Mathematical and Computational Modeling of Tonality (eBook) von Elaine Chew

Mathematical and Computational Modeling of Tonality
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Theory and Applications
 eBook
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149,79 €* eBook

ISBN-13:
9781461494751
Veröffentl:
2013
Einband:
eBook
Seiten:
305
Autor:
Elaine Chew
Serie:
204, International Series in Operations Research & Management Science
eBook Format:
PDF
eBook-Typ:
Reflowable eBook
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Kurzbeschreibung

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.

Inhaltsverzeichnis
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.
Beschreibung

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.


 

Schlagwörter zu:

Mathematical and Computational Modeling of Tonality von Elaine Chew - mit der ISBN: 9781461494751

cognitive science; computational models; mathematical programming; music information retrieval; music theory; operations research; tonality; B; Computational Mathematics and Numerical Analysis; Cognitive Psychology; Operations Research and Decision Theory; Music; Business and Management, Online-Buchhandlung


 

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