Math And Music

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Mathematics and Music

David Wright
Mathematics and Music Book PDF

Author : David Wright
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 52,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821848739

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Mathematics and Music by David Wright Pdf

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

Gareth E. Roberts
From Music to Mathematics Book PDF

Author : Gareth E. Roberts
Publisher : JHU Press
Page : 320 pages
File Size : 55,6 Mb
Release : 2016-02-15
Category : Mathematics
ISBN : 9781421419183

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From Music to Mathematics by Gareth E. Roberts Pdf

A guided tour of the mathematical principles inherent in music. 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, Math, and Mind

David Sulzer
Music Math and Mind Book PDF

Author : David Sulzer
Publisher : Unknown
Page : 240 pages
File Size : 47,7 Mb
Release : 2021-03-23
Category : Electronic
ISBN : 0231193785

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Music, Math, and Mind by David Sulzer Pdf

This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music. Written for musicians and music lovers with any level of science and math proficiency, including none, Music, Math, and Mind demystifies how music works while testifying to its beauty and wonder.

Music: A Mathematical Offering

Dave Benson
Music A Mathematical Offering Book PDF

Author : Dave Benson
Publisher : Cambridge University Press
Page : 426 pages
File Size : 54,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780521853873

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Music: A Mathematical Offering by Dave Benson Pdf

This book explores the interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.

Cool Math for Hot Music

Guerino Mazzola,Maria Mannone,Yan Pang
Cool Math for Hot Music Book PDF

Author : Guerino Mazzola,Maria Mannone,Yan Pang
Publisher : Springer
Page : 323 pages
File Size : 44,6 Mb
Release : 2016-10-26
Category : Computers
ISBN : 9783319429373

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Cool Math for Hot Music by Guerino Mazzola,Maria Mannone,Yan Pang Pdf

This textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and illustrated by examples from music theory (such as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions.

Math and Music

Trudi Hammel Garland,Charity Vaughan Kahn
Math and Music Book PDF

Author : Trudi Hammel Garland,Charity Vaughan Kahn
Publisher : Dale Seymour Publications Secondary
Page : 0 pages
File Size : 54,6 Mb
Release : 1995
Category : Music
ISBN : 0866518290

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Math and Music by Trudi Hammel Garland,Charity Vaughan Kahn Pdf

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.

Science, Music, And Mathematics: The Deepest Connections (Second Edition)

Michael Edgeworth Mcintyre
Science Music And Mathematics The Deepest Connections Second Edition Book PDF

Author : Michael Edgeworth Mcintyre
Publisher : World Scientific
Page : 239 pages
File Size : 50,8 Mb
Release : 2023-08-02
Category : Mathematics
ISBN : 9789811276996

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Science, Music, And Mathematics: The Deepest Connections (Second Edition) by Michael Edgeworth Mcintyre Pdf

Professor Michael Edgeworth McIntyre is an eminent scientist who has also had a part-time career as a musician. In this book he offers an extraordinary synthesis, revealing the many deep connections between science, music, and mathematics. He avoids equations and technical jargon. The connections are deep in the sense of being embedded in our very nature, rooted in biological evolution over hundreds of millions of years.Michael guides us through biological evolution, perception psychology, and even unconscious science and mathematics, all the way to the scientific uncertainties about the climate crisis.He also has a message of hope for the future. Contrary to popular belief, he holds that biological evolution has given us not only the nastiest, but also the most compassionate and cooperative parts of human nature. This insight comes from recognizing that biological evolution is far more than a simple competition between selfish genes. Instead, he argues, in some ways it is more like the turbulent, eddying flow in a river or in an atmospheric jet stream, a complex process spanning a vast range of timescales.Professor McIntyre is a Fellow of the Royal Society of London (FRS) and has long been interested in how different branches of science can better communicate with each other, and with the public. His work harnesses aspects of neuroscience and psychology that point toward the deep 'lucidity principles' that underlie skilful communication, principles related to the way music works — music of any genre.This Second Edition sharpens the previous discussion of communication skills and their importance for today's great problems, ranging from the widely discussed climate crisis to the need to understand the strengths and weaknesses of artificial intelligence.

Harmonograph

Anthony Ashton
Harmonograph Book PDF

Author : Anthony Ashton
Publisher : eBook Partnership
Page : 64 pages
File Size : 52,6 Mb
Release : 2018-04-01
Category : Music
ISBN : 9781912706051

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Harmonograph by Anthony Ashton Pdf

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. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.

Music Is Math

Oliver W. Luck
Music Is Math Book PDF

Author : Oliver W. Luck
Publisher : Trafford Publishing
Page : 51 pages
File Size : 52,7 Mb
Release : 2006
Category : Musical meter and rhythm
ISBN : 9781412059121

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Music Is Math by Oliver W. Luck Pdf

An easy method for reading and counting music rhythm patterns. Counting musically is enjoying music for life. Use the key to determine if you have counted correctly.

The Math Behind the Music

Leon Harkleroad
The Math Behind the Music Book PDF

Author : Leon Harkleroad
Publisher : Cambridge University Press
Page : 7 pages
File Size : 55,7 Mb
Release : 2006-08-14
Category : Mathematics
ISBN : 9780521810951

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The Math Behind the Music by Leon Harkleroad Pdf

Accompanying CD-ROM includes musical selections.

