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

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ISBN: 9780691176901 | 176 pages | 5 Mb

• Music by the Numbers: From Pythagoras to Schoenberg
• Eli Maor
• Page: 176
• Format: pdf, ePub, fb2, mobi
• 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.

"NUMBERS AND NUMBER CORRESPONDENCES IN OPUS 40 BY
These numbers, as used by Schoenberg, also express the Pythagorean theorem and the tetraktys. Further, Schoenberg used numbers to develop internal numerical correspondences between many of the various compositional components at both the micro and macro levels. The composition has many curious features. Undercurrents: The Hidden Wiring of Modern Music - Google Books Result
The Wire - ‎2002 - Social Science The Music of the Spheres, or The Metaphysics of Music | Future
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  “The Organ Music and Musical Philosophy of Charles W - Charles Ore
Numbers and number correspondences in Opus 40 by Arnold Schoenberg :Pythagoras and the Quadrivium Revisited by Charles Ore. This doctoral dissertation offers a numerical analysis of Schoenberg's Variations on a Recitative for Organ. It is Dr. Ore's thesis that the peculiarities of the score andSchoenberg's insistence  Music by the Numbers - Title – Rightsdesk Worldwide
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: From Pythagoras to - Amazon.com.au
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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