Music and MathematicsMusic and Mathematics



From Ancient Greek times, music has been seen as a mathematical art, and this relationship has fascinated generations.

Author: John Fauvel

Publisher: Oxford University Press on Demand

ISBN: 0199298939

Category:

Page: 189

View: 270

From Ancient Greek times, music has been seen as a mathematical art, and this relationship has fascinated generations. This new in paperback edition of diverse, comprehensive and fully-illustrated papers, authored by leading scholars, links the two fields in a lucid manner that is suitable for students of each subject as well as the general reader.

Mathematics and MusicMathematics and Music



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: David Wright

Publisher: American Mathematical Soc.

ISBN: 9780821848739

Category:

Page: 161

View: 463

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.

Mathematics and MusicMathematics and Music



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.

Author: Gerard Assayag

Publisher: Springer Science & Business Media

ISBN: 9783662049273

Category:

Page: 288

View: 228

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.

Mathemusical ConversationsMathemusical Conversations



This volume is a compilation of the invited talks given at the Mathemusical Conversations workshop that took place in Singapore from 13-15 February 2015, organized by Elaine Chew in partnership with Gérard Assayag for the scientific ...

Author: Jordan B L Smith

Publisher: World Scientific

ISBN: 9789813140110

Category:

Page: 316

View: 515

Mathemusical Conversations celebrates the understanding of music through mathematics, and the appreciation of mathematics through music. This volume is a compilation of the invited talks given at the Mathemusical Conversations workshop that took place in Singapore from 13–15 February 2015, organized by Elaine Chew in partnership with Gérard Assayag for the scientific program and with Bernard Lanskey for the artistic program. The contributors are world experts and leading scholars, writing on the intersection of music and mathematics. They also focus on performance and composition, two topics which are foundational both to the understanding of human creativity and to the creation of tomorrow's music technologies. This book is essential reading for researchers in both music and mathematics. It will also appeal more broadly to scholars, students, musicians, and anyone interested in new perspectives on the intimate relationship between these two universal human activities. Contents:Foreword by Series EditorsForeword by Workshop OrganizersMathemusical Engagement:Without Our Consent (Paul Schoenfield)Approaches to Musical Expression in Harmonix Video Games (Eran Egozy)Motion and Gravitation in the Musical Spheres (Elaine Chew)Mathemusical Creativity:Improvising in Creative Symbolic Interaction (Gérard Assayag)Music, Creativity, and Computers (Margaret A Boden)Tiling Canons as a Key to Approaching Open Mathematical Conjectures? (Moreno Andreatta)Shaping Performance:Musical Motives in Performance: A Study of Absolute Timing Patterns (Neta Spiro, Nicolas Gold and John Rink)Playing with Variables: Anticipating One Particular Performance of Bach's Goldberg Variations (Bernard Lanskey and Stephen Emmerson)The Informatics Philharmonic in the Indiana University Summer String Academy (Christopher Raphael)Educating the Mathemusical:Mathematical Thought and Empirical Approaches in Higher Education in Music (Jian Yang)Action and Symbol: An Essential Tension (Jeanne Bamberger)Educating the Mathemusical: Balancing the Equation (Don McLean)Geometries:Graph-theoretic and Geometric Models of Music (Richard Cohn)In Quest of Musical Vectors (Dmitri Tymoczko)A Topological Approach of Musical Relationships (Jean-Louis Giavitto and Antoine Spicher)List of Contributors Readership: Advanced secondary school students; post-secondary school students; and scientists, mathematicians, musicians and members of the public interested in the mathematical music sciences.

Musical MathematicsMusical Mathematics



Integrating mathematics, music history, and hands-on experience, this volume serves as a comprehensive guide to the tunings and scales of acoustic instruments from around the world.

Author: Cris Forster

Publisher: Chronicle Books

ISBN: 0811874079

Category:

Page: 952

View: 360

Musical Mathematics is the definitive tome for the adventurous musician. Integrating mathematics, music history, and hands-on experience, this volume serves as a comprehensive guide to the tunings and scales of acoustic instruments from around the world. Author, composer, and builder Cris Forster illuminates the mathematical principles of acoustic music, offering practical information and new discoveries about both traditional and innovative instruments.With this knowledge readers can improve, or begin to build, their own instruments inspired by Forster's creationsshown in 16 color plates. For those ready to step outside musical conventions and those whose curiosity about the science of sound is never satisfied, Musical Mathematics is the map to a new musical world.

Music A Mathematical OfferingMusic A Mathematical Offering



This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.

Author: Dave Benson

Publisher: Cambridge University Press

ISBN: 0521619998

Category:

Page: 426

View: 926

Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.

Mathematics and Computation in MusicMathematics and Computation in Music



This book constitutes the refereed proceedings of the Third International Conference on Mathematics and Computation in Music, MCM 2011, held in Paris, France, in June 2011.

Author: Carlos Agon

Publisher: Springer Science & Business Media

ISBN: 9783642215896

Category:

Page: 375

View: 545

This book constitutes the refereed proceedings of the Third International Conference on Mathematics and Computation in Music, MCM 2011, held in Paris, France, in June 2011. The 24 revised full papers presented and the 12 short papers were carefully reviewed and selected from 62 submissions. The MCM conference is the flagship conference of the Society for Mathematics and Computation in Music. This year’s conference aimed to provide a multi-disciplinary platform dedicated to the communication and exchange of ideas amongst researchers involved in mathematics, computer science, music theory, composition, musicology, or other related disciplines. Areas covered were formalization and geometrical representation of musical structures and processes; mathematical models for music improvisation and gestures theory; set-theoretical and transformational approaches; computational analysis and cognitive musicology as well as more general discussions on history, philosophy and epistemology of music and mathematics.

