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Music by the Numbers: From Pythagoras to Schoenberg
Eli Maor

ISBN: 9780691176901 | 176 pages | 5 Mb


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Music by the Numbers: From Pythagoras to Schoenberg Eli Maor

Publisher: Princeton University Press

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 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  Music by the numbers - CERN Document Server 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 ofSchönberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and  Reilly – Is Music Sacred? | The Philadelphia Society 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. Cassiodorus taught that In the 1920s, Arnold Schoenberg unleashed the centrifugal forces of disintegration in music through his denial of tonality.Schoenberg  Music by the Numbers - From Pythagoras to Schoenberg - Livros na Compre o livro Music by the Numbers - From Pythagoras to Schoenberg na Amazon.com.br: confira as ofertas para livros em inglês e importados. Chromatic scale - Wikipedia The chromatic scale is a musical scale with twelve pitches, each a semitone above or below its adjacent pitches. As a result, in 12-tone equal temperament the chromatic scale covers all 12 of the available pitches. Thus, there is only one chromatic scale. Moreover, in equal temperament, all the semitones have the same  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 

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