"Tuning is the secret lens through which the history of music falls into focus," says Kyle Gann. Yet in Western circles, no other musical issue is so ignored, so taken for granted, so shoved into the corners of musical discourse.

A classroom essential and an invaluable reference, The Arithmetic of Listening offers beginners the grounding in music theory necessary to find their own way into microtonality and the places it may take them. Moving from ancient Greece to the present, Kyle Gann delves into the infinite tunings available to any musician who feels straitjacketed by obedience to standardized Western European tuning. He introduces the concept of the harmonic series and demonstrates its relationship to equal-tempered and well-tempered tuning. He also explores recent experimental tuning models that exploit smaller intervals between pitches to create new sounds and harmonies.

Systematic and accessible, The Arithmetic of Listening provides a much-needed primer for the wide range of tuning systems that have informed Western music.

Audio examples demonstrating the musical ideas in The Arithmetic of Listening can be found at: https://www.kylegann.com/Arithmetic.html

| Cover Title Copyright Contents Acknowledgments Introduction 1. The Cosmic Joke 2. The Harmonic Series 3. Generating Scales Interlude A: Ptolemy and Ancient Greek "Parts" 4. The Pythagorean Scale Interlude B: Guillaume de Machaut's Notre Dame Mass 5. The Five Limit, the Second Dimension Interlude C: Some Modern Five-Limit Notions 6. Meantone Temperament and the Primacy of Thirds Interlude D: Meantone Examples 7. Well Temperament and Key Color Interlude E: Bach, Beethoven, and Temperament 8. Twelve-Step Equal Temperament 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 10. The Eleven Limit and the Fourth Dimension Interlude H: Harry Partch 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 12. Non-Twelve-Divisible Equal Temperaments Interlude L: Nicola Vicentino's Archicembalo 13. Twelve-Based Equal Temperaments Interlude M: Some Quarter-Tone Impressions (Hába, Ives, Wyschnegradsky) Interlude N: Ezra Sims's String Quartet No. 5 14. A Few Numbers Drawn from Non-Western Musics 15. Brief Miscellaneous Thoughts Appendix Notes Glossary of Tuning Terms Bibliography Index Back cover | "Not only explains the materials and history of this music in great detail, but also—and probably most importantly—illustrates how these scales and harmonies are used in actual, living, breathing music. What has always been missing from the literature is an overarching guide to the field that is clearly written for both the amateur and professional. This is that book."—John Schneider, Grammy Award-winning producer
"There is no other book that comes close to what Kyle Gann has accomplished here. The Arithmetic of Listening combines materials from ancient treatises and complex mathematical discussions of tunings with an artist's eye toward their expressive, musical use. It reads as though you are in a master class with a teacher who is patiently opening your eyes to a hidden history and your ears to hidden musical possibilities."—S. Andrew Granade, author Harry Partch: Hobo Composer
"A lot of fun . . . this is indeed a practical book, not just for its instructions, but also in the interludes." —The Wire
|Kyle Gann is a composer and the Taylor Hawver and Frances Bortle Hawver Professor of Music at Bard College. His...