The Topos of Music PDF Download

Author: Guerino Mazzola
Publisher: Birkhäuser
ISBN: 303488141X
Category : Mathematics
Languages : en
Pages : 1310

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Book Description
With contributions by numerous experts

Author: Guerino Mazzola
Publisher: Springer
ISBN: 3319643649
Category : Mathematics
Languages : en
Pages : 675

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Book Description
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: 364224517X
Category : Computers
Languages : en
Pages : 331

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Book Description
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: 0691140480
Category : Mathematics
Languages : en
Pages : 944

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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.

Author: P.T. Johnstone
Publisher: Courier Corporation
ISBN: 0486493369
Category : Mathematics
Languages : en
Pages : 401

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Book Description
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: 331942937X
Category : Computers
Languages : en
Pages : 314

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Book Description
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: Guerino Mazzola
Publisher: Springer
ISBN: 3319473344
Category : Computers
Languages : en
Pages : 185

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Book Description
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: Guerino Mazzola
Publisher: Springer Science & Business Media
ISBN: 3540921958
Category : Music
Languages : en
Pages : 140

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Book Description
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: John L. Bell
Publisher: Courier Corporation
ISBN: 0486462862
Category : Mathematics
Languages : en
Pages : 290

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Book Description
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: Reinhard Strohm
Publisher: Routledge
ISBN: 1351672746
Category : Music
Languages : en
Pages : 536

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Book Description
The idea of a global history of music may be traced back to the Enlightenment, and today, the question of a conceptual framework for a history of music that pays due attention to global relationships in music is often raised. But how might a historical interpretation of those relationships proceed? How should it position, or justify, itself? What would 'Western music' look like in an account of music history that aspires to be truly global? The studies presented in this volume aim to promote post-European historical thinking. They are based on the idea that a global history of music cannot be one single, hegemonic history. They rather explore the paradigms and terminologies that might describe a history of many different voices. The chapters address historical practices and interpretations of music in different parts of the world, from Japan to Argentina and from Mexico to India. Many of these narratives are about relations between these cultures and the Western tradition; several also consider socio-political and historical circumstances that have affected music in the various regions. The book addresses aspects that Western musical historiography has tended to neglect even when looking at its own culture: performance, dance, nostalgia, topicality, enlightenment, the relationships between traditional, classical, and pop musics, and the regards croisés between European, Asian, or Latin American interpretations of each other’s musical traditions. These studies have been derived from the Balzan Musicology Project Towards a Global History of Music (2013–2016), which was funded by the International Balzan Foundation through the award of the Balzan Prize in Musicology to the editor, and designed by music historians and ethnomusicologists together. A global history of music may never be written in its entirety, but will rather be realised through interaction, practice, and discussion, in all parts of the world.