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 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 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.

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.

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