Have you ever wondered how the shape of a trumpet affects its sound, or why a guitar string vibrates in perfect harmony with mathematical laws? In The Mathematics of Musical Instruments Pre-college Program, students will explore the deep connections between mathematics and music. From the wave equation that governs vibrating strings and air columns, to the geometry of resonant bodies and the structure of musical scales, we’ll uncover the elegant formulas behind the instruments we
love. Whether you’re drawn to percussion, strings, or wind instruments, this program invites you to hear math and see music in a whole new way.
Through hands-on activities, students will:
- investigate how equations shape sound
- study how frequency, amplitude, and harmonics emerge from physical systems, and how mathematical models predict the behavior of real-world instruments
- learn how scales are built from ratios
- discover how symmetry influences tone, and how mathematical patterns appear in musical compositions
- dive into famous equations like the wave equation and explore how boundary conditions and material properties influence sound production
The program culminates in a collaborative design challenge: students will work together to design a brand-new musical instrument inspired by mathematical principles. Using string length and tension, frame geometry, and acoustic modeling, we’ll prototype an elegant, expressive instrument that blends tradition with innovation.
Whether you’re a budding mathematician, a curious musician, or both, this program offers a unique opportunity to create, explore, and perform where math meets music.
To deepen our exploration, we’ll take a field trip to the Museum of Mathematics (MoMath) in New York City. This vibrant, hands-on museum brings mathematical ideas to life through interactive exhibits on motion, symmetry, geometry, and sound. Students will experience the beauty of equations in action from colorful patterns and dynamic shapes to musical harmonies and physical phenomena. It’s a joyful celebration of math’s creative power, and a chance to see
how numbers, physics, and imagination come together in surprising ways.
The Mathematics of Musical Instruments will run during Session II: Sunday, July 26 – Saturday, August 1, 2026. Apply Today!
Program Director
Professor Bogdan Nita, Ph.D
nitab@montclair.edu
Department of Mathematics