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Author : Guerino Mazzola
Publisher : Birkhäuser
ISBN 13 : 303488141X
Total Pages : 1310 pages
Book Rating : 4.0/5 (348 download)
Download or read book The Topos of Music written by Guerino Mazzola and published by Birkhäuser. This book was released on 2012-12-06 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts
Author : Guerino Mazzola
Publisher : Springer
ISBN 13 : 3319643649
Total Pages : 656 pages
Book Rating : 4.3/5 (196 download)
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 656 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.
Author : Guerino Mazzola
Publisher : Springer Science & Business Media
ISBN 13 : 364224517X
Total Pages : 337 pages
Book Rating : 4.6/5 (422 download)
Download or read book Musical Creativity written by Guerino Mazzola and published by Springer Science & Business Media. This book was released on 2011-11-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents a new approach to musical creativity, dealing with the semiotics, mathematical principles, and software for creativity processes. After a thorough introduction, the book offers a first practical part with a detailed tutorial for students in composition and improvisation, using musical instruments and music software. The second, theoretical part deals with historical, actual, and new principles of creative processes in music, based on the results and methods developed in the first author’s book Topos of Music and referring to semiotics, predicative objects, topos theory, and object-oriented concept architectures. The third part of the book details four case studies in musical creativity, including an analysis of the six variations of Beethoven's sonata op. 109, a discussion of the creative process in a CD coproduced in 2011 by the first and second authors, a recomposition of Boulez’s "Structures pour deux pianos" using the Rubato software module BigBang developed by the third author, and the Escher theorem from mathematical gesture theory in music. This is both a textbook addressed to undergraduate and graduate students of music composition and improvisation, and also a state-of-the-art survey addressed to researchers in creativity studies and music technology. The book contains summaries and end-of-chapter questions, and the authors have used the book as the main reference to teach an undergraduate creativity studies program and also to teach composition. The text is supported throughout with musical score examples.
Author : Jacob Lurie
Publisher : Princeton University Press
ISBN 13 : 1400830559
Total Pages : 944 pages
Book Rating : 4.4/5 (8 download)
Download or read book Higher Topos Theory (AM-170) written by Jacob Lurie and published by Princeton University Press. This book was released on 2009-07-06 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.
Author : John L. Bell
Publisher : Courier Corporation
ISBN 13 : 0486462862
Total Pages : 290 pages
Book Rating : 4.4/5 (864 download)
Download or read book Toposes and Local Set Theories written by John L. Bell and published by Courier Corporation. This book was released on 2008-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
Author : P.T. Johnstone
Publisher : Courier Corporation
ISBN 13 : 0486493369
Total Pages : 401 pages
Book Rating : 4.4/5 (864 download)
Download or read book Topos Theory written by P.T. Johnstone and published by Courier Corporation. This book was released on 2014-01-15 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, and other subjects. 1977 edition.
Author : Guerino Mazzola
Publisher : Springer
ISBN 13 : 331942937X
Total Pages : 323 pages
Book Rating : 4.3/5 (194 download)
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 323 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.
Author : Olivia Caramello
Publisher : Oxford University Press
ISBN 13 : 019875891X
Total Pages : 381 pages
Book Rating : 4.1/5 (987 download)
Download or read book Theories, Sites, Toposes written by Olivia Caramello and published by Oxford University Press. This book was released on 2018 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a set of methods and techniques for studying mathematical theories and relating them to each other through the use of Grothendieck toposes.
Author : Guerino Mazzola
Publisher : Springer Science & Business Media
ISBN 13 : 3642118380
Total Pages : 285 pages
Book Rating : 4.6/5 (421 download)
Download or read book Musical Performance written by Guerino Mazzola and published by Springer Science & Business Media. This book was released on 2010-11-16 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a first sketch of what the overall field of performance could look like as a modern scientific field but not its stylistically differentiated practice, pedagogy, and history. Musical performance is the most complex field of music. It comprises the study of a composition’s expression in terms of analysis, emotion, and gesture, and then its transformation into embodied reality, turning formulaic facts into dramatic movements of human cognition. Combining these components in a creative way is a sophisticated mix of knowledge and mastery, which more resembles the cooking of a delicate recipe than a rational procedure. This book is the first one aiming at such comprehensive coverage of the topic, and it does so also as a university text book. We include musicological and philosophical aspects as well as empirical performance research. Presenting analytical tools and case studies turns this project into a demanding enterprise in construction and experimental setups of performances, especially those generated by the music software Rubato. We are happy that this book was written following a course for performance students at the School of Music of the University of Minnesota. Their education should not be restricted to the canonical practice. They must know the rationale for their performance. It is not sufficient to learn performance with the old-fashioned imitation model of the teacher's antetype, this cannot be an exclusive tool since it dramatically lacks the poetical precision asked for by Adorno's and Benjamin's micrologic. Without such alternatives to intuitive imitation, performance risks being disconnected from the audience.
