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A Compendium Of Musical Mathematics
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Book Synopsis A Compendium Of Musical Mathematics by : Franck Jedrzejewski
Download or read book A Compendium Of Musical Mathematics written by Franck Jedrzejewski and published by World Scientific. This book was released on 2024-02-28 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide a concise introduction to the mathematical theory of music, opening each chapter to the most recent research. Despite the complexity of some sections, the book can be read by a large audience. Many examples illustrate the concepts introduced. The book is divided into 9 chapters.In the first chapter, we tackle the question of the classification of chords and scales. Chapter 2 is a mathematical presentation of David Lewin's Generalized Interval Systems. Chapter 3 offers a new theory of diatonicity in equal-tempered universes. Chapter 4 presents the Neo-Riemannian theories based on the work of David Lewin, Richard Cohn and Henry Klumpenhouwer. Chapter 5 is devoted to the application of word combinatorics to music. Chapter 6 studies the rhythmic canons and the tessellation of the line. Chapter 7 is devoted to serial knots. Chapter 8 presents combinatorial designs and their applications to music. The last chapter, chapter 9, is dedicated to the study of tuning systems.
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.
Book Synopsis Mathematics and Music by : James S. Walker
Download or read book Mathematics and Music written by James S. Walker and published by CRC Press. This book was released on 2019-09-24 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics and Music: Composition, Perception, and Performance, Second Edition includes many new sections and more consistent expectations of a student’s experience. The new edition of this popular text is more accessible for students with limited musical backgrounds and only high school mathematics is required. The new edition includes more illustrations than the previous one and the added sections deal with the XronoMorph rhythm generator, musical composition, and analyzing personal performance. The text teaches the basics of reading music, explaining how various patterns in music can be described with mathematics, providing mathematical explanations for musical scales, harmony, and rhythm. The book gives students a deeper appreciation showing how music is informed by both its mathematical and aesthetic structures. Highlights of the Second Edition: Now updated for more consistent expectations of students’ backgrounds More accessible for students with limited musical backgrounds Full-color presentation Includes more thorough coverage of spectrograms for analyzing recorded music Provides a basic introduction to reading music Features new coverage of building and evaluating rhythms
Book Synopsis The Math Behind the Music with CD-ROM by : Leon Harkleroad
Download or read book The Math Behind the Music with CD-ROM written by Leon Harkleroad and published by Cambridge University Press. This book was released on 2006-08-07 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has been used for centuries to describe, analyze, and create music. In this book, Leon Harkleroad explores the math related aspects of music from its acoustical bases to compositional techniques to music criticism, touching on - overtones, scales, and tuning systems - the musical dice game attributed to Mozart and Haydn - the several-hundred-year-old style of bell-playing known as ringing the changes - the twelve-tone school of composition that strongly influenced music throughout the 20th century and many other topics involving mathematical ideas from probability theory to Fourier series to group theory. He also relates some cautionary tales of misguided attempts to mix music and mathematics. Both the mathematical and the musical concepts are described in an elementary way, making the book accessible to general readers as well as to mathematicians and musicians of all levels. The book is accompanied by an audio CD of musical examples.
Book Synopsis Music and Mathematics by : John Fauvel
Download or read book Music and Mathematics written by John Fauvel and published by Oxford University Press, USA. This book was released on 2006 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: From ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This work links these two subjects in a manner that is suitable for students of both subjects, as well as the general reader with an interest in music.
Book Synopsis Music, Experiment and Mathematics in England, 1653-1705 by : Benjamin Wardhaugh
Download or read book Music, Experiment and Mathematics in England, 1653-1705 written by Benjamin Wardhaugh and published by Routledge. This book was released on 2017-07-05 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: How, in 1705, was Thomas Salmon, a parson from Bedfordshire, able to persuade the Royal Society that a musical performance could constitute a scientific experiment? Or that the judgement of a musical audience could provide evidence for a mathematically precise theory of musical tuning? This book presents answers to these questions. It constitutes a general history of quantitative music theory in the late seventeenth century as well as a detailed study of one part of that history: namely the applications of mathematical and mechanical methods of understanding to music that were produced in England between 1653 and 1705, beginning with the responses to Descartes's 1650 Compendium musicand ending with the Philosophical Transactions' account of the appearance of Thomas Salmon at the Royal Society in 1705. The book is organized around four key questions. Do musical pitches form a small set or a continuous spectrum? Is there a single faculty of hearing which can account for musical sensation, or is more than one faculty at work? What is the role of harmony in the mechanical world, and where can its effects be found? And what is the relationship between musical theory and musical practice? These are questions which are raised and discussed in the sources themselves, and they have wide significance for early modern theories of knowledge and sensation more generally, as well as providing a fascinating side light onto the world of the scientific revolution.
