Mathematical and Computational Modeling of Tonality: Theory and Applications

Elaine Chew

doi:10.1007/978-1-4614-9475-1

Mathematical and Computational Modeling of Tonality: Theory and Applications

Research output: Book/Report › Book

Abstract

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.

Original language	English
Place of Publication	New York
Publisher	Springer Science + Business Media
Number of pages	305
Volume	204
Edition	1
ISBN (Electronic)	978-1-4614-9475-1
ISBN (Print)	978-1-4614-9474-4, 978-1-4899-7929-2
DOIs	https://doi.org/10.1007/978-1-4614-9475-1
Publication status	Published - 2014

Publication series

Name	International Series in Operations Research & Management Science
Publisher	Springer Science+Business Media New York
Volume	204
ISSN (Print)	0884-8289
ISSN (Electronic)	2214-7934

Keywords

tonality
music theory
Geometric modelling
mathematical modeling
computational mathematics
music visualisation
key finding
operations research

Access to Document

10.1007/978-1-4614-9475-1Licence: Other

2 Conference paper
1 Article

MorpheuS: Generating Structured Music with Constrained Patterns and Tension
Herremans, D. & Chew, E., 1 Oct 2019, In: IEEE transactions on affective computing.
Research output: Contribution to journal › Article › peer-review

Open Access
A Walk Through Tonal Space: Charting the Establishing of the Key of a Melody
Chew, E., 30 Jul 2001, Proceedings 13th International Conference on Systems Research, Informatics and Cybernetics. Baden-Baden, Germany, July 30 - August 4, 2001. Windsor, Ontario: International Institute for Advanced Studies in Systems Research and Cybernetics, Vol. VIII. 6 p.
Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

File
Modeling Tonality: Applications to Music Cognition
Chew, E., 1 Aug 2001, Proceedings of the 23rd Annual Meeting of the Cognitive Science Society (CogSci), Edinburgh, UK, Aug 1-4, 2001. Moore, J. & Stenning, K. (eds.). Edinburgh, UK: Lawrence Erlbaum Associates, Publishers, Vol. 23. p. 206-211 4 p.
Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Open Access
File

Cite this

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title = "Mathematical and Computational Modeling of Tonality: Theory and Applications",

abstract = "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.",

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AB - 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.

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Mathematical and Computational Modeling of Tonality: Theory and Applications

Abstract

Publication series

Keywords

Access to Document

Fingerprint

Research output

MorpheuS: Generating Structured Music with Constrained Patterns and Tension

A Walk Through Tonal Space: Charting the Establishing of the Key of a Melody

Modeling Tonality: Applications to Music Cognition

Cite this