University of South Carolina
School of Music

BAIN MUSC 726G
Geometrical Music Theory

Spring 2025

MUSC 726G | Blackboard

C O U R S E   M O D U L E S
1. Introduction
2. The Geometry
of Pitch
3. The Geometry
of Rhythm
4. Exploring Musical
Spaces
5.
 Special Topics
Triangle icon Student Research

News

Thanks for a great semester!

Assignments/Activities

See Blackboard

Quotable

Left quote
Music theory is topological mainly because it provides so many examples of discontinuous motion through spaces with interesting structure.
 Right quote

– Dmitri Tymoczko


Course Description

An introduction to the theory and analysis of music using geometric models

Course Documents
  1. Syllabus (pdf)
  2. Topics
  3. Activities
  4. Digital Anthology
  5. Handouts
  6. Reading
  7. Explore
  8. Researchers
  9. Software
  10. Terms & Concepts
  11. Bibliography

Projects

  1. Midterm Research Project (pdf) – Due: Fri., March 28, 11:59 pm
  2. Final Presentation:

Online Media Resources

  1. Andreatta, The Tonnetz {Web app; Website; Besada et al. 2024}
  2. American Mathematical Society (AMS), Music and Mathematics
  3. Bach
  4. Brothers Technology, Creative Research
  5. Calter, Geometry in Art & Architecture (Calter 2008)
  6. Cheng, Math in Music (2020) {WFMT}
  7. Du Sautoy, Music and Mathematics
  8. Evanstein. Music.py {YouTube Channel}
  9. Euclid, Elements (c. 300 BCE)
  10. Frame and Urry, Fractal Geometry {Yale}
  11. Gotham, et al., Open Music Theory, Version 2 {OMT2}
  12. Gresham College Lectures
  13. Haran, Numberphile {YouTube Channel}
  14. Hofstadter, Douglas
  15. Institute of Mathematics & its Applications (IMA)
  16. Interlude Magazine {Interlude.hk}
  17. Johnson, Microsites
  18. Journal of Mathematics and Music {TCL; T&F}
  19. Malinowski
  20. McGill University, CIRMMT {YouTube Channel}
  21. Mermikides {Website}
  22. Milne and Herff, How a little mathematics can create some beautiful music {The Conversation} (Milne & Herff 2016)
  23. Morris, Mathematics and the Twelve-Tone System (Morris 2007); see BAIN MUSC 525
  24. Onishi, Visualizations {Keitaonishi.com}
  25. Plus Magazine: Bringing mathematics to life for non-expert audiences {Plus}
  26. Popoff, Alpof blog: Random thoughts about music and math, science and someties legos... {alpof.wordpress.com}
  27. Roberts, Bartók and the Golden Section {HolyCross.edu} (Roberts 2012)
  28. Sanderson, 3Blue1Brown {YouTube Channel}
  29. Science: Geometrical Music Theory (GMT) Articles: 2006-2008
  30. SanteFe Institute (SFI) {Website}
  31. Socratica, Abstract Algebra: Group Theory {Website; YouTube Playlist}
  32. Straus, Analyzing Modernist Music {YouTube Channel}
  33. Tepfer, Dan Tepfer's Blog {DanTepfer.com} 
  34. Tymoczko
Research Tools
  1. FindIt @ UofSC
  2. Dictionaries: Harvard Dictionary | Grove/Oxford
  3. Articles: JSTOR
  4. E-books: Ebook Central | EBSCOhost | Hathi Trust
  5. Scores: IMSLP; Alexander Street; CPDL
  6. Recordings: Naxos | Spotify | YouTube
  7. Audio & Video: TCL

Organizations

  1. American Mathematical Society (AMS): Mathematics & Music (AMS) – https://www.ams.org
  2. Bridges: Mathematics, Art, Music, Architecture, Culture (Bridges) – https://www.bridgesmathart.org
  3. Society for Multidisciplinary and Fundamental Research (SEMF) – https://semf.org.es

Journals

  1. Bridges: Mathematics, Art, Music, Architecture, Culture {The Bridges Archive}
  2. Engaging Students: Essays in Music Pedagogy {OSU Libraries}
  3. Indiana Theory Review {IU Press}
  4. Intégral: The Journal of Applied Musical Thought {Eastman}
  5. Journal of Mathematics and the Arts {Taylor & Francis}
  6. Journal of Music Theory {JMT; JSTOR}
  7. Journal of Music and Mathematics {Taylor & Francis}
  8. Journal of Music Theory {Duke}
  9. Journal of Music Theory Pedagogy {JMTP}
  10. Journal of New Music Research {Taylor & Francis}
  11. Leonardo {MIT Press} & Leonardo Music Journal {MIT Press}
  12. MusMat: Brazilian Journal of Music and Mathematics {musmat.org}
  13. Music Analysis {Wiley; JSTOR}
  14. Music and Science {Sage}
  15. Music Theory Online {MTO}
  16. Music Theory Spectrum {Oxford; JSTOR}
  17. Proceedings of the Mathematics and Computation in Music (MCM) Conference
  18. Music Theory Online {MTO}
  19. Music Theory Spectrum {Oxford Academic}
  20. Perspectives of New Music {PNM}
  21. Society for Music Theory (SMT)
  22. Theory and Practice {JSTOR}

Bibliography

See also: BAIN MUSC 726G Bibliography| | Articles

Cohn, Richard. 2012. Audacious Euphony: Chromatic Harmony and the Triad's Second Nature. New York: Oxford. {GB; Full text: TCL; Oxford}

Hook, Julian L. 2022. Exploring Musical Spaces: A Synthesis of Mathematical Approaches. New York: Oxford. {GB; Full text: TCL}

Lewin, David. 2007/1987. Generalized Musical Intervals and Transformations. New York: Oxford University Press. {GB; Full text: TCL}

Toussaint, Godfried T.  2019/2013. The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good?, 2nd ed. Boca Raton, FL: CRC Press. {GB; Full text: TCL}

Tymoczko, Dmitri. 2023. Tonality: An Owner's Manual. New York: Oxford University Press. {GB; Full text: TCL}

______________. 2011. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. New York: Oxford. {GB; Full text: TCL}



Updated: October 16, 2026

Reginald Bain | University of South Carolina | School of Music
https://reginaldbain.com/vc/musc726g/