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
Download for free ebooks Music by the Numbers: From Pythagoras to Schoenberg English version
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.
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. Pythagoras and the Quadrivium revisited
Type of publication: Phdthesis. Citation: Ore1986. Type: Thesis (D.M.A.). Year: 1986. Pages: 253. School: University of Nebraska. Key (?): Bibliothek : ML410. S2836V3 O73 1986. Keywords: Dissertations. University of Nebraska, Musical analysis, Schönberg Arnold. Variations on a Recitative op. 40 , Symbolism ofnumbers. Music and Mathematics: From Pythagoras to Fractals - Google Books Result
John Fauvel, Raymond Flood, Robin J. Wilson - 2003 - Mathematics The Sound of Numbers - SJU - Saint Joseph's University
The Sound of Numbers is a book on the mathematics of music theory—that is, the use of mathematics to describe, analyze, .. Xenakis, Messiaen, andSchoenberg [66, 49, 44, 40, 27]. Their mathematical mathematics. ThePythagoreans' discovery of the mathematical nature of musical sound gave rise to 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 READ DOWNLOAD FREE Music by the Numbers: From Pythagoras
Get Free Download Online Music by the Numbers: From Pythagoras toSchoenberg ↓ ↓ http://newmediabook.top/server1.php?asin=0691176906 ↑ ↑Music by the Numbers: From Pythagoras to Schoenberg Eli Maor pdf free. Musicby the Numbers: From Pythagoras to Schoenberg Eli Maor read online. Eli Maor Music by Music by the Numbers: From Pythagoras to - Amazon.com.au
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, 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