The Topos of Music

Guerino Mazzola
The Topos of Music Book PDF

Author : Guerino Mazzola
Publisher : Birkhäuser
Page : 1310 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881418

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The Topos of Music by Guerino Mazzola Pdf

With contributions by numerous experts

Prime Suspects

Andrew Granville,Jennifer Granville
Prime Suspects Book PDF

Author : Andrew Granville,Jennifer Granville
Publisher : Princeton University Press
Page : 233 pages
File Size : 42,9 Mb
Release : 2019-08-06
Category : Mathematics
ISBN : 9780691188737

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Prime Suspects by Andrew Granville,Jennifer Granville Pdf

An outrageous graphic novel that investigates key concepts in mathematics Integers and permutations—two of the most basic mathematical objects—are born of different fields and analyzed with separate techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body. Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics. Travel with Detective von Neumann as he leaves no clue unturned, from shepherds’ huts in the Pyrenees to secret societies in the cafés of Paris, from the hidden codes in the music of the stones to the grisly discoveries in Finite Fields. Tremble at the ferocity of the believers in deep and rigid abstraction. Feel the frustration—and the excitement—of our young heroine, Emmy Germain, as she blazes a trail for women in mathematical research and learns from Professor Gauss, the greatest forensic detective of them all. Beautifully drawn and exquisitely detailed, Prime Suspects is unique, astonishing, and witty—a once-in-a-lifetime opportunity to experience mathematics like never before.

Mathematics and Computation in Music

Mariana Montiel,Francisco Gomez-Martin,Octavio A. Agustín-Aquino
Mathematics and Computation in Music Book PDF

Author : Mariana Montiel,Francisco Gomez-Martin,Octavio A. Agustín-Aquino
Publisher : Springer
Page : 403 pages
File Size : 47,5 Mb
Release : 2019-06-11
Category : Computers
ISBN : 9783030213923

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Mathematics and Computation in Music by Mariana Montiel,Francisco Gomez-Martin,Octavio A. Agustín-Aquino Pdf

This book constitutes the thoroughly refereed proceedings of the 7th International Conference on Mathematics and Computation in Music, MCM 2019, held in Madrid, Spain, in June 2019. The 22 full papers and 10 short papers presented were carefully reviewed and selected from 48 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in topical sections on algebraic and other abstract mathematical approaches to understanding musical objects; remanaging Riemann: mathematical music theory as “experimental philosophy”?; octave division; computer-based approaches to composition and score structuring; models for music cognition and beat tracking; pedagogy of mathematical music theory. The chapter “Distant Neighbors and Interscalar Contiguities” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

A Geometry of Music

Dmitri Tymoczko
A Geometry of Music Book PDF

Author : Dmitri Tymoczko
Publisher : OUP USA
Page : 469 pages
File Size : 45,6 Mb
Release : 2011-03-21
Category : Mathematics
ISBN : 9780195336672

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A Geometry of Music by Dmitri Tymoczko Pdf

In this groundbreaking book, Tymoczko uses contemporary geometry to provide a new framework for thinking about music, one that emphasizes the commonalities among styles from Medieval polyphony to contemporary jazz.

Music Theory and Mathematics

Jack Moser Douthett,Martha M. Hyde,Charles J. Smith
Music Theory and Mathematics Book PDF

Author : Jack Moser Douthett,Martha M. Hyde,Charles J. Smith
Publisher : University Rochester Press
Page : 282 pages
File Size : 43,5 Mb
Release : 2008
Category : Mathematics
ISBN : 1580462669

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Music Theory and Mathematics by Jack Moser Douthett,Martha M. Hyde,Charles J. Smith Pdf

Essays in diatonic set theory, transformation theory, and neo-Riemannian theory -- the newest and most exciting fields in music theory today. The essays in Music Theory and Mathematics: Chords, Collections, and Transformations define the state of mathematically oriented music theory at the beginning of the twenty-first century. The volume includes essays in diatonic set theory, transformation theory, and neo-Riemannian theory -- the newest and most exciting fields in music theory today. The essays constitute a close-knit body of work -- a family in the sense of tracing their descentfrom a few key breakthroughs by John Clough, David Lewin, and Richard Cohn in the 1980s and 1990s. They are integrated by the ongoing dialogue they conduct with one another. The editors are Jack Douthett, a mathematician and music theorist who collaborated extensively with Clough; Martha M. Hyde, a distinguished scholar of twentieth-century music; and Charles J. Smith, a specialist in tonal theory. The contributors are all prominent scholars, teaching at institutions such as Harvard, Yale, Indiana University, and the University at Buffalo. Six of them (Clampitt, Clough, Cohn, Douthett, Hook, and Smith) have received the Society for Music Theory's prestigious PublicationAward, and one (Hyde) has received the ASCAP Deems Taylor Award. The collection includes the last paper written by Clough before his death, as well as the last paper written by David Lewin, an important music theorist also recently deceased. Contributors: David Clampitt, John Clough, Richard Cohn, Jack Douthett, Nora Engebretsen, Julian Hook, Martha Hyde, Timothy Johnson, Jon Kochavi, David Lewin, Charles J. Smith, and Stephen Soderberg.