University of South Carolina
School of Music

BAIN MUSC 726G
Geometrical Music Theory

Spring 2025

MUSC 726G | Blackboard | Listening/Analysis

C O U R S E   M O D U L E S
Triangle icon Introduction
2. The Geometry
of Pitch
3. The Geometry
of Rhythm
4. Visualizing
Musical Structure
5. Special Topics
6. Research

News

Welcome to MUSC 726!

Quotable

Left quote
There is geometry in the humming of the strings. There is music in the spacing of the spheres.
 Right quote

– Pythagoras


Course Description

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


Course Documents

  1. Syllabus (pdf)
  2. GMT Research
  3. Bibliography

Projects

  1. Midterm Project (TBA)
  2. Final Presentation (TBA)

Online Media Resources

  1. Calter, Pythagoras & Music of the Spheres {Dartmouth} (Calter 2008)
  2. Hall, Sounding Numbers Course
  3. Hofstadter
  4. Milne et al., XronoMorph {YouTube Channel}
  5. Plus Magazine, Mathematics and Music {Plus}
  6. Science Articles
  7. Sonic Visualiser
  8. Tymoczko {Website}
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 {Rochester.edu}
  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. Music Analysis {Wiley; JSTOR}
  12. Music Theory Online {MTO}
  13. Music Theory Spectrum {Oxford; JSTOR}
  14. Proceedings of the Mathematics and Computation in Music (MCM) Conference: 2007 | 2009 | 2011 | 2013 | 2015 | 2017 | 2019 | 2022
  15. Music Theory Online {MTO}
  16. Music Theory Spectrum {Oxford Academic}
  17. Perspectives of New Music {PNM}
  18. Society for Music Theory (SMT)
  19. Theory and Practice {JSTOR}


Main References

See also: BAIN MUSC 726G Bibliography

Cohn, Richard. 2012. Audacious Euphony. New York: Oxford. {GB; Oxford}

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

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

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

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



Updated: October 3, 2024

Reginald Bain | University of South Carolina | School of Music
https://reginaldbain.com/vc/musc726a/