Harmonograph

A Visual Guide to the Mathematics of Music

Author: Anthony Ashton

Publisher: Wooden Books

ISBN: 1912706059

Category: Music

Page: 64

View: 8909

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Why did Pythagoras pause outside a Blacksmith's workshop? Can the nature of Harmony really be understood visually? Why do harmonies leave gaps or 'commas' when added together? In this charming little book Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings this is a unique and original introduction to this timeless subject. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Harmonograph

A Visual Guide to the Mathematics of Music

Author: Anthony Ashton

Publisher: Bloomsbury Publishing USA

ISBN: 0802714099

Category: Mathematics

Page: 58

View: 1300

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Ashton presents a short, illustrated introduction to the evolution of simple harmonic theory. Illustrations.

How Equal Temperament Ruined Harmony (and Why You Should Care)

Author: Ross W. Duffin

Publisher: W. W. Norton & Company

ISBN: 9780393075649

Category: Music

Page: 208

View: 1779

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"A fascinating and genuinely accessible guide....Educating, enjoyable, and delightfully unscary."—Classical Music What if Bach and Mozart heard richer, more dramatic chords than we hear in music today? What sonorities and moods have we lost in playing music in "equal temperament"—the equal division of the octave into twelve notes that has become our standard tuning method? Thanks to How Equal Temperament Ruined Harmony, "we may soon be able to hear for ourselves what Beethoven really meant when he called B minor 'black'" (Wall Street Journal).In this "comprehensive plea for more variety in tuning methods" (Kirkus Reviews), Ross W. Duffin presents "a serious and well-argued case" (Goldberg Magazine) that "should make any contemporary musician think differently about tuning" (Saturday Guardian). Some images in the ebook are not displayed owing to permissions issues.

Mathematics and Music

Composition, Perception, and Performance

Author: James S. Walker,Gary W. Don

Publisher: CRC Press

ISBN: 1439867097

Category: Mathematics

Page: 342

View: 9640

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At first glance, mathematics and music seem to be from separate worlds—one from science, one from art. But in fact, the connections between the two go back thousands of years, such as Pythagoras’s ideas about how to quantify changes of pitch for musical tones (musical intervals). Mathematics and Music: Composition, Perception, and Performance explores the many links between mathematics and different genres of music, deepening students’ understanding of music through mathematics. In an accessible way, the text teaches the basics of reading music and explains how various patterns in music can be described with mathematics. The authors extensively use the powerful time-frequency method of spectrograms to analyze the sounds created in musical performance. Numerous examples of music notation assist students in understanding basic musical scores. The text also provides mathematical explanations for musical scales, harmony, and rhythm and includes a concise introduction to digital audio synthesis. Along with helping students master some fundamental mathematics, this book gives them a deeper appreciation of music by showing how music is informed by both its mathematical and aesthetic structures. Web Resource On the book’s CRC Press web page, students can access videos of many of the spectrograms discussed in the text as well as musical scores playable with the free music software MuseScore. An online bibliography offers many links to free downloadable articles on math and music. The web page also provides links to other websites related to math and music, including all the sites mentioned in the book.

Music and Mathematics

From Pythagoras to Fractals

Author: John Fauvel,Raymond Flood,Robin J. Wilson

Publisher: Oxford University Press on Demand

ISBN: 9780199298938

Category: Mathematics

Page: 189

View: 7130

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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.

Musimathics

The Mathematical Foundations of Music

Author: Gareth Loy

Publisher: MIT Press

ISBN: 0262516551

Category: Education

Page: 504

View: 9354

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"Mathematics can be as effortless as humming a tune, if you know the tune," writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music--a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science.In this volume, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Musimathics is carefully structured so that new topics depend strictly on topics already presented, carrying the reader progressively from basic subjects to more advanced ones. Cross-references point to related topics and an extensive glossary defines commonly used terms. The book explains the mathematics and physics of music for the reader whose mathematics may not have gone beyond the early undergraduate level. Calling himself "a composer seduced into mathematics," Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The topics are all subjects that contemporary composers, musicians, and musical engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Additional material can be found at a companion web site.

