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.

Music by the Numbers: From Pythagoras to Schoenberg
Trovi tutti i libri di Eli Maor - Music by the Numbers: From Pythagoras toSchoenberg. Su it.eurobuch.ch puoi confrontare libri antichi e libri nuovi e ordinarli subito al prezzo più conveniente. 9781400889891. 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. 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  Review | The Music Of The Spheres - Jamie James Author
James movingly outlines Schoenberg's Pythagorean belief in numerology as well as Hindemith's conception of musical intervals as being related to planetary . history of these phenomena right back to Pythagoras — credited with discovering the mathematics of musical intervals — and his cult of mystic number-crunchers. 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  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,  Consonance and dissonance - Wikipedia
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Consonance is associated with sweetness, pleasantness, and acceptability; dissonance is associated with harshness, unpleasantness, or unacceptability. The terms form a structural dichotomy in which they define each other 

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