The Topos of Music
Author: Guerino Mazzola
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 1310
ISBN-13: 303488141X
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The Topos of Music I: Theory
Author: Guerino Mazzola
Publisher: Springer
Published: 2018-03-28
Total Pages: 675
ISBN-13: 3319643649
DOWNLOAD EBOOKThis 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
Author: Guerino Mazzola
Publisher: Springer Science & Business Media
Published: 2011-11-03
Total Pages: 331
ISBN-13: 364224517X
DOWNLOAD EBOOKThis 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.
Higher Topos Theory
Author: Jacob Lurie
Publisher: Princeton University Press
Published: 2009-07-26
Total Pages: 944
ISBN-13: 0691140480
DOWNLOAD EBOOKIn '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
Author: John L. Bell
Publisher: Courier Corporation
Published: 2008-01-01
Total Pages: 290
ISBN-13: 0486462862
DOWNLOAD EBOOKThis 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.
Topos Theory
Author: P.T. Johnstone
Publisher: Courier Corporation
Published: 2014-01-15
Total Pages: 401
ISBN-13: 0486493369
DOWNLOAD EBOOKFocusing 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.
Cool Math for Hot Music
Author: Guerino Mazzola
Publisher: Springer
Published: 2016-10-26
Total Pages: 314
ISBN-13: 331942937X
DOWNLOAD EBOOKThis 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.
A First Course in Topos Quantum Theory
Author: Cecilia Flori
Publisher: Springer
Published: 2013-03-27
Total Pages: 452
ISBN-13: 364235713X
DOWNLOAD EBOOKIn the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer – is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory. This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a “neo-realist” classical physics theory again.
Flow, Gesture, and Spaces in Free Jazz
Author: Guerino Mazzola
Publisher: Springer Science & Business Media
Published: 2008-12-21
Total Pages: 140
ISBN-13: 3540921958
DOWNLOAD EBOOKFree 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.
Musical Performance
Author: Guerino Mazzola
Publisher: Springer Science & Business Media
Published: 2010-11-16
Total Pages: 285
ISBN-13: 3642118380
DOWNLOAD EBOOKThis 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.
