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Geometry And Topology In Music
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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. This book was released on 2018-04-12 with total page 1580 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometry and Topology in Music by : Moreno Andreatta
Download or read book Geometry and Topology in Music written by Moreno Andreatta and published by CRC Press. This book was released on 2024-11-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification. Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice-leading geometries in the most recent advances in this mathematical approach to representing how chords are connected through the motion of voices, leading to analytically useful simplified models of high-dimensional spaces; It generalizes the idea of a Tonnetz, a geometrical map of tones or chords, and shows how topological aspects of these maps can correspond to many concepts from music theory. The resulting framework embeds the chord maps of neo-Riemannian theory in continuous spaces that relate chords of different sizes and includes extensions of this approach to rhythm theory. It further introduces an application of topology to automatic music classification, drawing upon both static topological representations and time-series evolution, showing how static and dynamic features of music interact as features of musical style. This volume will be a key resource for academics, researchers, and advanced students of music, music analyses, music composition, mathematical music theory, computational musicology, and music informatics. It was originally published as a special issue of the Journal of Mathematics and Music.
Book Synopsis Mathematical Music Theory by : Mariana Montiel
Download or read book Mathematical Music Theory written by Mariana Montiel and published by World Scientific Publishing. This book was released on 2018-11-14 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis The Topos of Music I: Theory by : Guerino Mazzola
Download or read book The Topos of Music I: Theory written by Guerino Mazzola and published by Springer. This book was released on 2018-03-28 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the second edition of the now classic book “The Topos of Music”. 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.
Book Synopsis A Geometry of Music by : Dmitri Tymoczko
Download or read book A Geometry of Music written by Dmitri Tymoczko and published by OUP USA. This book was released on 2011-03-21 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Topos of Music by : Guerino Mazzola
Download or read book The Topos of Music written by Guerino Mazzola and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an upgraded extension of 'Geometrie der Tone', published in 1990. It reflects the dramatic progress of mathematical music theory and its implementation by information technology. The conceptual basis has been generalized to topos-theoretic foundations.
Book Synopsis Topology and Geometry by : Glen E. Bredon
Download or read book Topology and Geometry written by Glen E. Bredon and published by Springer Science & Business Media. This book was released on 1993-06-24 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS
Book Synopsis Fractals in Music by : Charles B. Madden
Download or read book Fractals in Music written by Charles B. Madden and published by . This book was released on 2007 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A New Geometry of Musical Chords in Interval Representation: Dissonance, Enrichment, Degeneracy and Complementation by : Miguel Gutierrez; Makoto Taniguchi
Download or read book A New Geometry of Musical Chords in Interval Representation: Dissonance, Enrichment, Degeneracy and Complementation written by Miguel Gutierrez; Makoto Taniguchi and published by iUniverse. This book was released on 2010-07-07 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers a fresh and original look at musical chords. The idea emanates from the fact that an intervallic representation of the chord leads naturally to a discrete barycentric condition. This condition itself leads to a convenient geometric representation of the chordal space as a simplicial grid. Chords appear as points in this grid and musical inversions of the chord would generate beautiful polyhedra inscribed in concentric spheres centered at the barycenter. The radii of these spheres would effectively quantify the evenness and thus the consonance of the chord. Internal symmetries would collapse these chordal structures into polar or equatorial displays, creating a platform for a thorough degeneracy study. Appropiate morphisms would allow us to navigate through different chordal cardinalities and ultimately to characterise complementary chords.
Book Synopsis The Geometry of Musical Rhythm by : Godfried T. Toussaint
Download or read book The Geometry of Musical Rhythm written by Godfried T. Toussaint and published by CRC Press. This book was released on 2013-01-11 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 disparate fields. For the music community, the book also introduces the distance approach to phylogenetic analysis and illustrates its application to the study of musical rhythm. Accessible to both academics and musicians, the text requires a minimal set of prerequisites. Emphasizing a visual geometric treatment of musical rhythm and its underlying structures, the author—an eminent computer scientist and music theory researcher—presents new symbolic geometric approaches and often compares them to existing methods. He shows how distance geometry and phylogenetic analysis can be used in comparative musicology, ethnomusicology, and evolutionary musicology research. The book also strengthens the bridge between these disciplines and mathematical music theory. Many concepts are illustrated with examples using a group of six distinguished rhythms that feature prominently in world music, including the clave son. Exploring the mathematical properties of good rhythms, this book offers an original computational geometric approach for analyzing musical rhythm and its underlying structures. With numerous figures to complement the explanations, it is suitable for a wide audience, from musicians, composers, and electronic music programmers to music theorists and psychologists to computer scientists and mathematicians. It can also be used in an undergraduate course on music technology, music and computers, or music and mathematics.
Book Synopsis Cool Math for Hot Music by : Guerino Mazzola
Download or read book Cool Math for Hot Music written by Guerino Mazzola and published by Springer. This book was released on 2016-10-26 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Topos of Music IV: Roots by : Guerino Mazzola
Download or read book The Topos of Music IV: Roots written by Guerino Mazzola and published by Springer. This book was released on 2018-03-29 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth volume of the second edition of the now classic book “The Topos of Music”. The author presents appendices with background material on sound and auditory physiology; mathematical basics such as sets, relations, transformations, algebraic geometry, and categories; complements in physics, including a discussion on string theory; and tables with chord classes and modulation steps.
Book Synopsis The Geometry and Topology of Coxeter Groups by : Michael Davis
Download or read book The Geometry and Topology of Coxeter Groups written by Michael Davis and published by Princeton University Press. This book was released on 2008 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
Book Synopsis The Topos of Music III: Gestures by : Guerino Mazzola
Download or read book The Topos of Music III: Gestures written by Guerino Mazzola and published by Springer. This book was released on 2018-03-28 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the second edition of the now classic book “The Topos of Music”. The authors present 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.
Book Synopsis The Geometry of Musical Rhythm by : Godfried T. Toussaint
Download or read book The Geometry of Musical Rhythm written by Godfried T. Toussaint and published by CRC Press. This book was released on 2019-11-25 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original edition of The Geometry of Musical Rhythm was the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explained how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. The book also introduced the distance approach to phylogenetic analysis and illustrated its application to the study of musical rhythm. The new edition retains all of this, while also adding 100 pages, 93 figures, 225 new references, and six new chapters covering topics such as meter and metric complexity, rhythmic grouping, expressive timbre and timing in rhythmic performance, and evolution phylogenetic analysis of ancient Greek paeonic rhythms. In addition, further context is provided to give the reader a fuller and richer insight into the historical connections between music and mathematics.
Book Synopsis Music, Geometry and Mathematics by : Derrick Scott Van Heerden
Download or read book Music, Geometry and Mathematics written by Derrick Scott Van Heerden and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A New Geometry of Musical Chords in Interval Representation by : Miguel Gutierrez
Download or read book A New Geometry of Musical Chords in Interval Representation written by Miguel Gutierrez and published by . This book was released on 2010 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers a fresh and original look at musical chords. The idea emanates from the fact that an intervallic representation of the chord leads naturally to a discrete barycentric condition. This condition itself leads to a convenient geometric representation of the chordal space as a simplicial grid. Chords appear as points in this grid and musical inversions of the chord would generate beautiful polyhedra inscribed in concentric spheres centered at the barycenter. The radii of these spheres would effectively quantify the evenness and thus the consonance of the chord. Internal symmetries would collapse these chordal structures into polar or equatorial displays, creating a platform for a thorough degeneracy study. Appropiate morphisms would allow us to navigate through different chordal cardinalities and ultimately to characterise complementary chords.
