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

by Kyle Gann

Overview

"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

Product Details

ISBN-13:	9780252084416
Publisher:	University of Illinois Press
Publication date:	09/04/2019
Pages:	312
Product dimensions:	6.90(w) x 9.90(h) x 0.90(d)

About the Author

Kyle Gann is a composer and the Taylor Hawver and Frances Bortle Hawver Professor of Music at Bard College. His books include Charles Ives's Concord, No Such Thing as Silence: John Cage's 4'33" and Robert Ashley.

Table of Contents

Acknowledgments ix

Introduction 1

1 The Cosmic Joke 9

2 The Harmonic Series 20

3 Generating Scales 25

Interlude A Ptolemy and Ancient Greek "Parts" 42

4 The Pythagorean Scale 48

Interlude B Guillaume de Machaut's Notre Dame Mass 53

5 The Five Limit, the Second Dimension 55

Interlude C Some Modern Five-Limit Notions 63

6 Meantone Temperament and the Primacy of Thirds 67

Interlude D Meantone Examples 82

7 Well Temperament and Key Color 87

Interlude E Bach, Beethoven, and Temperament 97

8 Twelve-Step Equal Temperament 102

9 The Seven Limit and Johnston Notation 109

Interlude F La Monte Young's The Well-Tuned Piano 125

Interlude G Ben Johnston's String Quartet No. 4 132

10 The Eleven Limit and the Fourth Dimension 138

Interlude H Harry Partch 141

11 The Thirteen Limit and Beyond 148

Interlude I Ben Johnston's String Quartet No. 7, Movement 3 159

Interlude J Kyle Gann's Hyperchromatica 165

Interlude K Toby Twining's Chrysalid Requiem 170

12 Non-Twelve-Divisible Equal Temperaments 174

Interlude L Nicola Vicentino's Archicembalo 199

13 Twelve-Based Equal Temperaments 205

Interlude M Some Quarter-Tone Impressions (Hába, Ives, Wyschnegradsky) 218

Interlude N Ezra Sims's String Quartet No. 5 226

14 A Few Numbers Drawn from Non-Western Musics 231

15 Brief Miscellaneous Thoughts 241

Appendix 245

Notes 263

Glossary of Tuning Terms 277

Bibliography 283

Index 291

Editorial Reviews

"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

From the Publisher