The Topos of Music

Geometric Logic of Concepts, Theory, and Performance

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Author: Guerino Mazzola

Publisher: Birkhäuser

ISBN: 303488141X

Category: Mathematics

Page: 1344

View: 4349

With contributions by numerous experts

The Topos of Music

Geometric Logic of Concepts, Theory, and Performance

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Author: Guerino Mazzola

Publisher: Springer Science & Business Media

ISBN: 9783764357313

Category: Mathematics

Page: 1335

View: 1469

With contributions by numerous experts

The Topos of Music

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Author: Guerino Mazzola

Publisher: Springer

ISBN: 9783319644332

Category: Mathematics

Page: 1580

View: 3875

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.

Cool Math for Hot Music

A First Introduction to Mathematics for Music Theorists

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Author: Guerino Mazzola,Maria Mannone,Yan Pang

Publisher: Springer

ISBN: 331942937X

Category: Computers

Page: 323

View: 2043

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.

Music Through Fourier Space

Discrete Fourier Transform in Music Theory

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Author: Emmanuel Amiot

Publisher: Springer

ISBN: 3319455818

Category: Computers

Page: 206

View: 447

This book explains the state of the art in the use of the discrete Fourier transform (DFT) of musical structures such as rhythms or scales. In particular the author explains the DFT of pitch-class distributions, homometry and the phase retrieval problem, nil Fourier coefficients and tilings, saliency, extrapolation to the continuous Fourier transform and continuous spaces, and the meaning of the phases of Fourier coefficients. This is the first textbook dedicated to this subject, and with supporting examples and exercises this is suitable for researchers and advanced undergraduate and graduate students of music, computer science and engineering. The author has made online supplementary material available, and the book is also suitable for practitioners who want to learn about techniques for understanding musical notions and who want to gain musical insights into mathematical problems.

Comprehensive Mathematics for Computer Scientists 1

Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry

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Author: Guerino Mazzola,Gérard Milmeister,Jody Weissmann

Publisher: Springer Science & Business Media

ISBN: 3540368744

Category: Computers

Page: 388

View: 2593

Contains all the mathematics that computer scientists need to know in one place.

The Geometry of Musical Rhythm

What Makes a "Good" Rhythm Good?

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Author: Godfried T. Toussaint

Publisher: CRC Press

ISBN: 1466512032

Category: Mathematics

Page: 365

View: 831

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.

Mathematics and Computation in Music

4th International Conference, MCM 2013, Montreal, Canada, June 12-14, 2013, Proceedings

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Author: Jason Yust,Jonathan Wild,John Ashley Burgoyne

Publisher: Springer

ISBN: 3642393578

Category: Computers

Page: 241

View: 1308

This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013. The 18 papers presented were carefully reviewed and selected from numerous submissions. They are promoting the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition and other related fields.

Understanding Understanding

Essays on Cybernetics and Cognition

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Author: Heinz von Foerster

Publisher: Springer Science & Business Media

ISBN: 0387217223

Category: Computers

Page: 362

View: 4608

In these ground-breaking essays, Heinz von Foerster discusses some of the fundamental principles that govern how we know the world and how we process the information from which we derive that knowledge. The author was one of the founders of the science of cybernetics.

A Generative Theory of Shape

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Author: Michael Leyton

Publisher: Springer

ISBN: 3540454888

Category: Computers

Page: 549

View: 5272

The purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence –(1) maximization of transfer: whenever possible, new structure should be described as the transfer of existing structure; and (2) maximization of recoverability: the generative operations in the theory must allow maximal inferentiability from data sets. We shall show that, if generativity satis?es these two basic criteria of - telligence, then it has a powerful mathematical structure and considerable applicability to the computational disciplines. The requirement of intelligence is particularly important in the gene- tion of complex shape. There are plenty of theories of shape that make the generation of complex shape unintelligible. However, our theory takes the opposite direction: we are concerned with the conversion of complexity into understandability. In this, we will develop a mathematical theory of und- standability. The issue of understandability comes down to the two basic principles of intelligence - maximization of transfer and maximization of recoverability. We shall show how to formulate these conditions group-theoretically. (1) Ma- mization of transfer will be formulated in terms of wreath products. Wreath products are groups in which there is an upper subgroup (which we will call a control group) that transfers a lower subgroup (which we will call a ?ber group) onto copies of itself. (2) maximization of recoverability is insured when the control group is symmetry-breaking with respect to the ?ber group.

