscholarship.com). (c) Copyright The MIT Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in MITSO for personal use.date: 04 July 2022

Euler: The Mathematics of Musical Sadness

Euler: The Mathematics of Musical Sadness

(p.133) 9 Euler: The Mathematics of Musical Sadness
Music and the Making of Modern Science

Peter Pesic

The MIT Press

Throughout his life, the great mathematician Leonhard Euler spent most of his free time on music, to which he devoted his first book. This chapter discusses how he reformulated the ordering of musical intervals on a new mathematical basis. For this purpose, Euler devised a “degree of agreeableness” that numerically indexed musical intervals and chords, replacing ancient canons of numerical simplicity with a new criterion based on pleasure. Euler applied this criterion (and Aristotle’s teachings about the pleasure of tragedy) to argue that minor intervals and chords evoke sadness through their greater numerical complexity, hence lower degree of agreeableness than the major. This work involved extensive attention to ratios and numerical factorization immediately preceding his subsequent interest in continued fractions and number theory. Having devised a new kind of index, Euler was prepared to put forward indices that would address novel problems like the Königsberg bridge problem and the construction of polyhedra, basic concepts of what we now call topology. Throughout the book where various sound examples are referenced, please see http://mitpress.mit.edu/musicandmodernscience (please note that the sound examples should be viewed in Chrome or Safari Web browsers).

Keywords:   Leonhard Euler, Musical Theory, Pleasure, Aristotelian theory of tragic pleasure, Continued fractions, Number theory, Königsberg bridge problem, Topology

MIT Press Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs, and if you can't find the answer there, please contact us.