Mathematical and Computational Modeling of Tonality: Theory and Applications by

The Nile on eBay   Mathematical and Computational Modeling of Tonality by Elaine Chew

Connecting mathematical representations of music to computational problem-solving, the author's spiral array geometric model for tonality benefits from his unique perspective-as concert pianist and successful PhD candidate in operations research.

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description

From the Preface:Blending ideas from operations research, music psychology, music theory, and cognitive science, this book aims to tell a coherent story of how tonality pervades our experience, and hence our models, of music.The story is told through the developmental stages of the Spiral Array model for tonality, a geometric model designed to incorporate and represent principles of tonal cognition, thereby lending itself to practical applications of tonal recognition, segmentation, and visualization. Mathematically speaking, the coils that make up the Spiral Array model are in effect helices, a spiral referring to a curve emanating from a central point. The use of "spiral" here is inspired by spiral staircases, intertwined spiral staircases: nested double helices within an outer spiral.The book serves as a compilation of knowledge about the Spiral Array model and its applications, and is written for a broad audience, ranging from the layperson interested in music, mathematics, and computing to the music scientist-engineer interested in computational approaches to music representation and analysis, from the music-mathematical and computational sciences student interested in learning about tonality from a formal modeling standpoint to the computer musician interested in applying these technologies in interactive composition and performance. Some chapters assume no musical or technical knowledge, and some are more musically or computationally involved.

Back Cover

From the Preface: Blending ideas from operations research, music psychology, music theory, and cognitive science, this book aims to tell a coherent story of how tonality pervades our experience, and hence our models, of music. The story is told through the developmental stages of the Spiral Array model for tonality, a geometric model designed to incorporate and represent principles of tonal cognition, thereby lending itself to practical applications of tonal recognition, segmentation, and visualization. Mathematically speaking, the coils that make up the Spiral Array model are in effect helices, a spiral referring to a curve emanating from a central point. The use of "spiral" here is inspired by spiral staircases, intertwined spiral staircases: nested double helices within an outer spiral. The book serves as a compilation of knowledge about the Spiral Array model and its applications, and is written for a broad audience, ranging from the layperson interested in music, mathematics, and computing to the music scientist-engineer interested in computational approaches to music representation and analysis, from the music-mathematical and computational sciences student interested in learning about tonality from a formal modeling standpoint to the computer musician interested in applying these technologies in interactive composition and performance. Some chapters assume no musical or technical knowledge, and some are more musically or computationally involved.

Table of Contents

Tonality.- An Abbreviated Survey.- The Spiral Array.- The CEG Algorithm (Part I).- The CEG Algorithm (Part II): Validation.- Determining Key Boundaries.- Argus Segmentation Method.- Real-Time Pitch Spelling.- MuSA.RT.- Visible Humor.- Sensitivity Analysis.- Model Calibration.- CEG Key Finding: Bach's WTC book I.

Review

I have watched with interest and appreciation as Elaine Chew s Spiral Array model has developed over the last 15 years. It is unique in representing pitches, intervals, chords, and keys in the same elegant geometric representation. In this way, the model addresses the fundamental problem of how to represent the hierarchical nature of tonal listening. The monograph presents in-depth analyses of a wide variety of interesting musical examples as well as large-scale, quantitative tests of algorithms for key-finding, pitch spelling, and musical segmentation. The reader will be amply rewarded with mathematical and musical insights and intrigued by the power of mathematics to reveal the inner workings of music cognition." Carol Lynne Krumhansl, Professor of Psychology Cornell University"What do you mean by key?" The seemingly innocent question asked once to the author by a student initiates a fascinating scientific journey into the concept of tonality addressed through its cognitive, mathematical and computational ramifications. This essential yet accessible and entertaining book results from years of research and experimentation by one of today's prominent minds in music science, with the right balance of formal modelling, experimentation and musical knowledge, always situated in the history of ideas. The student and the professional in computation and music related domains will benefit greatly from reading this book, as well as the music lover interested in reflecting on the way we apprehend tonality." Gerard Assayag, Research Director, Sciences and Technologies for Music and Sound Laboratory (IRCAM, CNRS, and Pierre et Marie Curie University)"From its imaginative opening pages to its rigorous appendices, Chew's book takes the reader on an engrossing tour through the theory and applications of her ingenious multiple-helix model of musical tonality. She approaches music theory and cognition from a fresh perspective inspired by operations research,

