University of South Carolina
School of Music

BAIN MUSC 726T
Tuning Theory

Spring 2026

Return to: Blackboard; Listening/Analysis

C O U R S E   M O D U L E S
Triangle icon
 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)
SELECTED TOPICS 
(Ch. 7 & 9-15)
7. Well Temperament (Ch. 7)
8. Extended
Just Intonation (Ch. 9-11)
9. Equal Divisions of
the Octave (Ch. 12-13)

Bandcamp | Naxos
Soundcloud
Spotify | YouTube

News

Welcome to MUSC 726T!

Quotable

Left quote
Any tuning in which beautiful music has been written has earned its right to exist forever.
 Right quote
  – Kyle Gann

Course Description

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

Required Textbook

Kyle Gann, The Arithmetic of Listening {GB; TOC; Full text: TCL; Audio Examples} (Gann 2019)

Course Documents

  1. Syllabus (pdf)
  2. Listening/Analysis
  3. Handouts
  4. Activities
  5. Digital Anthology
  6. The Geometry of Tuning Theory
  7. Software
  8. Terms & Concepts
  9. Bibliography


Projects

  1. Midterm Research Project
  2. Final Presentation

Online Resources

  1. Chalmers, Divisions of the Tetrachord (Chalmers 1992)
  2. Cymatic music
  3. Deutsch, Illusions and Research
  4. Duffin, Just Intonation in Renaissance Theory & Practice {Case Western; MTO} (Duffin 2006)
  5. Erose, 31-EDO Music {YouTube Playlist}
  6. Frog Peak Music: A Composer's Collective {Frogpeak.org}
  7. Gann, Information on Alternate Tunings
  8. Giedraitis, Alternative Tunings: Theory, Notation and Practice {TallKite.com} (Giedraitis 2019)
  9. Goodstein, The Mechanical Universe (1985), a Caltech physics telecourse {WP; YouTube Playlist}
  10. Grady, The [Erv] Wilson Archives
  11. Hogan, The Nikil Hogan Show
  12. Huygens-Fokker Foundation, Centre for Microtonal Music
  13. James, Learning Lumatone {YouTube Playlist}
  14. Lamb, Sacred Realism
  15. Mannfishh
  16. McClain, Microtonal Music Theory
  17. Mermikides, The Nature of Music {Gresham}
  18. MIT, Chromotone: Visual Music Language {Chromotone.center}
  19. Monzo, Tonalsoft Encyclopedia of Microtonal Music Theory
  20. Partch Instruments
  21. Plainsound, Just Intonation and Microtonal Resources {Plainsound.org}
  22. Reich, Minute Physics
  23. Rotem, Early Music Sources (EMS) {Website; YouTube Channel}
  24. Schulter, Pythagorean Tuning and Medieval Polyphony {Medieval.org} (Schulter 1998)
  25. Sethares, Tuning, Timbre, Spectrum & Scale (Sethares 2005)
  26. Sevish, Sevish Music
  27. Temperley, Tuning and Temperament, in Britannica Academic {BA}
  28. Tepfer, Blog
  29. Terpstra, Siemen Terpstra's musical tuning website {SiemenTerpstra.com}
  30. Weigel, Now and Xen Podcast
  31. Wolf, Acoustics: Note Names, MIDI numbers and frequencies {UNSW}
  32. Xenharmonic Wiki

Journals & Professional Societies

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

Research Tools

  1. Thomas Cooper Library
  2. Dictionaries: Harvard Dictionary | Grove/Oxford
  3. Articles: JSTOR
  4. E-books: Ebook Central | EBSCOhost | Hathi Trust
  5. Scores: Alexander Street | CPDL |  IMSLP
  6. Recordings: BandCamp | Naxos | Spotify | YouTube

References

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

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

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: TCL; Website}

Blackwood, Easley. 2014/1985. The Structure of Recognizable Diatonic Tunings. Princeton NJ: Princeton University Press. {GB; 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; U. of Illinois Press; Full text: TCL; Audio Examples}

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

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}

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

Tenney, James. 2015. From Scratch, edited by Larry Polansky, et al. Urbana, IL: University of Illinois Press. {GB; Full text: TCL}

TCL - Thomas Cooper Library, FindIt @ USC
Updated: December 2, 2025

Reginald Bain | University of South Carolina | School of Music
https://reginaldbain.com/vc/musc726t/