University of South Carolina
School of Music

Tuning Theory

Spring 2024

Return to: Blackboard | Handouts | Listening/Analysis | Activities

C O U R S E   M O D U L E S
1. The Harmonic Series (Ch. 1-2)
2. Generating Scales (Ch. 3)
3. Pythagorean Tuning (Ch. 4)
4. Just Intonation (Ch. 5)
5. Meantone
Temperament (Ch. 6)
6. Equal Temperament (Ch. 8)
(Ch. 7 & 9-15)
7. Well Temperament (Ch. 7)
8. Extended
Just Intonation (Ch. 9-11)
Triangle icon Equal Divisions of
the Octave (Ch. 12-13

BandCamp | Naxos
Spotify | YouTube


The Final Project presentations will take place on:

Mon., April 15: Day 1. Mon., April 15

Wed., April 17: Day 2. Wed., April 17

Mon., April 22: Day 3. Mon., April 22

The presentation schedule is available below.


Left quote
In my opinion, the striking and characteristic moods of many tuning-systems will become the most powerful and compelling reason for exploring beyond 12-tone equal temperament.
Right quote
  – Ivor Darreg

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

Required Textbook

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:
EBSCOhost; IUP Website}

Course Documents

  1. Syllabus (pdf)
  2. Listening/Analysis
  3. Handouts Updated icon
  4. Digital Anthology
  5. Terms & Concepts:
  6. Software
  7. Bibliography


  1. Teaching Demo (pdf)
  2. Final Project (pdf)

Online Resources

  1. Chalmers, Divisions of the Tetrachord {Dartmouth} (Chalmers 1992)
  2. Cymatic music
  3. Deutsch, Illusions and Research
  4. Duffin, Just Intonation in Renaissance Theory & Practice {Case Western; MTO} (Duffin 2006)
  5. Frog Peak Music: A Composer's Collective {}
  6. Gann, Information on Alternate Tunings
  7. Giedraitis, Alternative Tunings: Theory, Notation and Practice {} (Giedraitis 2019)
  8. Grady, The [Erv] Wilson Archives
  9. Huygens-Fokker Foundation, Centre for Microtonal Music
  10. Lamb, Sacred Realism
  11. Lumantone Keyboard, Learning Lumatone {YouTube Playlist}
  12. Mannfishh, Interval Studies {YouTube Playlist}
  13. Mermikides, The Art and Science of Tuning {YouTube}
  14. Monzo, Tonalsoft Encyclopedia of Microtonal Music Theory
  15. Partch Instruments
  16. Plainsound, Just Intonation and Microtonal Resources {}
  17. Rotem, Early Music Sources (EMS), Tuning & Temperament in Early Music {YouTube Channel}
  18. Sabat, Music & Writings
  19. Schulter, Pythagorean Tuning and Medieval Polyphony {} (Schulter 1998)
  20. Sethares, Tuning, Timbre, Spectrum & Scale (Sethares 2005)
  21. Sevish, Sevish Music
  22. Temperley, Tuning and Temperament, in Britannica Academic {Discus}
  23. Terpstra, Siemen Terpstra's musical tuning website {}
  24. Wolf, Acoustics: Note Names, MIDI numbers and frequencies {UNSW}
  25. Xenharmonic Wiki


  1. Sevish & Weigel, Now and Xen Podcast
  2. Grosse, Art + Music + Technology podcast {Libsyn}


  1. 1/1: The Journal of the Just Intonation Network (1985-2007) {Frog Peak
  2. Bridges Organization: Art and Mathematics {Bridges}
  3. Early Music {See also: JSTOR}
  4. Journal of Interdisciplinary Music Studies {}
  5. Journal of the Acoustical Society of America {JASA}
  6. Journal of the American Musicological Society {JAMS}
  7. Journal of Mathematics and Music {Taylor & Francis; Music Library}
  8. Music Theory Online {MTO}
  9. New Music Box {New Music Box}
  10. Perspectives of New Music {PNM}
  11. Society for Music Theory (SMT)
  12. Sound American: The Just Intonation Issue {SA20}
  13. Tempo {See also: JSTOR}
  14. Untwelve: Exploring the notes between the notes {Untwelve}
  15. Xenharmonikon

Research Tools

  1. FindIt @ USC
  2. Dictionaries: Harvard Dictionary | Grove/Oxford
  3. Articles: JSTOR
  4. E-books: Ebook Central | EBSCOhost | Hathi Trust
  5. Scores: Alexander Street | CPDLMSLP
  6. Recordings: BandCamp | Naxos | Spotify | YouTube

Main References

See also: BAIN MUSC 726T: Bibliography & Articles, and the Huygens-Fokker Foundation's Tuning & Temperament Bibliography

Barbour, J. Murray. 2004/1951. Tuning and Temperament: A Historical Survey. Mineola, NY: Dover. {GB; Full text: HathiTrust}

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

Benson, David. 2007. Music: A Mathematical Offering. Cambridge: Cambridge University Press. {GB; Full-Text: EBSCOhost; Website}

Blackwood, Easley. 2014/1985. The Structure of Recognizable Diatonic Tunings. Princeton NJ: Princeton University Press. {GB; TOC: JSTOR}

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

Doty, David B. 2002/1993. The Just Intonation Primer.: An Introduction to the Theory and Practice of Just Intonation. San Francisco: The Just Intonation Network. {GB; Website}

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

Johnston, Ben. 2006. Maximum Clarity and Other Writings on Music. Urbana: University of Illinois Press. {GB; Full text: Ebook Central}

Narushima, Terumi. 2017. Microtonality and the Tuning Systems of Erv Wilson. New York: Routledge. {GB; Full text: TCL}

Partch, Harry. 1974/1949. Genesis of a Music, 2nd ed. New York: Da Capo Press. {GBd}

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

Rossing, Thomas, F. Richard Moore and Paul Wheeler. 2002. The Science of Sound, Third Edition. New York: Addison Wesley. {GB}

Updated: April 13, 2024

Reginald Bain | University of South Carolina | School of Music