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

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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 "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.

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Music and Mathematics: From Pythagoras to Fractals: Amazon.co.uk
Extraordinary insight with plenty of musical and technical knowledge shared and explained. The book is a collection of essays that do (as they say) take you from early tunings and temperament, through the maths of sound, to the odd approaches to composing (e.g. Schoenberg). You need to be dedicated to the 
MUSICAGE: CAGE MUSES on Words * Art * Music – Google Books Result
John Cage, Joan Retallack – ‎2011 – Music
Library : Is Music Sacred? | Catholic Culture
From the music of the spheres to Schoenberg’s serialism, Robert Reilly searches for the divine in musical arts. As Aristotle explained in Metaphysics, thePythagoreans “supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.” This was meant literally.
Music by the Numbers From Pythagoras to Schoenberg von Eli Maor
Music by the Numbers From Pythagoras to Schoenberg – (EAN:9780691176901)
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The Music of the Spheres, or the Metaphysics of Music
Arnold Schoenberg and John Cage, is often celebrated as just another change in the techniques Pythagoras thought that number was the key to the universe. 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.
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 
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Reilly – Is Music Sacred? | The Philadelphia Society
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. Cassiodorus taught that In the 1920s, Arnold Schoenberg unleashed the centrifugal forces of disintegration in music through his denial of tonality.Schoenberg 
Music by the Numbers ― From Pythagoras to – 三民書局
Music by the Numbers ― From Pythagoras to Schoenberg. ISBN13: 9780691176901; ISBN9:069117690; 出版社: Princeton Univ Pr; 作者:Eli Maor; 裝訂/頁數:精裝/192頁; 規格:21.6cm*14cm (高/寬); 出版日:2018/05/08 
Music by the Numbers: From Pythagoras to Schoenberg: Eli Maor
Music by the Numbers: From Pythagoras to Schoenberg [Eli Maor] on Amazon. com. *FREE* shipping on qualifying offers. How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements.

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