Mathematical and Computational Modeling of Tonality

Mathematical and Computational Modeling of Tonality

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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 a€œspirala€ 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.... motif are assumed to be full-valued sixteenth notes in this encoding and all ornaments are grouped with the notes that they embellish. ... 7.6 Manual segmentation of Messiaena#39;s Regard IV into component sections 134 195 301 535 662 719 825 385 423 451. 118 7 Argus Segmentation Method 7.3.2 Automatic Segmentation.


Title:Mathematical and Computational Modeling of Tonality
Author: Elaine Chew
Publisher:Springer Science & Business Media - 2013-12-13
ISBN-13:

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