The Topos of Music

The Topos of Music

Author: Guerino Mazzola

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 1310

ISBN-13: 303488141X

DOWNLOAD EBOOK

With contributions by numerous experts


The Topos of Music I: Theory

The Topos of Music I: Theory

Author: Guerino Mazzola

Publisher: Springer

Published: 2018-03-28

Total Pages: 675

ISBN-13: 3319643649

DOWNLOAD EBOOK

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.


Musical Creativity

Musical Creativity

Author: Guerino Mazzola

Publisher: Springer Science & Business Media

Published: 2011-11-03

Total Pages: 331

ISBN-13: 364224517X

DOWNLOAD EBOOK

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.


Topos Theory

Topos Theory

Author: P.T. Johnstone

Publisher: Courier Corporation

Published: 2014-01-15

Total Pages: 401

ISBN-13: 0486493369

DOWNLOAD EBOOK

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.


The Topos of Music IV: Roots

The Topos of Music IV: Roots

Author: Guerino Mazzola

Publisher: Springer

Published: 2018-03-29

Total Pages: 353

ISBN-13: 3319644955

DOWNLOAD EBOOK

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.


The Topos of Music III: Gestures

The Topos of Music III: Gestures

Author: Guerino Mazzola

Publisher: Springer

Published: 2018-03-28

Total Pages: 626

ISBN-13: 3319644815

DOWNLOAD EBOOK

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.


All About Music

All About Music

Author: Guerino Mazzola

Publisher: Springer

Published: 2016-11-23

Total Pages: 185

ISBN-13: 3319473344

DOWNLOAD EBOOK

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.


Cool Math for Hot Music

Cool Math for Hot Music

Author: Guerino Mazzola

Publisher: Springer

Published: 2016-10-26

Total Pages: 314

ISBN-13: 331942937X

DOWNLOAD EBOOK

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.


Higher Topos Theory

Higher Topos Theory

Author: Jacob Lurie

Publisher: Princeton University Press

Published: 2009-07-26

Total Pages: 944

ISBN-13: 0691140480

DOWNLOAD EBOOK

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.


Toposes and Local Set Theories

Toposes and Local Set Theories

Author: John L. Bell

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 290

ISBN-13: 0486462862

DOWNLOAD EBOOK

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.