Category Archives: Syllabus


Sounding Number: Music and Mathematics from Ancient to Modern Times

Instructor: Dr. Rachel Hall
Office: 238 Barbelin
Office Hours: Tues 10-11, Weds 10-12, Thurs 9-10, and by appointment

Class URL:

Course description: Music has many connections to mathematics. The ancient Greeks discovered that chords with pleasing sounds are related to simple ratios of integers. Other connections include equations describing the sounds of musical instruments, the mathematics of digital recording, the use of symmetry in composition, and the systematic exploration of patterns by African and Indian drummers. This course introduces basic concepts in set theory, trigonometry, and combinatorics and investigates their applications in the analysis, recording, and composition of music. Along the way, we consider the role of creativity in mathematics and the ways in which mathematics has inspired musicians. The course will involve hands-on activities in playing and creating music. There is no prerequisite.

Course goals: The student who successfully completes this course should

  • Be familiar with the fundamentals of musical rhythm and the relationship between cyclic and linear time.
  • Understand the physical properties of musical sound, including frequency, pitch, and overtones, and be able to represent sound waves using periodic functions.
  • Use basic musical notation for rhythm and melody.
  • Identify consonant intervals and explain the role that consonance plays in chord and scale construction.
  • Know the definition of a set and an equivalence class and be able to use these definitions to describe rhythms, scales, and chords.
  • Understand the need for formal definitions and rigorous arguments in mathematics and be able to prove some basic mathematical statements related to music theory.
  • Be able to identify musical forms such as verse and chorus, theme and variations, and canon.
  • Be able to implement mathematical ideas in musical analysis and composition.

Prerequisite: None.

Text: I am developing a text for this class and will post chapters, vocabulary, sample problems and solutions, and practice tests on this site as they become available. You may be asked to purchase a course pack later in the semester.

Technology and other supplies: You will need a scientific calculator that can perform basic functions such as square roots and trigonometric calculations. You do not need a graphing calculator, but may use one if you have it. You should bring your calculator to every class.

Homework: Homework assignments include computational problems, short musical compositions that demonstrate the concepts covered in class, and written assignments designed to develop deeper mathematical thinking and communication skills.

Quizzes: There will be 10-minute quizzes given in class every Thursday. Quizzes are based on readings, lectures, in-class work, and homework problems. There are no makeup quizzes, but your lowest three grades will be dropped.

Tests: There will be two tests. A cumulative final exam will be given during final exam period, May 5-11. Makeup tests will only be given to students who contact me by email (rhall@sju.eduwithin 48 hours of missing a test. Students with a valid, verifiable reason for missing a test or the final may take a makeup without penalty if they bring validation; those who have missed a test without a valid, verifiable reason may take a makeup with a 30% penalty, assuming that they contact me within 48 hours. Valid excuses include illness (verified by a doctor’s note), death in the family, or an official university activity such as an athletic event or field trip.

Grades: Grades will be assigned on the following basis:

15% Quizzes (lowest three grades dropped)
10% Homework (lowest grade dropped)
40% Two tests
35% Final exam

The grade cutoffs are 93.3% A, 90% A-, 86.7% B+, 83.3% B, 80% B-, 76.7% C+, 73.3% C, 70% C-, 66.7% D+, 60% D, and below 60% F.

Academic honesty: Dishonesty includes cheating on a test, falsifying data, misrepresenting the work of others as your own (plagiarism), and helping another student cheat or plagiarize. At the very least, an academic honesty infraction will result in the filing of a violation report and a grade of zero on that particular assignment; serious or repeated infractions of the Academic Honesty policy will result in failure of the course. For complete information about the University’s policy on Academic Honesty, consult the Student Handbook.

Attendance: Participation in class activities is an essential component of the course. If you do miss a class, it is your responsibility to obtain the notes and assignments from another student, to make sure your homework is turned in on time, and to reschedule class presentations, if necessary. In case of illness or other emergency that results in two or more consecutive absences, notify me by e-mail (

Classroom policies: With the exception of calculators and planned class activities, you will not need technology in class. Laptops and phones should be placed under your seat. Students who feel that they need an exemption from this policy should discuss it with me in advance.

Students with disabilities: Reasonable academic accommodations may be provided to students who submit appropriate documentation of their disability. More information is at

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