BAIN MUSC 726T
Tuning Theory
GANN 2019
Table of Contents
Required Textbook
Gann, Kyle. 2019. The
Arithmetic of Listening: Tuning Theory and History for the
Impractical Musician. Urbana,
IL: University of Illinois Press. {GB; U.
of Illinois Press; Full
text: TCL; Audio
Examples}
Table of Contents
Acknowledgments
Introduction
Chapter 1. The Cosmic Joke
Chapter 2. The Harmonic Series
Chapter 3. Generating Scales
Interlude A: Ptolemy and Ancient Greek “Parts”
Chapter 4. The Pythagorean Scale
Interlude B: Guillaume de Machaut’s Notre Dame
Mass
Chapter 5. The Five Limit, the Second Dimension
Interlude C: Some Modern Five-Limit Notions
Chapter 6. Meantone Temperament and the Primacy
of Thirds
Interlude D: Meantone Examples
Chapter 7. Well Temperament and Key Color
Interlude E: Bach, Beethoven, and Temperament
Chapter 8. Twelve-Step Equal Temperament
Chapter 9. The Seven Limit and Johnston Notation
Interlude F: La Monte Young’s The Well-Tuned
Piano
Interlude G: Ben Johnston’s String Quartet No. 4
Chapter 10. The Eleven Limit and the Fourth
Dimension
Interlude H: Harry Partch
Chapter 11. The Thirteen Limit and Beyond
Interlude I: Ben Johnston’s String Quartet No.
7, Movement 3
Interlude J: Kyle Gann’s Hyperchromatica
Interlude K: Toby Twining’s Chrysalid Requiem
Chapter 12. Non-Twelve-Divisible Equal
Temperaments
Interlude L: Nicola Vicentino’s Archicembalo
Chapter 13. Twelve-Based Equal Temperaments
Interlude M: Some Quarter-Tone Impressions
(Hába, Ives, Wyschnegradsky)
Interlude N: Ezra Sims’s String Quartet No. 5
Chapter 14. A Few Numbers Drawn from Non-Western
Musics
Chapter 15. Brief Miscellaneous Thoughts
Appendix
Notes
Glossary of Tuning Terms
Bibliography
Index
Updated: December 2, 2025