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

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.