Microtonality and the Tuning Systems of Erv Wilson: 1st Edition (Hardback) book cover

Microtonality and the Tuning Systems of Erv Wilson

1st Edition

By Terumi Narushima


218 pages | 39 B/W Illus.

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Hardback: 9781138857568
pub: 2017-11-21
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This book explores the emerging area of microtonality through an examination of the tuning theories of Erv Wilson. It is the first publication to offer a broad discussion of this influential theorist whose innovations have far-reaching ramifications for microtonal tuning systems. This study addresses the breadth and complexity of Wilson’s work by focusing on his microtonal keyboard designs as a means to investigate his tuning concepts and their practical applications. Narushima examines materials ranging from historical and experimental tunings to instrument design, as well as musical applications of mathematical theories and multidimensional geometry. The volume provides an analysis of some of Wilson’s most significant theoretical ideas, including the Scale Tree, Moments of Symmetry, Constant Structures, and Combination-Product Sets. These theories offer ways to conceptualize musical scales as patterns with structural integrity and whose shapes can be altered to produce infinitely varying forms. The book shows how these structural properties can be used to map scales onto a microtonal keyboard by providing step-by-step guidelines and clearly illustrated examples. Most importantly, it brings together theoretical and practical methods of tuning to enable composers, performers, and instrument designers to explore previously uncharted areas of microtonality, making a significant contribution to the fields of music theory, composition and music technology.


'This text provides a unique and also comprehensive view of microtonality, represented by the important work of Erv Wilson, and links microtonal theory to instrument design in a very compelling way. It provides both a conceptual and practical approach to microtonal music and does so within a global musical perspective.'

Mathew Rosenblum, University of Pittsburgh

Table of Contents

1. Introduction: Microtonality and the Enigma of Erv Wilson 2. Microtonal Keyboards 3. Mapping Linear Scales on Wilson’s Generalized Keyboard 4. Moments of Symmetry and the Scale Tree 5. Mapping Constant Structures and Navigating New Pathways 6. Cross-Sets, Diamonds and Combination-Product Sets 7. Conclusion

About the Author

Terumi Narushima is a senior lecturer in music at the University of Wollongong, Australia. She is a composer, performer, and sound designer specialising in microtonal tuning systems. Her projects include acoustic and electronic music, works for film and theatre, and a research collaboration to develop microtonal flutes using 3D printing.

About the Series

Routledge Studies in Music Theory

This series is our home for cutting-edge, upper-level scholarly studies and edited collections on a wide range of topics in music theory, including analysis, tonality, rhythm, discourse, aesthetics, and composition. Titles are characterized by dynamic interventions into established subjects and innovative studies covering many disciplines, such as history, performance, cognition, gesture, critical theory, math, and popular music.

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Subject Categories

BISAC Subject Codes/Headings:
MUSIC / General