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.
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*
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*
Exploring Musical Spaces fills a necessary place in music-theory
literature and is sure to be as important as the books by George
Perle, Allen Forte, and David Lewin. Hook's cross-disciplinary
double doctorates enable this book to be at such a high level.
*Paul Lombardi, Notes*
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