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
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)
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)
New icon Student Research

Bandcamp | Naxos
Soundcloud
Spotify | YouTube

News

Wed., April 22: Student Presentations: Day 2

The Final Exam will be posted on Wed., April 29. The Final Exam is due Mon., May 4, 11:59 pm

Assignments/Activities

See Blackboard

Quotable

Left quote
The twelve notes on the piano that make up the entire pitch vocabulary of contemporary Western culture is not only one of many historical pitch sets coexisting on this planet, but is merely one of an infinite number of stable tone universes, yet to be explored.
Right quote
  – Stephen James Taylor

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. Software
  7. Terms & Concepts
  8. Bibliography


Research Project

  1. Midterm Research Project (pdf) – Due: Fri., March 27
  2. Final Presentation (pdf)

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. Carroll, Mindscape Podcast
  4. Chalmers, Divisions of the Tetrachord (Chalmers 1992)
  5. Collier
  6. Cymatic music
  7. Detlefsen, Barbershop Theory {YouTube Playlist}
  8. Deutsch, Illusions and Research
  9. Doty
  10. Duffin, Just Intonation in Renaissance Theory & Practice {Case Western; MTO} (Duffin 2006)
  11. Evanstein, music.py {YouTube Channel}
  12. Gann, Information on Alternate Tunings
  13. Giedraitis, Alternative Tunings: Theory, Notation and Practice {TallKite.com} (Giedraitis 2019)
  14. Goodstein, The Mechanical Universe (1985), a Caltech physics telecourse {WP; YouTube Playlist}
  15. Grady, The [Erv] Wilson Archives
  16. Hogan, The Nikil Hogan Show
  17. Huygens-Fokker Foundation, Centre for Microtonal Music
  18. Interlude Magazine {Interlude.hk}
  19. James, Learning Lumatone {YouTube Playlist}
  20. Lamb, Sacred Realism
  21. Mannfishh {YouTube Channel}
  22. McClain, Microtonal Music Theory
  23. Mermikides, The Nature of Music {Gresham}
  24. Monzo, Tonalsoft Encyclopedia of Microtonal Music Theory
  25. Partch Instruments
  26. Plainsound, Just Intonation and Microtonal Resources {Plainsound.org}
  27. Reich, Minute Physics
  28. Rotem, Early Music Sources (EMS) {Website; YouTube Channel}
  29. Schulter, Pythagorean Tuning and Medieval Polyphony {Medieval.org} (Schulter 1998)
  30. Sevish, Sevish Music
  31. Sound American, The Just Intonation Issue (Vol. 20, 2018) {Index: SA}
    Articles on just intonation by Brook, Doty, Gibson, Modney, Polansky, Wooley
  32. Starov, Chromatone Center {Chromotone.center}
  33. Strum & Olsen, Hear Between the Lines {YouTube Channel}
  34. Temperley, Tuning and Temperament, in Britannica Academic {TCL}
  35. Tepfer, Blog
  36. Terpstra, Musical Tuning Website {SiemenTerpstra.com}
  37. Weigel, Now and Xen Podcast
  38. Whipple Museum (Cambridge), Instruments: Acoustics {whipplemuseum.cam.ac.uk}
  39. Wolf, Acoustics: Note Names, MIDI numbers and frequencies {UNSW}
  40. 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. 1994. 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. {GB}

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; Website; Sound Examples}

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: April 18, 2026

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