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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

Full downloadable books free Music by the Numbers: From Pythagoras to Schoenberg (English Edition) iBook by Eli Maor 9780691176901

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.

Music by the Numbers: From Pythagoras to Schoenberg - H-Net
Citation: H-Net Book Channel. New Book - Music by the Numbers: FromPythagoras to Schoenberg. The H-Net Book Channel. 12-0-. -2017. https:// networks.h-net.org/node/1883/pages/1036404/new-book-music-numbers-pythagoras-schoenberg. Licensed under a Creative Commons  Sterne, Pythagoras and Pierrot (PNM 21-1+2, 1982) | Interval (Music
Pythagoras and Pierrot: An Approach to Schoenberg's Use of Numerology in the Construction of 'Pierrot lunaire' Author(s): Colin C.Sterne Source: suggestssong inPierrot, there.5 described view ofthePoet-Pierrot-Schoenberg figure berg's because itfigures 11 is also important Number amongSchoenthat it it interest  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  Is Music Sacred? - Catholic Education Resource Center
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 number. This was . 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 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,  Magic numbers: composers and their clandestine codes | Tom
The real importance of this discovery, as Kennedy says, is that it allies Plato with the heretical, Pythagorean idea that "mathematical law governed the universe and not Zeus". It's a clandestine code that ties Plato's work to the scientific arcana of music as it was understood by the ancient Greeks. And it may  Representations of Beauty in Choral Music at the Beginning of the
Representations of Beauty in Choral Music at the Beginning of the 20th and 21st Centuries: Schoenberg's “Friede auf Erden” and Lauridsen's “O Nata Lux” The origins of harmony—influenced by the Pythagorean mathematical ideal of whole-number ratios—adored perfect intervals in parallel motion. "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. Eli Maor: Music by the Numbers: From Pythagoras to Schoenberg
Eli Maor: Music by the Numbers: From Pythagoras to Schoenberg - Sprache: Englisch. (Buch) - portofrei bei eBook.de.

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