Tuning and Temperament

A Historical Survey

Author: J. Murray Barbour

Publisher: Courier Corporation

ISBN: 0486317358

Category: Music

Page: 256

View: 2309

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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.

The Jazz of Physics

The Secret Link Between Music and the Structure of the Universe

Author: Stephon Alexander

Publisher: Basic Books

ISBN: 0465098509

Category: Science

Page: 272

View: 9687

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More than fifty years ago, John Coltrane drew the twelve musical notes in a circle and connected them by straight lines, forming a five-pointed star. Inspired by Einstein, Coltrane put physics and geometry at the core of his music. Physicist and jazz musician Stephon Alexander follows suit, using jazz to answer physics' most vexing questions about the past and future of the universe. Following the great minds that first drew the links between music and physics-a list including Pythagoras, Kepler, Newton, Einstein, and Rakim-The Jazz of Physics reveals that the ancient poetic idea of the Music of the Spheres," taken seriously, clarifies confounding issues in physics. The Jazz of Physics will fascinate and inspire anyone interested in the mysteries of our universe, music, and life itself.

The Music of the Spheres

Music, Science, and the Natural Order of the Universe

Author: Jamie James

Publisher: Springer Science & Business Media

ISBN: 9780387944746

Category: Music

Page: 262

View: 4280

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For centuries, scientists and philosophers believed that the universe was a stately, ordered mechanism, both mathematical and musical. The perceived distances between objects in the sky mirrored (and were mirrored by) the spaces between notes forming chords and scales. The smooth operation of the cosmos created a divine harmony that composers sought to capture and express. Jamie James allows readers to see how this scientific philosophy emerged, how it was shattered by changing views of the universe and the rise of Romanticism, and to what extent it survives today - if at all. From Pythagoras to Newton, Bach to Beethoven, and on to the twentieth century of Einstein, Schoenberg, Stravinsky, Cage and Glass. A spellbinding examination of the interwoven fates of science and music throughout history.

Platonic & Archimedean Solids

Author: Daud Sutton

Publisher: Bloomsbury Publishing USA

ISBN: 0802713866

Category: Mathematics

Page: 58

View: 9576

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Looks at the relationship between the five Platonic and thirteen Archimedean solids.

From Music to Mathematics

Exploring the Connections

Author: N.A

Publisher: JHU Press

ISBN: 142141919X

Category: Mathematics

Page: 320

View: 5691

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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.

The Elements of Music

Melody, Rhythm and Harmony

Author: Jason Martineau

Publisher: Wooden Books

ISBN: 1912706083

Category: Music

Page: 64

View: 3493

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What is the secret code behind so many musical compositions? How do you substitute chords to create greater musical complexity? Why is music so good at playing with people's emotions? In this compact book, composer and pianist Jason Martineau presents the elements of music in clear and comprehensible terms. Packed with superb diagrams and a wealth of fascinating hard-to-come-by musical tips, this is a great primer, and an invaluable resource for novice and professional alike.WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Physics and Music

The Science of Musical Sound

Author: Harvey E. White,Donald H. White

Publisher: Courier Corporation

ISBN: 0486794008

Category: Science

Page: 448

View: 1020

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Comprehensive and accessible, this foundational text surveys general principles of sound, musical scales, characteristics of instruments, mechanical and electronic recording devices, and many other topics. More than 300 illustrations plus questions, problems, and projects.

Q.E.D.

Beauty in Mathematical Proof

Author: Burkard Polster

Publisher: Bloomsbury Publishing USA

ISBN: 0802714315

Category: Mathematics

Page: 58

View: 4181

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Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.

