Exploring Musical Spaces

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