Author : Guerino Mazzola
Publisher : Springer Science & Business Media
ISBN 13 : 3540921958
Total Pages : 140 pages
Book Rating : 4.5/5 (49 download)
Download or read book Flow, Gesture, and Spaces in Free Jazz written by Guerino Mazzola and published by Springer Science & Business Media. This book was released on 2008-12-21 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free jazz, as performed by such artists as John Coltrone and Archie Shepp, is a creative, collaborative art form. This book examines free jazz and develops geometric theories of gestures and distributed identities, also known as swarm intelligence.
Author : Guerino Mazzola
Publisher : Springer
ISBN 13 : 3319644815
Total Pages : 604 pages
Book Rating : 4.3/5 (196 download)
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 604 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.
Author : Guerino Mazzola
Publisher : Springer
ISBN 13 : 3319473344
Total Pages : 185 pages
Book Rating : 4.3/5 (194 download)
Download or read book All About Music written by Guerino Mazzola and published by Springer. This book was released on 2016-11-23 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains music’s comprehensive ontology, its way of existence and processing, as specified in its compact characterization: music embodies meaningful communication and mediates physically between its emotional and mental layers. The book unfolds in a basic discourse in everyday language that is accessible to everybody who wants to understand what this topic is about. Musical ontology is delayed in its fundamental dimensions: its realities, its meaningful communication, and its embodied utterance from musical creators to an interested audience. The authors' approach is applicable to every musical genre and is scientific, the book is suitable for non-musicians and non-scientists alike.
Author : Colin McLarty
Publisher : Clarendon Press
ISBN 13 : 0191589497
Total Pages : 282 pages
Book Rating : 4.1/5 (915 download)
Download or read book Elementary Categories, Elementary Toposes written by Colin McLarty and published by Clarendon Press. This book was released on 1992-06-04 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis. - ;Introduction; PART I: CATEGORIES: Rudimentary structures in a category; Products, equalizers, and their duals; Groups; Sub-objects, pullbacks, and limits; Relations; Cartesian closed categories; Product operators and others; PART II: THE CATEGORY OF CATEGORIES: Functors and categories; Natural transformations; Adjunctions; Slice categories; Mathematical foundations; PART III: TOPOSES: Basics; The internal language; A soundness proof for topos logic; From the internal language to the topos; The fundamental theorem; External semantics; Natural number objects; Categories in a topos; Topologies; PART IV: SOME TOPOSES: Sets; Synthetic differential geometry; The effective topos; Relations in regular categories; Further reading; Bibliography; Index. -
Author : Gabriel Pareyon
Publisher : Springer
ISBN 13 : 3319473379
Total Pages : 345 pages
Book Rating : 4.3/5 (194 download)
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.
Author : Gerard Assayag
Publisher : Springer Science & Business Media
ISBN 13 : 3662049279
Total Pages : 294 pages
Book Rating : 4.6/5 (62 download)
Download or read book Mathematics and Music written by Gerard Assayag and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Guerino Mazzola
Publisher : Springer Science & Business Media
ISBN 13 : 3540368744
Total Pages : 388 pages
Book Rating : 4.5/5 (43 download)
Download or read book Comprehensive Mathematics for Computer Scientists 1 written by Guerino Mazzola and published by Springer Science & Business Media. This book was released on 2006-10-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains all the mathematics that computer scientists need to know in one place.
Author : Alexander Rehding
Publisher : Oxford University Press
ISBN 13 : 0199888892
Total Pages : 522 pages
Book Rating : 4.1/5 (998 download)
Download or read book Music and Monumentality written by Alexander Rehding and published by Oxford University Press. This book was released on 2009-08-19 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This critical study locates musical monumentality, a central property of the nineteenth-century German repertoire, at the intersections of aesthetics and memory. In examples including Beethoven, Liszt, Wagner and Bruckner, Rehding explores how monumentality contributes to an experiential music history and how it conveys the sublime to the listening public.