Promotional

"I have watched with interest and appreciation as Elaine Chew's Spiral Array model has developed over the last 15 years. It is unique in representing pitches, intervals, chords, and keys in the same elegant geometric representation. In this way, the model addresses the fundamental problem of how to represent the hierarchical nature of tonal listening. The monograph presents in-depth analyses of a wide variety of interesting musical examples as well as large-scale, quantitative tests of algorithms for key-finding, pitch spelling, and musical segmentation. The reader will be amply rewarded with mathematical and musical insights - and intrigued by the power of mathematics to reveal the inner workings of music cognition." (Carol Lynne Krumhansl, Professor of Psychology Cornell University) "What do you mean by key?" The seemingly innocent question asked once to the author by a student initiates a fascinating scientific journey into the concept of tonality addressed through its cognitive, mathematical and computational ramifications. This essential yet accessible and entertaining book results from years of research and experimentation by one of today's prominent minds in music science, with the right balance of formal modelling, experimentation and musical knowledge, always situated in the history of ideas. The student and the professional in computation and music related domains will benefit greatly from reading this book, as well as the music lover interested in reflecting on the way we apprehend tonality." (Gerard Assayag, Research Director, Sciences and Technologies for Music and Sound Laboratory (IRCAM, CNRS, and Pierre et Marie Curie University)) "From its imaginative opening pages to its rigorous appendices, Chew's book takes the reader on an engrossing tour through the theory and applications of her ingenious multiple-helix model of musical tonality. She approaches music theory and cognition from a fresh perspective inspired by operations research, to great advantage. One comes away with the clear sense that this approach will continue to bear fruit, whether through elaboration of the underlying model or through discovery of its applicability to new practical problems. No one interested in pitch representation, computational music analysis, or music visualization should miss this important volume." (Douglas Keislar, Editor, Computer Music Journal (MIT Press))

Long Description

This proposed addition to the ISOR series is perhaps the most novel application of OR techniques ever conceived: the mathematical and computational modeling of tonality. This is the first book ever to apply problem-solving computational analysis to the realm of music, and author Elaine Chew is the one person in the world bringing together the mathematical and computational in a sharply focused coherent text/reference book. An accomplished scholar, pianist, and instructor (OR) at the Viterbi School of Engineering, USC, Chew has also just completed a year-long Fellowship at the Harvard University Radcliffe Institute of Advanced Studies. She is also the inventor of the Spiral Array algorithm for the study of tonality, and that is the cornerstone of her proposed book. Taking interior point optimization methods far beyond the more traditional engineering, financial and logistics arenas, Chew applies OR techniques to the computational analysis of music, technological requirements for digital music storage and retrieval, and the study of human traits inherent in composition, performance, hearing, and analysis. Chew shows how the Spiral Array algorithm can be used in tonal analysis and solutions to music cognition phenomena. Individual sections of the book first introduce the notion of computational modeling of cognition of music structures, and then present the geometric models of tonality, including the Spiral Array, and then look at applications to specific areas like key finding; interactive visual analysis of tonal patterns; audio key finding; and segmentation and similarity assessment. Anyone involved in research in any of these areas will likely know of Chew's work, and will very likely want this book handy. The research and advances are applicable to a broad range of study, from digital storage and retrieval through human cognition and understanding of musical structure and form.

Review Quote

I have watched with interest and appreciation as Elaine Chew s Spiral Array model has developed over the last 15 years. It is unique in representing pitches, intervals, chords, and keys in the same elegant geometric representation. In this way, the model addresses the fundamental problem of how to represent the hierarchical nature of tonal listening. The monograph presents in-depth analyses of a wide variety of interesting musical examples as well as large-scale, quantitative tests of algorithms for key-finding, pitch spelling, and musical segmentation. The reader will be amply rewarded with mathematical and musical insights and intrigued by the power of mathematics to reveal the inner workings of music cognition. " Carol Lynne Krumhansl, Professor of Psychology Cornell University " What do you mean by key?" The seemingly innocent question asked once to the author by a student initiates a fascinating scientific journey into the concept of tonality addressed through its cognitive, mathematical and computational ramifications. This essential yet accessible and entertaining book results from years of research and experimentation by one of today's prominent minds in music science, with the right balance of formal modelling, experimentation and musical knowledge, always situated in the history of ideas. The student and the professional in computation and music related domains will benefit greatly from reading this book, as well as the music lover interested in reflecting on the way we apprehend tonality. " Gerard Assayag, Research Director, Sciences and Technologies for Music and Sound Laboratory (IRCAM, CNRS, and Pierre et Marie Curie University)" From its imaginative opening pages to its rigorous appendices, Chew's book takes the reader on an engrossing tour through the theory and applications of her ingenious multiple-helix model of musical tonality. She approaches music theory and cognition from a fresh perspective inspired by operations research,

Feature

First book to connect mathematical representations of music with computational approaches to problem solving Presents author's Spiral Array geometric model for tonality Author is known worldwide and uniquely qualified as both concert pianist and PhD in Operations Research

Details ISBN1489979298 Author Elaine Chew Year 2016 ISBN-10 1489979298 ISBN-13 9781489979292 Format Paperback Language English Media Book DEWEY 153 Imprint Springer-Verlag New York Inc. Subtitle Theory and Applications Place of Publication New York Country of Publication United States Publication Date 2016-08-27 Pages 305 Short Title Mathematical and Computational Modeling of Tonality Series Number 204 AU Release Date 2016-08-27 NZ Release Date 2016-08-27 US Release Date 2016-08-27 UK Release Date 2016-08-27 Edited by Nicole Smith Dahmen Birth 1945 Affiliation University of Southern Queensland Position Professor Qualifications PhD Publisher Springer-Verlag New York Inc. Edition Description Softcover reprint of the original 1st ed. 2014 Series International Series in Operations Research & Management Science Alternative 9781461494744 Audience Professional & Vocational Illustrations 46 Illustrations, color; 108 Illustrations, black and white; XIV, 305 p. 154 illus., 46 illus. in color. We've got this

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