Math 131       Survey – Math & Music        Spring 2011


Professor:       Dave Kung

Office:               175 Schaefer Hall, x4433 or 240-895-4433


TA:                     Jennifer Kunze (

Texts:                Mathematics and Music, by David Wright, published by the AMS


Office Hours:               













Great minds have long sought to explain the relationship between mathematics and music. This course will take you inside a fascinating subject filled with beautiful symmetries and simple mathematical explanations of the sounds you hear every day. Exploring the connections between math and music will help you understand the seemingly simple sound of a vibrating string, the full sound of a symphony orchestra, and even the voice of a loved one on the other end of the phone. We will explore an array of topics: vibrating strings and pitch, why a piano is never in tune, the tradeoff between resonance and modulation and how Indian music and Western music make different choices, how number theory explains complex rhythms, the similarity between algebraic functions and composition, the role of symmetry and group theory in modern music, and avant garde attempts to apply the principles of probability to music. You will have the opportunity to apply this new knowledge in myriad ways, from simple mathematical assignments, to elementary compositions, to your own invented instruments, built using the mathematical principles we will discuss in class. By the end of this course, you will hear and appreciate the world around you in entirely new ways.




Music starts with a vibrating object, which produces a sound. Composers combine these sounds into scales, harmonies and melodies, creating compositions. These compositions are played by musicians with the sound recorded onto an electronic format and delivered to your ear via a CD or an mp3 player. Mathematics informs every step of this process, from a single vibrating string to how you hear the end product in your ear buds.


This course will follow this musical journey, covering the following topics, each for between one and two weeks:

        vibrating objects, fundamental frequencies, overtone series

        the mathematics of timbre

        auditory illusions

        intervals, scales

        beats: their origins and implications

        rhythm, meter and number theory

        musical form and abstract algebra

        self-reference in mathematics & music

        the mathematics of chord progression

        probability and musical composition

        digital delivery of music



There will be two major projects this semester:


Make Your Own Instrument (due Feb. 10th): Music starts when an instrument vibrates. All instruments that can change pitches do so using mathematical principles. For this project, you will design and make your own instrument, using mathematics to aid in the design. This assignment is to be completed in groups of two students, with three students allowed in any group that tackles a more complicated instrument.


Math & Music Final Project (due April 26th): The second project will be of your choosing, with two requirements. First, it must incorporate ideas of both mathematics and music. Second, it must be performable (including at least a brief description of the mathematics) at the end-of-semester concert (date & time TBA). I am open to groups of students completing this assignment together, as well as individual projects.



A short paper (3-4 pages, single spaced) exploring a topic that connects mathematics and music will be due on Tuesday, April 5th. Details about the paper will follow.


Homework: Homework assignments will come in different shapes and sizes, including problems drawn from the textbook, short writing assignments, reflections on the reading, etc. You will always have at least a day and a half to complete these assignments.



Your course grade will be determined by:


Attendance & Participation


Midterm Exam (March 10, in class)




Make Your Own Instrument




Final Project


Final Exam




Late Assignments: Late assignments will only be accepted under the following circumstances: an arrangement is agreed on before the due date, or a documented emergency situation occurs. Generally late work (when allowed) will be subject to at least a 10% deduction.


Student Conduct:  Violations of Student Code of Conduct, such as copying, plagiarizing, and lying about a death in the family will not be tolerated. The rules are clear, and the consequences stiff.

Documented Learning Issues: Anyone who suffers from a documented learning disability should contact me via email and set up a time to meet within the first two weeks of the semester.