The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician

PDF The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician © 2019 by the Board of Trustees

Book author
  1. Kyle Gann
The Arithmetic of Listening Tuning Theory and History for the Impractical Musician

"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.


I must first of all thank Ben Johnston for, with an offhand comment (followed by four years of revelatory teaching), determining the subsequent direction of my life. Ben is a genius, a visionary, and his ten string quartets and many other just-intonation pieces have revealed more about what tuning can achieve than could have been rea- sonably expected from any one person in a lifetime. Second, for years, editors would ask me what book I was working on, and I would cheerily respond, “Well, I’ve got a microtonality textbook half finished,” just to enjoy the squeamish look on their faces as they changed the subject. Laurie Matheson was the first editor to reply, “Good, let’s do it.” She’s why you’re holding this book. Her faith in me has been gratifying. I roamed the world of academic publishing and finally found a home at the University of Illinois Press. Fittingly, Ben taught at the University of Illinois for thirty-two years (though I studied with him privately and was not enrolled there).

I thank my former student Lydia Spielberg, whose classics professors claimed that she knew ancient Greek better than they did and that her senior thesis could have been a doctoral dissertation. Her undergraduate paper on Ptolemy for my tuning class remains the clearest exposition I’ve been able to find on the subject. A few years later she is already doing postdocs and has gone on to what will doubtless be a stellar academic career. It was my great honor to have the manuscript read by microtonal experts John Schneider (a Partch performer and world’s leading expert on the microtonal guitar) and Andrew Granade (an important biographer of Partch), and I benefited from their every suggestion. I thank Kraig Grady, Juhani Nuorvala, Casey Hale, and Paul Erlich for providing materials on Regular Temperament Theory, particularly Paul, who patiently endured and answered many detailed technical questions. He taught me Regular Temperament Theory as he has taught so many others. Stephen Parris, director of Gamelan Encinal, provided me with important documents on gamelan
tuning. My Bard College colleague Maria Sonevytsky pulled me back from the brink of ethnomusicological faux pas, and our Baroque specialist, Alexander Bonus, found sources for me and knew exactly when to scoff. I hope I have not embarrassed either of them, nor any of my other benefactors, with further misconceptions. Most of all I thank my lovely wife, Nancy, for so uncomplainingly nurturing a decades-long obses- sion that began, after all, a few months after we married. She did not see this coming.
Extention type
File size
17.7 MB
First release
Last update
0.00 star(s) 0 ratings

More resources from Soundmain