{pdf download} Music by the Numbers: From Pythagoras to Schoenberg

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

• 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 "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 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's theory of relativity and Schoenberg's twelve-tone system. Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

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. 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  Music by the Numbers: From Pythagoras to Schoenberg - Books on
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 ofSchoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who  Music by the Numbers, Eli Maor - Shop Online for Books in Australia
Fishpond Australia, Music by the Numbers: From Pythagoras to Schoenberg by Eli Maor. Buy Books online: Music by the Numbers: From Pythagoras toSchoenberg, 2018, ISBN 0691176906, Eli Maor. The Music of the Spheres, or the Metaphysics of Music by Robert
When he found that harmonic music is expressed in exact numerical ratios of whole numbers, he concluded that music was the ordering principle of the world. The fact that music was . Like Pythagoras, Schoenberg believed that number was the key to the universe. Unlike Pythagoras, he believed his  Music by the Numbers: From Pythagoras to Schoenberg eBook: Eli
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 "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, 

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