Music Theory And Mathematics

Author : Jack Moser Douthett,Martha M. Hyde,Charles J. Smith
Publisher : University Rochester Press
Page : 282 pages
File Size : 44,9 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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,5 Mb
Release : 2019
Category : Electronic
ISBN : 9813235306

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Mathematical Music Theory by Anonim Pdf

Author : David Wright
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 51,6 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.

Author : Gareth E. Roberts
Publisher : JHU Press
Page : 320 pages
File Size : 52,6 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.

Author : Guerino Mazzola
Publisher : Birkhäuser
Page : 1310 pages
File Size : 40,8 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

Author : Gerard Assayag,Hans G. Feichtinger
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 42,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662049273

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Mathematics and Music by Gerard Assayag,Hans G. Feichtinger Pdf

In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.

Author : Dave Benson
Publisher : Cambridge University Press
Page : 426 pages
File Size : 41,5 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.

Author : James S. Walker,Gary W. Don
Publisher : CRC Press
Page : 344 pages
File Size : 46,9 Mb
Release : 2013-04-10
Category : Mathematics
ISBN : 9781439867099

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Mathematics and Music by James S. Walker,Gary W. Don Pdf

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.

Author : Dmitri Tymoczko
Publisher : OUP USA
Page : 469 pages
File Size : 54,5 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.

Author : Guerino Mazzola,Maria Mannone,Yan Pang
Publisher : Springer
Page : 323 pages
File Size : 51,9 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.

Author : David Sulzer
Publisher : Unknown
Page : 240 pages
File Size : 42,7 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.

Author : Mariana Montiel,Robert W Peck
Publisher : World Scientific Publishing
Page : 372 pages
File Size : 47,5 Mb
Release : 2018-11-14
Category : Technology & Engineering
ISBN : 9789813235328

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Mathematical Music Theory by Mariana Montiel,Robert W Peck Pdf

Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself. The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music. remove

Author : Classical Conversations MultiMedia
Publisher : Unknown
Page : 128 pages
File Size : 49,8 Mb
Release : 2015-11-04
Category : Electronic
ISBN : 0996566007

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Math in Motion by Classical Conversations MultiMedia Pdf

Author : Timothy A. Johnson
Publisher : Scarecrow Press
Page : 196 pages
File Size : 50,7 Mb
Release : 2008-09-26
Category : Mathematics
ISBN : 9780810862333

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Foundations of Diatonic Theory by Timothy A. Johnson Pdf

Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals is an introductory, undergraduate-level textbook that provides an easy entry point into the challenging field of diatonic set theory, a division of music theory that applies the techniques of discrete mathematics to the properties of diatonic scales. After introducing mathematical concepts that relate directly to music theory, the text concentrates on these mathematical relationships, firmly establishing a link between introductory pedagogy and recent scholarship in music theory. It then relates concepts in diatonic set theory directly to the study of music fundamentals through pedagogical exercises and instructions. Ideal for introductory music majors, the book requires only a general knowledge of mathematics, and the exercises are provided with solutions and detailed explanations. With its basic description of musical elements, this textbook is suitable for courses in music fundamentals, music theory for non-music majors, music and mathematics, and other similar courses that allow students to improve their mathematics skills while pursuing the study of music.

Author : Godfried T. Toussaint
Publisher : CRC Press
Page : 357 pages
File Size : 50,5 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466512030

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The Geometry of Musical Rhythm by Godfried T. Toussaint Pdf

The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly dispara