Core 101       Math, Music & the Mind        Fall 2012


Professor:      Dave Kung

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


Peer Mentor:             Hattie Schiavone ( )

Library Liaison: Pamela Mann (, x4285)

Text:               This is Your Brain on Music: the Science of a Human Obsession, by Daniel Levitin, Mathematics and Music, by David Wright

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. Exploring how we make sense of these sounds will lead us to study the human mind. 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. The musical/mathematical topics will be interwoven with readings from Levitin, which will help us understand how the mind interprets music.


By the end of this course, you will hear, think about, 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. The last step in the listening process involves your mind – how you interpret the sounds you hear.


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

Š      vibrating objects, fundamental frequencies, overtone series

Š      the mathematics of timbre

Š      auditory illusions

Š      intervals, scales

Š      temperaments and tunings

Š      beats: their origins and implications

Š      rhythm, meter and number theory

Š      musical form and abstract algebra

Š      self-reference in mathematics & music

Š      probability and musical composition

Š      digital delivery of music


Four Core Skills:

As you know from reading the SMCM catalog (right?) your First Year Seminar is designed to introduce four fundamental skills:

Š      Critical Thinking

Š      Written Expression

Š      Oral Expression

Š      Information Literacy

These skills will be introduced early in the course and practiced throughout the semester, with the goal of preparing you to use these skills (and further build them) in later courses.


Writing & Presentation Assignments: 

There will be a variety of writing assignments and oral presentations this semester. All written assignments are to be turned in via Google Docs (see below for more on this). More information on these assignments will be provided at a later date. In all written work, the use of sources must be documented with a citation in the text and a corresponding entry in the list of references at the end. Any style (e.g. MLA is common in the humanities, APA in the social sciences, etc.) is fine, as long as the reader could reasonably find the reference. (Some professors are very exacting about citation styles in their classes; I am not one of them.)


Mathematical Autobiography: (due Thurs., August 30th, 1 full page single-spaced, to be handed in via Google Docs) Tell us about your history with mathematics.


Musical Autobiograpy: (due Thurs., Sept. 6th) The same as above, but regarding you and music.


Musical Definition: (due Thurs., Sept. 13th, 1-2p. single spaced) You will be assigned a word in class and asked to write about it, defining what it means and explaining that definition. In class, you will give a short oral presentation about your word.


The Mathematics of _________. (draft due Oct. 4th, final copy due Oct. 25th, 3-4p)


Choose an instrument and write about the mathematics behind it. Your paper must cover different material from what we cover in class. In class, you will give a five-minute presentation about your findings.


Math, Music and the Mind in the Media, (due Nov. 13th, 2-3p) Take a piece of writing in the popular media (e.g. NYTimes, Newsweek, the Atlantic) and analyze it, comparing it with a research article on the same topic.


Math Concert (tentatively 8pm on Dec. 5th): By popular vote, we will end the semester with a performance! The guidelines are simple: everyone’s piece must tie together two of the three main topics covered in class (Math, Music and the Mind) and everyone must speak to introduce and explain their performance. Students may complete this assignment alone or in pairs, as long as the guidelines are met. The entire college campus will be invited.



Online Tools:

We will make extensive use of two digital tools:

Blackboard: You should have access via your SMCM login:

Google Docs: You’ve already signed up for an account – thanks! Take a few minutes to play around with the features. See if you can start a document, share it with another person so that they can edit it, or so they can read it but not edit it. It will also be helpful if you learn how to insert a comment and look at the revision history of a document.


Exams:  On Oct. 18th in-class, we will hold a midterm exam. On Dec. 13th at noon we will hold a final exam. (And yes, the final is comprehensive.)


Attendance & Participation: You are expected to come to class everyday (with two excused absences during the semester), participate in class discussions and activities, complete reading assignments, and

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


Fifth Hour: The SMCM community offers a stunning array of interesting things to do and events to attend. Like all students in First Year Seminars, you are required to partake in at least five of these (though I hope you do more). For our seminar, the five must come from the following categories:

§  a live music concert (any genre)

§  a math- or science-related talk in the NSM Colloquium Series (usually Wednesdays at 4:40pm) or a department-sponsored talk.

§  an exploration of a near-by natural area (Historic St. Mary’s City, North Field trails, Fishers Creek a.k.a. ‘Nam, kayaking on the river, Point Lookout, etc.)

§  a meeting of a student club

§  an event or organizational meeting where you are an outsider, where you feel like you don’t belong.

Please make sure to start in on these five activities early in the semester. For one of them, you will write up a one-page reflection on the experience and submit it to receive credit for the “Fifth Hour”.


Your course grade will be determined as follows:


Attendance & Participation


Midterm Exam




Fifth Hour


Oral Presentations




Math Concert Performance


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. Generally late work (when allowed) will be subject to at least a 10% deduction (with greater deductions for extremely late work, at Dave’s discretion). Thank you for reading this document so thoroughly; when you get to class on Thursday, only sit in a blue or yellow chair to indicate that you read the syllabus.


Student Conduct:  Violations of Student Code of Conduct, such as copying, plagiarizing, handing in others’ work, and lying about a death in the family will not be tolerated. The rules are clear, and the consequences stiff and range from receiving a zero for the assignment to a failing grade for the course, to being expelled from the college.


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.