Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing from the outset a number of simple geometric modelsDLthe first examples of the musical spaces of the book's titleDLdepicting relationships among musical entities of various kinds such as notes, chords, scales, or rhythmic values. These spaces take many forms and become a unifying thread in initiating readers into several areas of active recent scholarship, including transformation theory, neo-Riemannian theory, geometric music theory, diatonic theory, and scale theory. Concepts and techniques from mathematical set theory, graph theory, group theory, geometry, and topology are introduced as needed to address musical questions. Musical examples ranging from Bach to the late twentieth century keep the underlying musical motivations close at hand. The book includes hundreds of figures to aid in visualizing the structure of the spaces, as well as exercises offering readers hands-on practice with a diverse assortment of concepts and techniques.
By:
Julian Hook
Imprint: Oxford University Press Inc
Country of Publication: United States
Dimensions:
Height: 187mm,
Width: 256mm,
Spine: 37mm
Weight: 1.406kg
ISBN: 9780190246013
ISBN 10: 0190246014
Series: Oxford Studies in Music Theory
Pages: 864
Publication Date: 08 September 2022
Audience:
Professional and scholarly
,
Undergraduate
Format: Paperback
Publisher's Status: Active
Preface Acknowledgments Part I Foundations of Mathematical Music Theory: Spaces, Sets, Graphs, and Groups Chapter 1: Spaces I: Pitch and Pitch-Class Spaces Chapter 2: Sets, Functions, and Relations Chapter 3: Graphs Chapter 4: Spaces II: Chordal, Tonal, and Serial Spaces Chapter 5: Groups I: Interval Groups and Transformation Groups Part II Transformation Theory: Intervals and Transformations, including Neo-Riemannian Theory Chapter 6: Groups II: Permutations, Isomorphisms, and Other Topics in Group Theory Chapter 7: Intervals Chapter 8: Transformations I: Triadic Transformations Chapter 9: Transformations II: Transformation Graphs and Networks; Serial Transformations Part III Geometric Music Theory: The OPTIC Voice-Leading Spaces Chapter 10: Spaces III: Introduction to Voice-Leading Spaces Chapter 11: Spaces IV: The Geometry of OPTIC Spaces Chapter 12: Distances Part IV Theory of Scales: Diatonic and Beyond Chapter 13: Scales I: Diatonic Spaces Chapter 14: Scales II: Beyond the Diatonic Appendix 1: List of Musical Spaces Appendix 2: List of Sets and Groups References
Julian Hook holds PhDs in both mathematics and music theory, as well as graduate degrees in architecture and piano performance. His work involving mathematical approaches to the study of music has appeared primarily in music theory journals but also at conferences of the American Mathematical Society and in the pages of Science. Since 2003 he has taught at Indiana University, where he is a former chair of the music theory department. He is a past president of Music Theory Midwest and was the founding reviews editor of the Journal of Mathematics and Music.
Reviews for Exploring Musical Spaces: A Synthesis of Mathematical Approaches
The 'mathy' quality of much recent music theory has long been a barrier to its comprehension. No more. Julian Hook is a master explainer and, thanks to this book, music theorists and interested musicians now have an effective on-ramp not only to understanding but also to deep enjoyment of the rich regularities that can be heard to underpin musical experience. * Joseph Straus, CUNY Graduate Center * Exploring Musical Spaces draws together the most important results in algebraic and geometric music theory of the last fifty years. Julian Hook's treatise, featuring the author's signature clarity and depth of insight, will open this dazzling field to a new generation of scholars. * - Ian Quinn, Yale University *
- Winner of Winner, 2023 Wallace Berry Award, Society for Music Theory.