Mathematics and Computation in MusicMathematics and Computation in Music



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.

Author: Mariana Montiel

Publisher: Springer

ISBN: 3030213919

Category:

Page: 399

View: 118

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.

Music Math and MindMusic Math and Mind



How might a musician use math to come up with new ideas? This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow.

Author: David Sulzer

Publisher: Columbia University Press

ISBN: 9780231550505

Category:

Page:

View: 171

Why does a clarinet play at lower pitches than a flute? What does it mean for sounds to be in or out of tune? How are emotions carried by music? Do other animals perceive sound like we do? How might a musician use math to come up with new ideas? This book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music in a way that readers without scientific background can follow. David Sulzer, also known in the musical world as Dave Soldier, explains why the perception of music encompasses the physics of sound, the functions of the ear and deep-brain auditory pathways, and the physiology of emotion. He delves into topics such as the math by which musical scales, rhythms, tuning, and harmonies are derived, from the days of Pythagoras to technological manipulation of sound waves. Sulzer ranges from styles from around the world to canonical composers to hip-hop, the history of experimental music, and animal sound by songbirds, cetaceans, bats, and insects. He makes accessible a vast range of material, helping readers discover the universal principles behind the music they find meaningful. 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 by the NumbersMusic by the Numbers



Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age ...

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 9781400889891

Category:

Page: 176

View: 561

How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century Music is filled with mathematical elements, the works of Bach are often said to possess a math-like logic, and Igor Stravinsky said "musical form is close to mathematics," while Arnold Schoenberg, Iannis Xenakis, and Karlheinz Stockhausen went further, writing music explicitly based on mathematical principles. Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system. Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

Mathematics and Computation in MusicMathematics and Computation in Music



This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013.

Author: Jason Yust

Publisher: Springer

ISBN: 9783642393570

Category:

Page: 241

View: 300

This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013. The 18 papers presented were carefully reviewed and selected from numerous submissions. They are promoting the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition and other related fields.

Cool Math for Hot MusicCool Math for Hot Music



The book includes many illustrations, and exercises with solutions.

Author: Guerino Mazzola

Publisher: Springer

ISBN: 9783319429373

Category:

Page: 323

View: 482

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.

Emblems of MindEmblems of Mind



Unravels the mystery of the relationship between music and mathematics, discussing their differences and their surprising similarities--including their origins and historical links

Author: Edward Rothstein

Publisher: Crown

ISBN: STANFORD:36105004211715

Category:

Page: 263

View: 196

Unravels the mystery of the relationship between music and mathematics, discussing their differences and their surprising similarities--including their origins and historical links

Music Via MathMusic Via Math



This book demonstrates how mathematics can be useful to better understand and explore music and how to increase appreciation of the relationship between mathematics and music.

Author: Dirk Schlingmann

Publisher:

ISBN: 1733367616

Category:

Page:

View: 358

This book demonstrates how mathematics can be useful to better understand and explore music and how to increase appreciation of the relationship between mathematics and music. An understanding of mathematics is important to having a greater appreciation of music. Mathematics can be useful to analyze, manipulate, and create music. The book discusses topics that are fundamentally related to music such as pleasing and unpleasing sounds, digital sound files, mathematical modeling of sound, pitch, timbre, dynamics, rhythm, consonance and dissonance, musical tone systems, musical notation, instrument design, MIDI (Musical Instrument Digital Interface), statistical analysis of musical compositions, and artistic creation of new styles of music using computing. Computer code has been included whenever possible to highlight the importance of computer programming.

Fractals in MusicFractals in Music



Fractals in Music is intended for advanced students of music theory, whether individuals, composers, students, or teachers.

Author: Charles B. Madden

Publisher: Springer Science & Business

ISBN: 0967172756

Category:

Page: 210

View: 317

Fractals in Music is intended for advanced students of music theory, whether individuals, composers, students, or teachers. It is intelligible to anyone having some knowledge of algebra and trigonometry. The many illustrations clarify such concepts as self-similarity and transforms. Book jacket.

The Topos of MusicThe Topos of Music



This four-volume set is the second edition of the now classic book “The Topos of Music”.

Author: Guerino Mazzola

Publisher: Springer

ISBN: 3319644335

Category:

Page: 1580

View: 379

This four-volume set is the second edition of the now classic book “The Topos of Music”. In Vol. I the author explains the theory's conceptual framework of denotators and forms, the classification of local and global musical objects, the mathematical models of harmony and counterpoint, and topologies for rhythm and motives. In Vol. II the author explains his theory of musical performance, developed in the language of differential geometry, introducing performance vector fields that generalize tempo and intonation. Volume III presents gesture theory, including a gesture philosophy for music, the mathematics of gestures, concept architectures and software for musical gesture theory, the multiverse perspective which reveals the relationship between gesture theory and the string theory in theoretical physics, and applications of gesture theory to a number of musical themes, including counterpoint, modulation theory, free jazz, Hindustani music, and vocal gestures. Finally, Vol. IV contains appendices, explaining background topics in sound, mathematics, and music.