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
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.
Fractals in Music – Introductory Mathematics for Musical Analysis, High Art Press. Max V. Mathews, 1969. The Technology of Computer Music, MIT Press. W. A. Mathieu, 1997. Harmonic Experience, Inner Traditions International.
Author: Dave Benson
Publisher: Cambridge University Press
This book explores the interaction between music and mathematics including harmony, symmetry, digital music and perception of sound.
In other words, if the new fourth and fifth are inverse musical intervals (they combine to create an octave), then each is the same distance from its ... Benson, D. J.: 2007, Music: A Mathematical Offering, Cambridge University Press.
Author: Gareth E. Roberts
Publisher: JHU Press
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.
A lengthy bibliography on mathematics and music can be found in David J. Benson's grand treatise Music: A Mathematical Offering , which gives far more technical and in-depth coverage of nearly all ...
Author: David Wright
Publisher: American Mathematical Soc.
Category: Music theory
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.
References 1. Agust ́ın-Aquino, O.A., Mazzola, G.: Modulation in tetradic harmony and its role in jazz. J. Math. Music 14(1), 58–65 (2020). https://doi.org/10.1080/17459737. 2019.1655673 2. Benson, D.: Music: A Mathematical Offering.
Author: Mariana Montiel
Publisher: Springer Nature
Category: Language Arts & Disciplines
This book constitutes the thoroughly refereed proceedings of the 8th International Conference on Mathematics and Computation in Music, MCM 2022, held in Atlanta, GA, USA, in June 2022. The 29 full papers and 8 short papers presented were carefully reviewed and selected from 45 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in Mathematical Scale and Rhythm Theory: Combinatorial, Graph Theoretic, Group Theoretic and Transformational Approaches; Categorical and Algebraic Approaches to Music; Algorithms and Modeling for Music and Music-Related Phenomena; Applications of Mathematics to Musical Analysis; Mathematical Techniques and Microtonality
Author: Octavio A. Agustín-AquinoPublish On: 2017-11-17
Benson, D.: Music: A Mathematical Offering. Cambridge University Press, Cambridge (2006) 4. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algoritms. Plenum Press, New York (1981) 5. Downie, J.S.: Evaluating a simple ...
Author: Octavio A. Agustín-Aquino
This book constitutes the thoroughly refereed proceedings of the 6th International Conference on Mathematics and Computation in Music, MCM 2017, held in Mexico City, Mexico, in June 2017. The 26 full papers and 2 short papers presented were carefully reviewed and selected from 40 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 models, computer assisted performance, Fourier analysis, Gesture Theory, Graph Theory and Combinatorics, Machine Learning, and Probability and Statistics in Musical Analysis and Composition.
Benson, D.: Music: a Mathematical Offering. Cambridge University Press, Cambridge (2006) 2. Borup, H.: A History of String Intonation, http://www.hasseborup.com/ahistoryofintonationfinal1.pdf 3. Carlsson, C., Fullér, R.: Fuzzy Reasoning ...
Author: Elaine Chew
Publisher: Springer Science & Business Media
This book constitutes the refereed proceedings of the Second International Conference on Mathematics and Computation in Music, MCM 2009, held in New Haven, CT, USA, in June 2009. The 26 revised full papers presented were carefully reviewed and selected from 38 submissions. The MCM conference is the flagship conference of the Society for Mathematics and Computation in Music. The papers deal with topics within applied mathematics, computational models, mathematical modelling and various further aspects of the theory of music. This year’s conference is dedicated to the honor of John Clough whose research modeled the virtues of collaborative work across the disciplines.
On the contrary , -1 e , § 9 ૐ -2 -3 -4 -4 -5 9 9 2 Chapter 3 Music as Formal Language What's so special about. renders the circle of fourths . ... D. Benson , Music : A Mathematical Offering ( Cambridge University Press , 2007 ) 2.
Author: Keiji Hirata
Publisher: Springer Nature
Category: Electronic books
This book presents a new approach to computational musicology in which music becomes a computational entity based on human cognition, allowing us to calculate music like numbers. Does music have semantics? Can the meaning of music be revealed using symbols and described using language? The authors seek to answer these questions in order to reveal the essence of music. Chapter 1 addresses a very fundamental point, the meaning of music, while referring to semiotics, gestalt, Schenkerian analysis and cognitive reality. Chapter 2 considers why the 12-tone equal temperament came to be prevalent. This chapter serves as an introduction to the mathematical definition of harmony, which concerns the ratios of frequency in tonic waves. Chapter 3, "Music and Language", explains the fundamentals of grammar theory and the compositionality principle, which states that the semantics of a sentence can be composed in parallel to its syntactic structure. In turn, Chapter 4 explains the most prevalent score notation the Berklee method, which originated at the Berklee School of Music in Boston from a different point of view, namely, symbolic computation based on music theory. Chapters 5 and 6 introduce readers to two important theories, the implication-realization model and generative theory of tonal music (GTTM), and explain the essence of these theories, also from a computational standpoint. The authors seek to reinterpret these theories, aiming at their formalization and implementation on a computer. Chapter 7 presents the outcomes of this attempt, describing the framework that the authors have developed, in which music is formalized and becomes computable. Chapters 8 and 9 are devoted to GTTM analyzers and the applications of GTTM. Lastly, Chapter 10 discusses the future of music in connection with computation and artificial intelligence. This book is intended both for general readers who are interested in music, and scientists whose research focuses on music information processing. In order to make the content as accessible as possible, each chapter is self-contained.
Computer Music Journal 35, no. 3 (2011): 40–56. Benson, David J. Music: A Mathematical Offering. Cambridge: Cambridge University Press, 2006. Bibby, N. 'Tuning and Temperament: Closing the Spiral'. In Music and Mathematics: From ...
Author: R. T. Dean
Publisher: Oxford University Press
Featuring chapters by emerging and established scholars as well as by leading practitioners in the field, this Handbook both describes the state of algorithmic composition and also set the agenda for critical research on and analysis of algorithmic music.