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

• Music by the Numbers: From Pythagoras to Schoenberg
• Eli Maor
• Page: 176
• Format: pdf, ePub, mobi, fb2
• ISBN: 9780691176901
• Publisher: Princeton University Press

Download Music by the Numbers: From Pythagoras to Schoenberg

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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.

Arnold Schoenberg http - MUSIC SOUND TONE THERAPY
What is not known is that his variations and use of the "Tone Map" are strikingly similar to some of the techniques employed by Number Harmonics, which are derived from Ancient Pythagorean Techniques. Perhaps it only goes to show that there is nothing new under the Sun. Links to some of the Schoenberg Techniques  Music by the Numbers, Eli Maor - Shop Online for Books in Fiji
Fishpond Fiji, Music by the Numbers: From Pythagoras to Schoenberg by Eli Maor. Buy Books online: Music by the Numbers: From Pythagoras to Schoenberg , 2018, ISBN 0691176906, Eli Maor. Pythagorean Longings and Cosmic Symphonies: The Musical
Even after World War II, physics re-engaged archaic Pythagorean imagery in the service of new theoretical initiatives; at the same time, electronic and film music created new “sounds of space” that contrasted with the “cosmic sublime” invoked by Beethoven, Stravinsky, and Schoenberg. So far, though, the sonifications of  Music by the Numbers: From Pythagoras to Schoenberg: Amazon.es
Encuentra Music by the Numbers: From Pythagoras to Schoenberg de Eli Maor ( ISBN: 9780691176901) en Amazon. Envíos gratis a partir de 19€. 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. New Book - Music by the Numbers: From Pythagoras to Schoenberg
Author: Eli Maor Title: Music by the Numbers: From Pythagoras to Schoenberg Publisher: Princeton University Press Publication Date: 5/8/2018. ISBN: 9780691176901 Hardcover (English). Find in WorldCat - Find on Amazon.com  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  The Music of the Spheres, or the Metaphysics of Music
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 took the twelve equal semi-tones from the chromatic scale and declared that music must be written in such a way that each of these twelve semi- tones  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 

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