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.
Book Synopsis The Topos of Music by : Guerino Mazzola
Download or read book The Topos of Music written by Guerino Mazzola and published by Springer Science & Business Media. This book was released on 2002-09-23 with total page 1372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples.
Book Synopsis The Compendium Musicæ of René Descartes by : René Descartes
Download or read book The Compendium Musicæ of René Descartes written by René Descartes and published by Brepols Publishers. This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rene Descartes's Compendium musicAe was one of the most widely-read texts on the mathematics of music in the second half of the seventeenth century, offering a succinct and lucid summary of its subject. It was translated into English, French and Dutch before the end of the century--though its idiosyncratic geometrical approach to music drew criticism as well as praise--and its sophisticated mathematical thinking attracted a number of later scholars to explore its ideas further in print or manuscript. This volume presents for the first time a critical edition of the English translation of the Compendium, published in 1653 by the natural philosopher Walter Charleton. Also included are the unpublished manuscript treatises written by Nicolaus Mercator and Isaac Newton developing similar ideas to those in the Compendium, and the printed remarks of William Brouncker which appeared with Charleton's translation. This rich collection of texts, most of them appearing in critical editions for the first time, provides a unique view of the early reception of Descartes's musical treatise in England.
Book Synopsis The Musical-Mathematical Mind by : Gabriel Pareyon
Download or read book The Musical-Mathematical Mind written by Gabriel Pareyon and published by Springer. This book was released on 2017-10-20 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Music by the Numbers written by Eli Maor and published by Princeton University Press. This book was released on 2020-03-10 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: How music has influenced mathematics, physics, and astronomy from ancient Greece to the twentieth century.
Book Synopsis "Music, Experiment and Mathematics in England, 1653?705 " by : Benjamin Wardhaugh
Download or read book "Music, Experiment and Mathematics in England, 1653?705 " written by Benjamin Wardhaugh and published by Routledge. This book was released on 2017-07-05 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: How, in 1705, was Thomas Salmon, a parson from Bedfordshire, able to persuade the Royal Society that a musical performance could constitute a scientific experiment? Or that the judgement of a musical audience could provide evidence for a mathematically precise theory of musical tuning? This book presents answers to these questions. It constitutes a general history of quantitative music theory in the late seventeenth century as well as a detailed study of one part of that history: namely the applications of mathematical and mechanical methods of understanding to music that were produced in England between 1653 and 1705, beginning with the responses to Descartes's 1650 Compendium music?and ending with the Philosophical Transactions' account of the appearance of Thomas Salmon at the Royal Society in 1705. The book is organized around four key questions. Do musical pitches form a small set or a continuous spectrum? Is there a single faculty of hearing which can account for musical sensation, or is more than one faculty at work? What is the role of harmony in the mechanical world, and where can its effects be found? And what is the relationship between musical theory and musical practice? These are questions which are raised and discussed in the sources themselves, and they have wide significance for early modern theories of knowledge and sensation more generally, as well as providing a fascinating side light onto the world of the scientific revolution.
Book Synopsis Music Via Math by : Dirk Schlingmann
Download or read book Music Via Math written by Dirk Schlingmann and published by . This book was released on 2019-07-31 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Exploring Musical Spaces by : Julian Hook
Download or read book Exploring Musical Spaces written by Julian Hook and published by Oxford University Press. This book was released on 2022-09-08 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing from the outset a number of simple geometric models--the first examples of the musical spaces of the book's title--depicting relationships among musical entities of various kinds such as notes, chords, scales, or rhythmic values. These spaces take many forms and become a unifying thread in initiating readers into several areas of active recent scholarship, including transformation theory, neo-Riemannian theory, geometric music theory, diatonic theory, and scale theory. Concepts and techniques from mathematical set theory, graph theory, group theory, geometry, and topology are introduced as needed to address musical questions. Musical examples ranging from Bach to the late twentieth century keep the underlying musical motivations close at hand. The book includes hundreds of figures to aid in visualizing the structure of the spaces, as well as exercises offering readers hands-on practice with a diverse assortment of concepts and techniques.
Book Synopsis Mathematics and Music by : James S. Walker
Download or read book Mathematics and Music written by James S. Walker and published by Chapman & Hall/CRC. This book was released on 2017-07-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ResourceOn 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.
Book Synopsis Fractals in Music by : Charles B. Madden
Download or read book Fractals in Music written by Charles B. Madden and published by High Art Press. This book was released on 1999 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
