December 6, 2023

Musical Numbers: Understanding How Math and Music Merge

In building a thongophone for mathematical analysis of its pipes for pitch, Montclair students find the connection between music and math

Posted in: Homepage News, Research, Science and Technology, Uncategorized, University

Two students play the thongophone, striking different size pipes with rubber thong like sandals. — Seniors Vish Naik, Mathematics Education, and Taiwo Akingbesote, Mathematics, play the thongophone researched and built in their Mathematics and Music class. The percussion instrument gets its name from the rubber thongs or flip-flops traditionally used to strike the pipes.

For anyone who believes math and music are an odd couple, Montclair State University Mathematics Professor Bogdan Nita may have you changing your tune. Nita conducts Mathematics and Music to teach students to see beyond formulas and to make connections by designing and building musical instruments to understand how musical elements can be analyzed numerically.

This semester, the class collaborated on studying a percussion instrument known as the thongophone. Built with recycled PVC pipes, the instrument produces a sound that varies according to the length of the pipes, one pipe per pitch arranged like the keyboard of a piano. It gets its name for the way it is played: The top of the pipes are struck with something flexible, like rubber thongs or flip-flops, the handiest things to use where the instrument originated in Australia and Papua New Guinea.

In building their own thongophone, the Math majors covered a wide variety of mathematical concepts – algebra, geometry, differential equations, a bit of topology and vector calculus – and all of it related to music. “You talk about algebra and suddenly you talk about scales and then how can you invent your own scale? We do complicated algebra and the students can’t tell because they’re captivated by the music,” Nita says.

A professor plays the thongophone. — Mathematics Professor Bogdan Nita demonstrates the thongophone. The length of the pipes creates different pitches, a musical element that can be analyzed numerically.

Hands holding rubber sandals taped on to spatulas strike white pipes of different sizes. — A close-up view of the thongophone and rubber pieces taped onto spatulas and wooden utensils.

The instrument and student research were displayed at the Math and Music Showcase presented on November 29 by the Department of Mathematics. “We studied how sound is created inside the pipes because of pressure, the different ways you can create that pressure and how the length of the pipes relate to the pitch that is produced,” Nita explains. “We wrote equations, we solved them, we looked at thongophones that already exist and we built our own that’s sort of like a pipe organ you play with thongs.”

The Mathematics and Music course was developed as part of a University effort to connect math and the general sciences with different areas of creativity, including art, architecture, poetry, painting and music, Nita says. The initiative includes the launching in 2023 of the LASER Journal, an open access, peer-reviewed, online journal dedicated to research at the interface of mathematics and arts. The journal gets its name from the acronym Linking Art and Science through Education and Research.

A harp against a window with a view of campus behind it. — Two years ago, mathematics students designed and built a harp to study, in part, the vibration of strings. Research from the project contributed to an article published in the *Journal of Humanistic Mathematics*.

Mathematics and Music has also contributed research on new and innovative harp shapes, with Nita and mathematics students Cristina Carr and Vlad Nita contributing to an article published in July in the Journal of Humanistic Mathematics. In their article, titled “The Mathematics of the Harp: Modeling the Classical Instrument and Designing Futuristic Ones,” the research team shares how they analyzed and modeled the neck of the classical harp based on the length, tension and density of the strings.

A smiling student wearing a black and gold laughs. — Garnisha Pierre, a senior Mathematics major, is among the students who contributed to this year’s research connecting math and music with the thongophone. “My biggest takeaway from the project is that math is so universal,” she says. “The range of things that you can learn and do with it is infinite.”

Story by Staff Writer Marilyn Joyce Lehren. Photos by John J. LaRosa