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The Arithmetic of Listening: Tuning Theory & History for the Impractical Musician – Kyle Gann

Thoughts: I read The Arithmetic of Listening for a seminar I sat in on in Winter 2021 on Tuning and Temperament. Its subject matter is quite niche, but for those interested in alternate/extended musical tuning systems, Gann’s book is both mind- and ear-opening.

(The notes below are not a summary of the book, but rather raw notes - whatever I thought, at the time, might be worth remembering.)

Gann, Kyle. 2019. The Arithmetic of Listening: Tuning Theory & History for the Impractical Musician. University of Illinois Press.

You can listen to audio examples for the book at https://www.kylegann.com/Arithmetic.html.

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-Tempered Piano

Interlude G: Ben Johnston’s String Quartet No. 4

10: The Eleven Limit and the Fourth Dimension

Interlude H: Harry Partch

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

Posted: Dec 21, 2021. Last updated: Dec 21, 2021.