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

Wed., Jan. 21: The Harmonic Series (cont.), in Zoom

Reading

Ch. 1 The Cosmic Joke

Ch. 2 The Harmonic Series

Assignments/Activities

See Blackboard

Quotable

Left quote
...tuning is the secret lens through which the history of music falls into place.
 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. Activities
  4. Handouts
  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. American Mavericks, Just Intonation by Preston Wright (2003) {American Public Media}
  2. Cambridge Research, Pythagoras was wrong: there are no universal musical harmonies (2025) {YouTube; Cambridge Research}
  3. Chalmers, Divisions of the Tetrachord (Chalmers 1992)
  4. Cymatic music
  5. Detlefsen, Barbershop Theory {YouTube Playlist}
  6. Deutsch, Illusions and Research
  7. Doty, Musical Ratios: The Why, How, and Wherefore {Sound American} (Doty 2002)
  8. Duffin, Just Intonation in Renaissance Theory & Practice {Case Western; MTO} (Duffin 2006)
  9. Erose, 31-EDO Music {YouTube Playlist}
  10. Evanstein, music.py {YouTube Channel}
  11. Gann, Information on Alternate Tunings
  12. Giedraitis, Alternative Tunings: Theory, Notation and Practice {TallKite.com} (Giedraitis 2019)
  13. Goodstein, The Mechanical Universe (1985), a Caltech physics telecourse {WP; YouTube Playlist}
  14. Grady, The [Erv] Wilson Archives
  15. Hogan, The Nikil Hogan Show
  16. Huygens-Fokker Foundation, Centre for Microtonal Music
  17. James, Learning Lumatone {YouTube Playlist}
  18. Lamb, Sacred Realism
  19. Mannfishh {YouTube Channel}
  20. McClain, Microtonal Music Theory
  21. Mermikides, The Nature of Music {Gresham}
  22. MIT, Chromotone: Visual Music Language {Chromotone.center}
  23. Monzo, Tonalsoft Encyclopedia of Microtonal Music Theory
  24. Partch Instruments
  25. Plainsound, Just Intonation and Microtonal Resources {Plainsound.org}
  26. Reich, Minute Physics
  27. Rotem, Early Music Sources (EMS) {Website; YouTube Channel}
  28. Schulter, Pythagorean Tuning and Medieval Polyphony {Medieval.org} (Schulter 1998)
  29. Sethares, Tuning, Timbre, Spectrum & Scale (Sethares 2005)
  30. Sevish, Sevish Music
  31. Strum & Olsen, Hear Between the Lines {YouTube Channel}
  32. Temperley, Tuning and Temperament, in Britannica Academic {BA}
  33. Tepfer, Blog
  34. Terpstra, Musical Tuning Website {SiemenTerpstra.com}
  35. Weigel, Now and Xen Podcast
  36. Whipple Museum (Cambridge), Instruments: Acoustics {whipplemuseum.cam.ac.uk}
  37. Wolf, Acoustics: Note Names, MIDI numbers and frequencies {UNSW}
  38. 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 {SA}
  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; Full text: TCL}

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}

GB - Google Books
TCL - Thomas Cooper Library, FindIt @ USC
Updated: January 19, 2025

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