Admission requirements
None.
Description
Many people think of music as a purely subjective art form, unbound by rules and driven by emotion and personal experience. But music is built out of a collection of concepts – harmony, melody, scales, rhythm, tuning, timbre, form, and more – that work together in precise ways to effectively communicate a feeling or an idea. Mathematics provides us with a set of conceptual frameworks that can be used to better understand the structure underlying these concepts and the interplay between them.
The objective of this course is to develop mathematical ideas that can be used both to analyze the structure of existing musical pieces and to aid in the expression of new musical ideas. The course introduces a selection of mathematical concepts – including but not limited to geometric series, logarithms, trigonometric functions, least common multiples, modular arithmetic, rational and irrational numbers, and group theory – and applies them to various topics in music theory. Labs throughout the term will provide opportunities to explore the structural features of music using digital tools. As a final project students will create a musical composition that applies the principles they’ve learned, and present a mathematical analysis of their new piece.
Course Objectives
After successful completion of this course, students are able to:
Knowledge
Appreciate the role mathematics plays in the liberal arts
Discuss the mathematical principles of number theory covered in the course
Explain the multiple connections between mathematics and music
Display a deeper appreciation for music and understanding of music theory
Skills
Apply mathematical reasoning to the study of music theory
Collect numerical data from musical pieces and collaboratively discuss how quantitative measurements affect qualitative musical experience
Create new musical ideas based on mathematical relations
Seek out and identify mathematical relationships in any field, both outside their studies and in more advanced courses
Timetable
Timetables for courses offered at Leiden University College in 2025-2026 will be published on this page of the e-Prospectus.
Mode of instruction
The course will have interactive lectures to introduce and illustrate mathematical concepts and definitions, and to explain their applications to music. Students will be expected to read about these concepts before coming to class. In-class activities will focus on reinforcing this learning and building skills in both mathematical reasoning and music theory.
In lab sessions, students will experiment with digital sound production, in order to discover how mathematical operations impact the nature of sound. Some of these lab sessions will be collaborative, requiring students to work together to find patterns and to present their findings to the rest of the lab.
Assessment Method
Participation. 10%
Final project: 25%
Homework assignments: 25%
Final exam: 40%
Reading list
The required textbook is:
- Roberts, G. E. (2016). From Music to Mathematics: Exploring the Connections. Johns Hopkins University Press. http://www.frommusictomath.com/
Optional additional resources include:
Loy, Gareth. (2006). Musimathics: The Mathematical Foundations of Music (Volume 1). The MIT Press. http://www.musimathics.com/
Benson, David. (2006). Music: A Mathematical Offering. Cambridge University Press. https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-music.html
Registration
Courses offered at Leiden University College (LUC) are usually only open to LUC students and LUC exchange students. Leiden University students who participate in one of the university’s Honours tracks or programmes may register for one LUC course, if availability permits. Registration is coordinated by the Education Coordinator, course.administration@luc.leidenuniv.nl.
Contact
TBC
Remarks
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