Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological And Applied Approaches To Understanding Musical Phenomena

Musical structures have long intrigued musicians and mathematicians, and mathematical models can be found from theoretical analysis to actual composition or sound production. This volume presents significant contributions to mathematical music theory, covering Algebraic and Combinatorial Approaches, Geometric, Topological, and Graph-Theoretical Approaches, and Distance and Similarity Measures in Music.

Format: Hardback
Length: 372 pages
Publication date: 28 December 2018
Publisher: World Scientific Publishing Co Pte Ltd

Musicians and mathematicians have long been fascinated by the study of musical structures, encompassing variation, similarity, enumeration, and classification. Mathematical models can be traced from theoretical analysis to actual composition or sound production. In recent decades, there has been a growing integration of modern mathematical concepts into musical scholarship. One notable example is the application of methods from Algebraic Combinatorics, Topology, and Graph Theory to classify various musical objects. These mathematical approaches have not only enriched our understanding of music but have also generated intriguing open problems in mathematics.

The contributions to mathematical music theory presented in this volume are truly remarkable. Spanning across Algebraic and Combinatorial Approaches, Geometric, Topological, and Graph-Theoretical Approaches, and Distance and Similarity Measures in Music, each contribution offers a deep insight into these diverse subjects.

Algebraic and Combinatorial Approaches delve into the study of musical structures using algebraic and combinatorial tools. Contributors explore topics such as chord progressions, tonal systems, and musical patterns, employing techniques from group theory, combinatorics, and graph theory. These approaches shed light on the underlying mathematical structures that shape musical compositions and provide new insights into the relationships between different musical elements.

Geometric, Topological, and Graph-Theoretical Approaches focus on the geometric and topological aspects of musical structures. Contributors examine the properties of musical spaces, networks, and graphs, using tools from differential geometry, topology, and graph theory. These approaches offer a fresh perspective on musical analysis, highlighting the connections between spatial and structural elements in music.

Distance and Similarity Measures in Music explore the use of mathematical measures to quantify the similarity and distance between musical objects. Contributors discuss various distance and similarity metrics, such as pitch distance, chromatic distance, and structural similarity, and their applications in music analysis, composition, and retrieval. These measures provide a quantitative framework for understanding the structural relationships within music.

In conclusion, the contributions to mathematical music theory presented in this volume showcase the profound interplay between music and mathematics. By exploring the diverse mathematical approaches, we gain a deeper understanding of the underlying structures and patterns that shape musical compositions and performances. The open problems raised in this field encourage further research and collaboration, pushing the boundaries of our knowledge and creativity. This volume serves as a valuable resource for musicians, mathematicians, and scholars interested in advancing the understanding of musical structures and their mathematical foundations.

Weight: 674g
Dimension: 161 x 237 x 21 (mm)
ISBN-13: 9789813235304