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
Triangle icon Special Topics
6. Student Research

News

Wed., April 2: Fibonacci Numbers and the Golden Section

Reading

Brian Evans, Number as Form and Content, pp. 303-306 (Evans 1992)

Assignments/Activities

See Blackboard

Quotable

Left quote
One of the luxuries of the artist is that art is validated by the work itself and does not require subservience to the rigors of mathematics or logical proof. As an artist I allow myself full indulgence in that luxury.
 Right quote

– Brian Evans


Course Description

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

Course Documents
  1. Syllabus (pdf)
  2. Topics Updated icon
  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 (pdf) 
  3. Final Presentation Reflections & File Submission (pdf) – Due: Wed., 4/30, 11:59 pm

Online Media Resources

  1. American Mathematical Society (AMS), Music and Mathematics
  2. Brothers Technology, Creative Research
  3. Calter, Geometry in Art & Architecture (Calter 2008)
  4. Cheng, Math in Music (2020) {WFMT}
  5. du Sautoy, Music and Mathematics
  6. Evanstein. Music.py {YouTube Channel}
  7. Euclid, Elements of Geometry (c. 300 BCE) {Texas} (Fitzpatrick 2008)
  8. Frame and Urry, Fractal Geometry {Yale}
  9. Gotham, et al., Open Music Theory, Version 2 {OMT2}
  10. Gresham College Lectures
  11. Haran, Numberphile {YouTube Channel}
  12. Hofstadter, Douglas
  13. Institute of Mathematics & its Applications (IMA)
  14. Interlude Magazine {Interlude.hk}
  15. Johnson, Microsites
  16. McGill University, CIRMMT {YouTube Channel}
  17. Milne and Herff, How a little mathematics can create some beautiful music {The Conversation} (Milne & Herff 2016)
  18. Morris, Mathematics and the Twelve-Tone System (Morris 2007; see BAIN MUSC 525}
  19. Plus Magazine: Bringing mathematics to life for non-expert audiences
  20. Roberts, Bartók and the Golden Section {HolyCross.edu} (Roberts 2012)
  21. Sanderson, 3Blue1Brown {YouTube Channel}
  22. Santa Fe Institute (SFI) {santafe.edu}
  23. Science: Geometrical Music Theory (GMT) Articles: 2006-2008
  24. Socratica, Abstract Algebra {YouTube Playlist}
  25. Straus, Analyzing Modernist Music {YouTube Channel}
  26. Tepfer, Dan Tepfer's Blog {DanTepfer.com} 
  27. 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 Pedagogy {JMTP}
  9. Journal of New Music Research {Taylor & Francis}
  10. Leonardo {MIT Press} & Leonardo Music Journal {MIT Press}
  11. MusMat: Brazilian Journal of Music and Mathematics {musmat.org}
  12. Music Analysis {Wiley; JSTOR}
  13. Music Theory Online {MTO}
  14. Music Theory Spectrum {Oxford; JSTOR}
  15. Proceedings of the Mathematics and Computation in Music (MCM) Conference
  16. Music Theory Online {MTO}
  17. Music Theory Spectrum {Oxford Academic}
  18. Perspectives of New Music {PNM}
  19. Society for Music Theory (SMT)
  20. Theory and Practice {JSTOR}


Main References

See also: BAIN MUSC 726G Bibliography

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

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

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

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

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

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



Updated: April 1, 2025

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