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Music by the Numbers: From Pythagoras to Schoenberg

Eli Maor

Page: 176

Format: pdf, ePub, mobi, fb2

ISBN: 9780691176901

Publisher: Princeton University Press

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Music by the Numbers: From Pythagoras to Schoenberg by Eli Maor How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said &quot;musical form is close to mathematics,&quot; while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein&#039;s theory of relativity and Schoenberg&#039;s twelve-tone system. Weaving these compelling historical episodes with Maor&#039;s personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

Pythagorean Longings and Cosmic Symphonies: The Musical

Even after World War II, physics re-engaged archaic Pythagorean imagery in the service of new theoretical initiatives; at the same time, electronic and film music created new “sounds of space” that contrasted with the “cosmic sublime” invoked by Beethoven, Stravinsky, and Schoenberg. So far, though, the sonifications of

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Robert Reilly: Is Music Sacred? - CatholiCity.com

As Aristotle explained in Metaphysics, the Pythagoreans "supposed the elements of numbers to be the elements of all things, and the whole heaven to be amusical scale and a . In the 1920s, Arnold Schoenberg unleashed the centrifugal forces of disintegration in music through his denial of tonality.

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Music by numbers - The Imaginatorium

So in its place he invented a completely new system of music. The blinkered empiricist's eyebrows rise, of course, when it turns out this largely means a return to numerological nonsense. But whereas numerology from Pythagoras to Kepler was a post hoc affair, fitting numbers to music that already existed, Schoenberg

First Principles - The Music of the Spheres

He wrote a massive work called Institutiones, which echoes Plato's teaching on the ethical content of music, as well as Pythagoras's on the power of number. Schoenberg contended that tonality does not exist in nature as the very property of sound itself, as Pythagoras had claimed, but was simply an arbitrary construct of

Music by the Numbers - From Pythagoras to Schoenberg - Eli Maor

Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor

Amazon | Music by the Numbers: From Pythagoras to - アマゾン

Music by the Numbers: From Pythagoras to Schoenberg [Kindle edition] by Eli Maor. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Music bythe Numbers: From Pythagoras to Schoenberg.

Music by the Numbers: From Pythagoras to Schoenberg by Eli Maor

Music by the Numbers: From Pythagoras to Schoenberg. by Eli Maor. Hardcover, 192 Pages, Published 2018. ISBN-10: 0-691-17690-6 / 0691176906. ISBN-13: 978-0-691-17690-1 / 9780691176901. The description for this book, Music by theNumbers: From Pythagoras to Schoenberg, will be forthcom more »ing. « less

Is Music Sacred? - Crisis Magazine

As Aristotle explained in Metaphysics, the Pythagoreans “supposed the elements of numbers to be the elements of all things, and the whole heaven to be amusical scale and a . In the 1920s, Arnold Schoenberg unleashed the centrifugal forces of disintegration in music through his denial of tonality.

Maor, E.: Music by the Numbers: From Pythagoras to Schoenberg

Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor