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

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.

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Tonality and Scale Theory · R. Wilding-White; Journal of Music Theory , Vol. 5, No . 2 (Winter, 1961), pp. 275-286; Subjects: Music; Key terms: tonality, pitch, gamut, scale, musical, diatonic, tonic, octave, formula, transposition, cyclical, triad, tone, major, chord, chromatic, mode, identical, system, schoenberg; CiteRank: 0.6295   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,  The Music of the Spheres - The Imaginative Conservative
This idea of “the music of the spheres” runs through the history of Western civilization with an extraordinary consistency, even up to the twentieth century. Like Pythagoras, Schoenberg believed that number was the key to the universe. Unlike Pythagoras, he believed his manipulation of number could alter  Music by the Numbers: From Pythagoras to Schoenberg: 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,  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 and Mathematics: From Pythagoras to Fractals - Google Books Result
John Fauvel, Raymond Flood, Robin J. Wilson - ‎2003 - Mathematics 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: Eli Maor
How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth centuryMusic 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,  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.

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