Musimathics

The Mathematical Foundations of Music

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Author: Gareth Loy

Publisher: MIT Press

ISBN: 0262516551

Category: Education

Page: 504

View: 8388

"Mathematics can be as effortless as humming a tune, if you know the tune," writes Gareth Loy. In Musimathics, Loy teaches us the tune, providing a friendly and spirited tour of the mathematics of music--a commonsense, self-contained introduction for the nonspecialist reader. It is designed for musicians who find their art increasingly mediated by technology, and for anyone who is interested in the intersection of art and science.In this volume, Loy presents the materials of music (notes, intervals, and scales); the physical properties of music (frequency, amplitude, duration, and timbre); the perception of music and sound (how we hear); and music composition. Musimathics is carefully structured so that new topics depend strictly on topics already presented, carrying the reader progressively from basic subjects to more advanced ones. Cross-references point to related topics and an extensive glossary defines commonly used terms. The book explains the mathematics and physics of music for the reader whose mathematics may not have gone beyond the early undergraduate level. Calling himself "a composer seduced into mathematics," Loy provides answers to foundational questions about the mathematics of music accessibly yet rigorously. The topics are all subjects that contemporary composers, musicians, and musical engineers have found to be important. The examples given are all practical problems in music and audio. The level of scholarship and the pedagogical approach also make Musimathics ideal for classroom use. Additional material can be found at a companion web site.

Etale Cohomology (PMS-33)

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Author: James S. Milne

Publisher: Princeton University Press

ISBN: 1400883989

Category: Mathematics

Page: 344

View: 7888

One of the most important mathematical achievements of the past several decades has been A. Grothendieck's work on algebraic geometry. In the early 1960s, he and M. Artin introduced étale cohomology in order to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry, but also in several different branches of number theory and in the representation theory of finite and p-adic groups. Yet until now, the work has been available only in the original massive and difficult papers. In order to provide an accessible introduction to étale cohomology, J. S. Milne offers this more elementary account covering the essential features of the theory. The author begins with a review of the basic properties of flat and étale morphisms and of the algebraic fundamental group. The next two chapters concern the basic theory of étale sheaves and elementary étale cohomology, and are followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves the fundamental theorems in étale cohomology -- those of base change, purity, Poincaré duality, and the Lefschetz trace formula. He then applies these theorems to show the rationality of some very general L-series. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Rigor and Structure

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Author: John P. Burgess

Publisher: Oxford University Press, USA

ISBN: 0198722222

Category: Mathematics

Page: 224

View: 4738

John P. Burgess presents an illuminating study of the nature of mathematical rigour and of mathematical structure, and above all of the relation between them. He considers recent developments in the field including experimental mathematics and computerised formal proofs, and surveys many historical developments in mathematics, philosophy, and logic.

Mathematics and Music

A Diderot Mathematical Forum

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Author: Gerard Assayag,Hans G. Feichtinger

Publisher: Springer Science & Business Media

ISBN: 9783540437277

Category: Mathematics

Page: 288

View: 5620

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.

The Topos of Music I: Theory

Geometric Logic, Classification, Harmony, Counterpoint, Motives, Rhythm

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Author: Guerino Mazzola

Publisher: Springer

ISBN: 3319643649

Category: Mathematics

Page: 656

View: 9064

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.

The Topos of Music IV: Roots

Appendices

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Author: Guerino Mazzola

Publisher: Springer

ISBN: 3319644955

Category: Mathematics

Page: 325

View: 6048

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 II: Performance

Theory, Software, and Case Studies

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Author: Guerino Mazzola

Publisher: Springer

ISBN: 3319644440

Category: Mathematics

Page: 408

View: 6403

This is the second volume of the second edition of the now classic book “The Topos of Music”. The author explains his theory of musical performance, developed in the language of differential geometry, introducing performance vector fields that generalize tempo and intonation. The author also shows how Rubato, a software platform for composition, analysis, and performance, allows an experimental evaluation of principles of expressive performance theories.

The Topos of Music III: Gestures

Musical Multiverse Ontologies

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Author: Guerino Mazzola,René Guitart,Jocelyn Ho,Alex Lubet,Maria Mannone,Matt Rahaim,Florian Thalmann

Publisher: Springer

ISBN: 3319644815

Category: Mathematics

Page: 604

View: 5244

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.

Mathematics and Computation in Music

Second International Conference, MCM 2009, New Haven, CT, USA, June 19-22, 2009. Proceedings

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Author: Elaine Chew,Adrian Childs,Ching-Hua Chuan

Publisher: Springer Science & Business Media

ISBN: 3642023940

Category: Computers

Page: 298

View: 9007

This book constitutes the refereed proceedings of the Second International Conference on Mathematics and Computation in Music, MCM 2009, held in New Haven, CT, USA, in June 2009. The 26 revised full papers presented were carefully reviewed and selected from 38 submissions. The MCM conference is the flagship conference of the Society for Mathematics and Computation in Music. The papers deal with topics within applied mathematics, computational models, mathematical modelling and various further aspects of the theory of music. This year’s conference is dedicated to the honor of John Clough whose research modeled the virtues of collaborative work across the disciplines.

Constructing Architecture

Materials, Processes, Structures

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Author: Andrea Deplazes

Publisher: Springer Science & Business Media

ISBN: 3764371900

Category: Architecture

Page: 508

View: 7501

Now in its second edition: the trailblazing introduction and textbook on construction includes a new section on translucent materials and an article on the use of glass.