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Music A Mathematical Offering

Music  A Mathematical Offering Author Dave Benson
ISBN-10 9780521853873
Release 2007
Pages 411
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Explores interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.



Musical Mathematics

Musical Mathematics Author Cris Forster
ISBN-10 0811874079
Release 2010-07-14
Pages 952
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Musical Mathematics is the definitive tome for the adventurous musician. Integrating mathematics, music history, and hands-on experience, this volume serves as a comprehensive guide to the tunings and scales of acoustic instruments from around the world. Author, composer, and builder Cris Forster illuminates the mathematical principles of acoustic music, offering practical information and new discoveries about both traditional and innovative instruments.With this knowledge readers can improve, or begin to build, their own instruments inspired by Forster's creationsshown in 16 color plates. For those ready to step outside musical conventions and those whose curiosity about the science of sound is never satisfied, Musical Mathematics is the map to a new musical world.



Mathematics and Music

Mathematics and Music Author David Wright
ISBN-10 9780821848739
Release 2009
Pages 161
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Many people intuitively sense that there is a connection between mathematics and music. If nothing else, both involve counting. There is, of course, much more to the association. David Wright's book is an investigation of the interrelationships between mathematics and music, reviewing the needed background concepts in each subject as they are encountered. Along the way, readers will augment their understanding of both mathematics and music. The text explores the common foundations of the two subjects, which are developed side by side. Musical and mathematical notions are brought together, such as scales and modular arithmetic, intervals and logarithms, tone and trigonometry, and timbre and harmonic analysis. When possible, discussions of musical and mathematical notions are directly interwoven. Occasionally the discourse dwells for a while on one subject and not the other, but eventually the connection is established, making this an integrative treatment of the two subjects. The book is a text for a freshman level college course suitable for musically inclined or mathematically inclined students, with the intent of breaking down any apprehension that either group might have for the other subject. Exercises are given at the end of each chapter. The mathematical prerequisites are a high-school level familiarity with algebra, trigonometry, functions, and graphs. Musically, the student should have had some exposure to musical staffs, standard clefs, and key signatures, though all of these are explained in the text.



From Music to Mathematics

From Music to Mathematics Author Gareth E. Roberts
ISBN-10 9781421419183
Release 2016-02-11
Pages 320
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Taking a "music first" approach, Gareth E. Roberts’s From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions, to manipulating trigonometric formulas, to constructing group multiplication tables and proving a number is irrational. Topics discussed in the book include ● Rhythm ● Introductory music theory ● The science of sound ● Tuning and temperament● Symmetry in music ● The Bartók controversy ● Change ringing ● Twelve-tone music● Mathematical modern music ● The Hemachandra–Fibonacci numbers and the golden ratio● Magic squares ● Phase shifting Featuring numerous musical excerpts, including several from jazz and popular music, each topic is presented in a clear and in-depth fashion. Sample problems are included as part of the exposition, with carefully written solutions provided to assist the reader. The book also contains more than 200 exercises designed to help develop students’ analytical skills and reinforce the material in the text. From the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity.



Music and Mathematics

Music and Mathematics Author John Fauvel
ISBN-10 0199298939
Release 2006
Pages 189
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From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques.



Music

Music Author David J. Benson
ISBN-10 1139641638
Release 2006
Pages 427
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Explores interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.



The Math Behind the Music

The Math Behind the Music Author Leon Harkleroad
ISBN-10 9780521810951
Release 2006-08-14
Pages 143
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Looks at the mathematical aspects of music, covering such topics as compositional techniques, scales, tuning systems, and music criticism.



Musimathics

Musimathics Author Gareth Loy
ISBN-10 9780262292764
Release 2011-08-19
Pages 584
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Volume 2 of Musimathics continues the story of music engineering begun in Volume 1, focusing on the digital and computational domain. Loy goes deeper into the mathematics of music and sound, beginning with digital audio, sampling, and binary numbers, as well as complex numbers and how they simplify representation of musical signals. Chapters cover the Fourier transform, convolution, filtering, resonance, the wave equation, acoustical systems, sound synthesis, the short-time Fourier transform, and the wavelet transform. These subjects provide the theoretical underpinnings of today's music technology. The examples given are all practical problems in music and audio. Additional material can be found at http://www.musimathics.com.



Mathematical Analysis of Physical Problems

Mathematical Analysis of Physical Problems Author Philip Russell Wallace
ISBN-10 9780486646763
Release 1972
Pages 616
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This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more. 1972 edition.



Mathematical Modelling Techniques

Mathematical Modelling Techniques Author Rutherford Aris
ISBN-10 9780486138893
Release 2012-06-29
Pages 288
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Highly useful volume discusses the types of models, how to formulate and manipulate them for best results. Numerous examples.



Our Mathematical Universe

Our Mathematical Universe Author Max Tegmark
ISBN-10 9780385350495
Release 2014-01-07
Pages 432
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Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.



Number Theory

Number Theory Author George E. Andrews
ISBN-10 9780486135106
Release 2012-04-30
Pages 288
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Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more



Ingenious Mathematical Problems and Methods

Ingenious Mathematical Problems and Methods Author Louis A. Graham
ISBN-10 9780486282930
Release 2013-04-10
Pages 246
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Collection of 100 of the best submissions to a math puzzle column features problems in engineering situations, logic, number theory, and geometry. Most solutions include details of several different methods.



Excursions in Number Theory

Excursions in Number Theory Author Charles Stanley Ogilvy
ISBN-10 0486257789
Release 1988
Pages 168
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Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.



Music by the Numbers

Music by the Numbers Author Eli Maor
ISBN-10 9781400889891
Release 2018-05-15
Pages 176
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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.



Curvature in Mathematics and Physics

Curvature in Mathematics and Physics Author Shlomo Sternberg
ISBN-10 9780486292717
Release 2013-04-17
Pages 416
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Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.



Tuning and Temperament

Tuning and Temperament Author J. Murray Barbour
ISBN-10 9780486317359
Release 2013-07-04
Pages 256
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The demands of tuning (attaining the perfect scale) and temperament (the compromises necessary for composing in every key) have challenged musicians from the earliest civilizations onward. This guide surveys these longstanding problems, devoting a chapter to each principal theory and offering a running account of the complete history of tuning and temperament. Organized chronologically, the book features a helpful glossary and numerous illustrative tables, and it requires minimal background in music theory. This new reissue is currently the only edition in print of a much-quoted classic. 9 figures. 180 tables.