Description
Book SynopsisExploring 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 models-the first examples of the musical spaces of the book''s title-depicting 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
Trade ReviewThe '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 *
For anyone looking for one book to read to help them better engage with or produce scholarship in mathematical music theory, I cannot recommend Exploring Musical Spaces highly enough. * Jordan Lenchitz, Journal of Mathematics and Music *
Table of ContentsPreface 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
