Exploring Musical Spaces

Description

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.

• Offers comprehensive and up-to-date coverage of mathematical approaches to music theory
• Adopts a visual, geometric orientation, using the idea of a musical space as a unifying concept
• Written for readers with no prior mathematical knowledge beyond basic algebra
• Features hundreds of exercises spanning a wide range of difficulty levels

About the Author(s)

Julian Hook, Associate Professor of Music Theory, Indiana University

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.

Table of Contents

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

Reviews

"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