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.
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