University of South Carolina
School of Music

Tuning Theory

Summer 2021

MUSC 726T | Blackboard | Listening/Analysis | Handouts

C O U R S E   M O D U L E S
1. The Harmonic Series
2. Generating Scales
3. Pythagorean Tuning
4. Just Intonation
5. Meantone Temperament
6. Well Temperament
7. Equal Temperament
Special Topics

Naxos | Spotify


Thanks for a great semester!


Left quote
Numbers...are eternal, and unvarying from culture to culture, from eon to eon.
Right quote

Kyle Gann, The Arithmetic of Listening

Course Description

Tuning theory for contemporary musicians with a focus on the theory, analysis, and
practice of microtonality in historical and contemporary contexts.

Prerequisite: Undergraduate tonal harmony and voice leading


Gann, Kyle. 2019. The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician.
Urbana, IL: University of Illinois Press. {Table of Contents}

Login at: EBSCOhost, or purchase the book {IUP Website}

Course Documents

  1. Syllabus (pdf)
  2. Research Project
  3. Homework Projects:
  4. Listening/Analysis
  5. Bibliography
  6. Articles
  7. Handouts
  8. Terms & Concepts:
  9. Software

Library Resources

  1. Grove/Oxford
  2. Harvard Dictionary
  3. JSTOR
  4. Naxos Music Library
  5. FindIt @ UofSC

Online Resources

  1. Acoustics
  2. Boston Microtonal Society
  3. Early Music Sources, Tuning & Temperament in Early Music {YouTube Channel}
  4. Gann, Information on Alternate Tunings
  5. Grady, The Wilson Archives
  6. Huygens-Fokker Foundation, Centre for Microtonal Music
  7. Lamb, Sacred Realism
  8. Monzo, Tonalsoft Encyclopedia of Microtonal Music Theory
  9. Sabat, Music & Writings
  10. Sethares, Tuning, Timbre, Spectrum & Scale (Sethares 2005)
  11. Sevish & Weigel, Now&Xen Podcast
  12. Xenharmonic Wiki


  1. 1/1: The Journal of the Just Intonation Network (1985-2007) {Frog Peak}
  2. Early Music {JSTOR}
  3. Journal of Interdisciplinary Music Studies {}
  4. Journal of the American Musicological Society {JAMS}
  5. Music Theory Online {MTO}
  6. New Music Box {NMB}
  7. Perspectives of New Music {PNM}
  8. Sound American: The Just Intonation Issue {SA20}
  9. Tempo {JSTOR}
  10. Xenharmonikon


See also: BAIN MUSC 726T: Bibliography & Articles

Benade, Arthur. Fundamentals of Musical Acoustics. 1990. Mineola, NY: Dover. {GB}

Blackwood, Easley. 2014/1985. The Structure of Recognizable Diatonic Tunings. Princeton NJ: Princeton University Press. {GB; Full-text: JSTOR}. See also: Equal Tunings 12-75, pp. 293-294 {JSTOR}.

Campbell, Murray and Clive Greated. 2001/1987. The Musician's Guide to Acoustics. New York: Oxford University Press. {GB}

Gann, Kyle. 2019. The Arithmetic of Listening: Tuning Theory and History for the Impractical Musician. Urbana, IL: University of Illinois Press. {GB; Audio Examples; Full text: EBSCOhost}

Pierce, John. 1992. The Science of Musical Sound. New York: W. H. Freeman. {GBd}

Roederer, Juan. 2008/1973. The Physics and Psychophysics of Music: An Introduction, 4th ed. New York: Springer. {GB}

Sethares, William A. 2005. Tuning, Timbre, Spectrum, Scale, 2nd ed. New York: Springer. {GB; Website}

Updated: January 9, 2022

Reginald Bain | University of South Carolina | School of Music