Mathematics and Music

Mathematics and Music

Author: David Wright

Publisher: American Mathematical Soc.

Published: 2009

Total Pages: 178

ISBN-13: 0821848739

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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.


Book Synopsis Mathematics and Music by : David Wright

Download or read book Mathematics and Music written by David Wright and published by American Mathematical Soc.. This book was released on 2009 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Publisher: JHU Press

Published: 2016-02-15

Total Pages: 320

ISBN-13: 1421419181

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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.


Book Synopsis From Music to Mathematics by : Gareth E. Roberts

Download or read book From Music to Mathematics written by Gareth E. Roberts and published by JHU Press. This book was released on 2016-02-15 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Music, Math, and Mind

Author: David Sulzer

Publisher:

Published: 2021-03-23

Total Pages: 240

ISBN-13: 9780231193788

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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.


Book Synopsis Music, Math, and Mind by : David Sulzer

Download or read book Music, Math, and Mind written by David Sulzer and published by . This book was released on 2021-03-23 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Music: A Mathematical Offering

Author: Dave Benson

Publisher: Cambridge University Press

Published: 2007

Total Pages: 426

ISBN-13: 0521853877

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


Book Synopsis Music: A Mathematical Offering by : Dave Benson

Download or read book Music: A Mathematical Offering written by Dave Benson and published by Cambridge University Press. This book was released on 2007 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the 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

Publisher: Cambridge University Press

Published: 2006-08-14

Total Pages: 7

ISBN-13: 0521810957

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Accompanying CD-ROM includes musical selections.


Book Synopsis The Math Behind the Music by : Leon Harkleroad

Download or read book The Math Behind the Music written by Leon Harkleroad and published by Cambridge University Press. This book was released on 2006-08-14 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying CD-ROM includes musical selections.

Math and Music

Math and Music

Author: Trudi Hammel Garland

Publisher: Dale Seymour Publications Secondary

Published: 1995

Total Pages: 0

ISBN-13: 9780866518291

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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.


Book Synopsis Math and Music by : Trudi Hammel Garland

Download or read book Math and Music written by Trudi Hammel Garland and published by Dale Seymour Publications Secondary. This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Cool Math for Hot Music

Cool Math for Hot Music

Author: Guerino Mazzola

Publisher: Springer

Published: 2016-10-26

Total Pages: 323

ISBN-13: 331942937X

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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.


Book Synopsis Cool Math for Hot Music by : Guerino Mazzola

Download or read book Cool Math for Hot Music written by Guerino Mazzola and published by Springer. This book was released on 2016-10-26 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Topos of Music

The Topos of Music

Author: Guerino Mazzola

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 1310

ISBN-13: 303488141X

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With contributions by numerous experts


Book Synopsis The Topos of Music by : Guerino Mazzola

Download or read book The Topos of Music written by Guerino Mazzola and published by Birkhäuser. This book was released on 2012-12-06 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts

Mathematical Music

Mathematical Music

Author: Nikita Braguinski

Publisher:

Published: 2022

Total Pages:

ISBN-13: 9781032062204

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"Mathematical Music offers a concise and easily accessible history of how mathematics was in fact used broadly to create music. The story presented in this short, engaging volume ranges from ratios in antiquity to random combinations in the 17th century, 20th-century statistics, and today's artificial intelligence. This book provides a fascinating panorama of the gradual mechanization of thought processes involved in the creation of music. How did Baroque authors envision a composition system based on combinatorics? What was it like to create musical algorithms at the beginning of the 20th century, before the computer became a reality? And how does this all explain today's use of artificial intelligence and machine learning in music? In addition to discussing the history and the present state of mathematical music, Braguinski also takes an imaginary look at what possibilities the near future of music AI might hold for listeners, musicians, and the society. Grounded in research findings from musicology and the history of technology, and written for the non-specialist general audience, this book helps the reader make sense of the discussions surrounding today's music AI by situating them in a continuous historical context"--


Book Synopsis Mathematical Music by : Nikita Braguinski

Download or read book Mathematical Music written by Nikita Braguinski and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical Music offers a concise and easily accessible history of how mathematics was in fact used broadly to create music. The story presented in this short, engaging volume ranges from ratios in antiquity to random combinations in the 17th century, 20th-century statistics, and today's artificial intelligence. This book provides a fascinating panorama of the gradual mechanization of thought processes involved in the creation of music. How did Baroque authors envision a composition system based on combinatorics? What was it like to create musical algorithms at the beginning of the 20th century, before the computer became a reality? And how does this all explain today's use of artificial intelligence and machine learning in music? In addition to discussing the history and the present state of mathematical music, Braguinski also takes an imaginary look at what possibilities the near future of music AI might hold for listeners, musicians, and the society. Grounded in research findings from musicology and the history of technology, and written for the non-specialist general audience, this book helps the reader make sense of the discussions surrounding today's music AI by situating them in a continuous historical context"--

A Geometry of Music

A Geometry of Music

Author: Dmitri Tymoczko

Publisher: OUP USA

Published: 2011-03-21

Total Pages: 469

ISBN-13: 0195336674

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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.


Book Synopsis A Geometry of Music by : Dmitri Tymoczko

Download or read book A Geometry of Music written by Dmitri Tymoczko and published by OUP USA. This book was released on 2011-03-21 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.