Mathematical Music

Author : Gareth E. Roberts
Publisher : JHU Press
Page : 320 pages
File Size : 50,9 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 : Nikita Braguinski
Publisher : CRC Press
Page : 127 pages
File Size : 49,7 Mb
Release : 2022-03-13
Category : Mathematics
ISBN : 9781000545500

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Mathematical Music by Nikita Braguinski Pdf

Mathematical Music offers a concise and easily accessible history of how mathematics was used 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 contemporary 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 a 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 both student and professional readers to make sense of today’s music AI by situating it in a continuous historical context.

Author : David Wright
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 53,6 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 : Gerard Assayag,Hans G. Feichtinger
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 45,9 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 : 41,8 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 : David Sulzer
Publisher : Unknown
Page : 240 pages
File Size : 50,9 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,Francisco Gomez
Publisher : World Scientific
Page : 324 pages
File Size : 43,8 Mb
Release : 2018-10-24
Category : Mathematics
ISBN : 9789813228368

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Theoretical And Practical Pedagogy Of Mathematical Music Theory: Music For Mathematics And Mathematics For Music, From School To Postgraduate Levels by Mariana Montiel,Francisco Gomez Pdf

During the past 40 years, mathematical music theory has grown and developed in both the fields of music and mathematics. In music pedagogy, the need to analyze patterns of modern composition has produced Musical Set Theory, and the use of Group Theory and other modern mathematical structures have become almost as common as the application of mathematics in the fields of engineering or chemistry. Mathematicians have been developing stimulating ideas when exploring mathematical applications to established musical relations. Mathematics students have seen in Music in Mathematics courses, how their accumulated knowledge of abstract ideas can be applied to an important human activity while reinforcing their dexterity in Mathematics. Similarly, new general education courses in Music and Mathematics are being developed and are arising at the university level, as well as for high school and general audiences without requiring a sophisticated background in either music nor mathematics. Mathematical Music Theorists have also been developing exciting, creative courses for high school teachers and students of mathematics. These courses and projects have been implemented in the USA, in China, Ireland, France, Australia, and Spain.The objective of this volume is to share the motivation and content of some of these exciting, new Mathematical Theory and Music in Mathematics courses while contributing concrete materials to interested readers.

Author : Mariana Montiel,Robert W Peck
Publisher : World Scientific Publishing
Page : 372 pages
File Size : 53,6 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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,8 Mb
Release : 2019
Category : Electronic
ISBN : 9813235306

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Mathematical Music Theory by Anonim Pdf

Author : Leon Harkleroad
Publisher : Cambridge University Press
Page : 7 pages
File Size : 51,5 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.

Author : Gabriel Pareyon,Silvia Pina-Romero,Octavio A. Agustín-Aquino,Emilio Lluis-Puebla
Publisher : Springer
Page : 345 pages
File Size : 54,9 Mb
Release : 2017-10-20
Category : Computers
ISBN : 9783319473376

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The Musical-Mathematical Mind by Gabriel Pareyon,Silvia Pina-Romero,Octavio A. Agustín-Aquino,Emilio Lluis-Puebla Pdf

This book presents a deep spectrum of musical, mathematical, physical, and philosophical perspectives that have emerged in this field at the intersection of music and mathematics. In particular the contributed chapters introduce advanced techniques and concepts from modern mathematics and physics, deriving from successes in domains such as Topos theory and physical string theory. The authors include many of the leading researchers in this domain, and the book will be of value to researchers working in computational music, particularly in the areas of counterpoint, gesture, and Topos theory.

Author : Trudi Hammel Garland,Charity Vaughan Kahn
Publisher : Dale Seymour Publications Secondary
Page : 0 pages
File Size : 41,9 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.

Author : Guerino Mazzola
Publisher : Birkhäuser
Page : 1310 pages
File Size : 49,5 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 : Guerino Mazzola,Maria Mannone,Yan Pang
Publisher : Springer
Page : 323 pages
File Size : 52,7 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 : Michael Edgeworth Mcintyre
Publisher : World Scientific
Page : 239 pages
File Size : 40,5 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.