Music and the Making of Modern Science

Author: Peter Pesic

Publisher: MIT Press

ISBN: 0262027275

Category: Music

Page: 360

View: 397

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In the natural science of ancient Greece, music formed the meeting place between numbers and perception; for the next two millennia, Pesic tells us in Music and the Making of Modern Science, "liberal education" connected music with arithmetic, geometry, and astronomy within a fourfold study, the quadrivium. Peter Pesic argues provocatively that music has had a formative effect on the development of modern science -- that music has been not just a charming accompaniment to thought but a conceptual force in its own right. Pesic explores a series of episodes in which music influenced science, moments in which prior developments in music arguably affected subsequent aspects of natural science. He describes encounters between harmony and fifteenth-century cosmological controversies, between musical initiatives and irrational numbers, between vibrating bodies and the emergent electromagnetism. He offers lively accounts of how Newton applied the musical scale to define the colors in the spectrum; how Euler and others applied musical ideas to develop the wave theory of light; and how a harmonium prepared Max Planck to find a quantum theory that reengaged the mathematics of vibration. Taken together, these cases document the peculiar power of music -- its autonomous force as a stream of experience, capable of stimulating insights different from those mediated by the verbal and the visual. An innovative e-book edition available for iOS devices will allow sound examples to be played by a touch and shows the score in a moving line.

Quadrivium

The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology

Author: Miranda Lundy,Anthony Ashton,Jason Martineau,Daud Sutton,John Martineau

Publisher: Walker

ISBN: 9780802778130

Category: Science

Page: 416

View: 7881

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The quadrivium—the classical curriculum—comprises the four liberal arts of number, geometry, music, and cosmology. It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences. Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series—Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence—it makes ancient wisdom and its astonishing interconnectedness accessible to us today. Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.

Math and Music

Harmonious Connections

Author: Trudi Hammel Garland,Charity Vaughan Kahn

Publisher: Dale Seymour Publication

ISBN: 9780866518291

Category: Education

Page: 162

View: 7926

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From the beat of a tribal drum to a choir of crickets--music is everywhere. Math and Music explores the music of various cultures and the sounds heard in nature while highlighting the mathematical concepts, such as proportion, patterns, Fibonacci numbers, geometric transformations, and trigonometry, found in music. The companion poster explores mysterious connections between seemingly different entities, such as music and animals! A four-page guide explains the connections students may discover.

A Little Book of Coincidence

In the Solar System

Author: John Martineau

Publisher: Wooden Books

ISBN: 1912706075

Category: Science

Page: 64

View: 1909

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Venus draws a beautiful pentagram around Earth every eight years. Jupiter's two largest moons draw a perfect four-fold flower. The Planets grandly play out the slow Music of the Spheres. Is there a secret structure hidden in the Solar System? Packed with great illustrations and serious research from many sources, this internationally bestselling little book by cosmologist John Martineau will instantly retune your cosmological circuits to the extraordinary and primary patterns behind Life, the Universe and Everything. WOODEN BOOKS are small but packed with information. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.

Science and Music

Author: Sir James H. Jeans

Publisher: Courier Corporation

ISBN: 0486139743

Category: Science

Page: 304

View: 3337

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Distinguished physicist describes the scientific principles of musical sound in a non-technical way: development of human hearing, properties of sound curves, transmission and reproduction of sound curves, more. Includes 75 illustrations.

Big Bangs

Author: Howard Goodall

Publisher: Random House

ISBN: 1446484548

Category: Music

Page: 256

View: 1092

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The dramatic story of five key turning points in a thousand years of Western music - discoveries that changed the course of history. Who first invented 'Doh Re Mi...'? What do we mean by "in tune"? Looking back down the corridor of a thousand years, Howard Goodall guides us through the stories of five seismic developments in the history of Western music. His "big bangs" may not be the ones we expect - some are surprising and some are so obvious we overlook them - but all have had an extraordinary impact. Goodall starts with the invention of notation by an 11th-century Italian monk, which removed the creation of music from the hands of the players to the pens of the composers; moves on to the first opera; then to the invention of the piano, and ends with the story of the first recording made in history. Howard Goodall has the gift of making these complicated musical advances both clear and utterly fascinating. Racy and vivid in a narrative full of colourful characters and graphic illustrations of technical processes, he also gives a wonderful sense of the culture of trial and error and competition, be it in 11th-century Italy or 19th-century America, in which all progress takes place. Big Bangs opens a window on the crucial moments in our musical culture - discoveries that made possible everything from Bach to the Beatles - and tells us a riveting story of a millennium of endeavour.