What does math and musical performance have in common? That's what Ami Radunskaya, a guest lecturer from Pomona College, answered for roughly 70 people during "A Celebration of Mathematics and Music" on Tuesday.
“I am excited to be here as the third speaker in the series, and of course, we know there are many connections between math and music,” Radunskaya said. “In particular, they look at their own weird notation, but, also, they share neural circuitry, fMRIs have shown us that... But today, I want to talk about how mathematics can be used in real time musical performance, but maybe a bit of a different take than we can see before.”
Radunskaya has worked in the math department at Pomona College since 1994. Her area of research, in simple layman terms, deals with patterns and systems within math, data and relationships and how the results can best be visualized.
Prior to focusing on her mathematical research, Radunskaya worked as a cellist and a composer, which she tries to incorporate into her mathematical research whenever possible.
“Chaos structures patterns. This is the kind of thing that pulled me into mathematics when I first started,” Radunskaya said. “How do we describe chaos, unpredictability, maybe, how do we define unpredictable? How do we quantify unpredictable? Well, maybe just have a pattern? Well, what's a pattern? All these things can be described with mathematics.”
After lecturing for about half an hour, Radunskaya invited the Pneum Quartet, a student string quartet-in-residence at Jacobs School of Music, to perform “Nefarious Networks,” a four-part piece she composed in 2020 that is accompanied with both visual and musical themes to demonstrate mathematical ideas.
The quartet is made up of four Jacobs students: master’s student and violinist Arthur Trælnes, violinist Gabriel Fedak, performance diploma violist Seung A. Jung and first-year performance diploma cellist John Sample. While the quartet played, Radunskaya showed different dynamic mathematical models as a physical manifestation of the music. She told each musician to wear a certain color that would coordinate with their respective nodes on visual models when performing “Nefarious Networks.”
“It was a lot of fun. It was different than music we played before, a lot of it was improvised as we didn't have too much time to put it together as well with all the technology and things, but it was a lot of fun to do together,” Sample said.
As opposed to a traditional score, Radunskaya encouraged improvisation and individuality when performing her piece. The performers were each given a few measures of sheet music which included their instrument’s distinct musical motif was as well as a device that showed them the visual chart the audience was shown too, allowing them to interpret the math as they saw it.
“In usual recitals, we have all the music laid out in front of us, right?” Sample said. “So, this one was a lot (different), we had a couple measures to kind of work with and improvise off of, but I think it works because we played together a lot, and we've done kind of similar things as well, so we have ideas from (Radunskaya) as well.”
Professor of mathematics Kevin Pilgrim and professor of music theory Julian “Jay” Hook created the annual event in early 2022. Their goal was to celebrate math and music and show something interesting to both mathematicians and musicians, but in a way that’s understandable and digestible to the general public.
Pilgrim emphasized that while the concepts discussed in the annual event may be specialized, the event is open to the public, who is encouraged to ask questions throughout the lecture. He said the variety of mediums is another way to make the event easier to understand.
“Today, so we cannot only hear the speaker's voice and see the words, but we can see the pictures and we noticed she was illustrating the behavior of these different kinds of orbit sequences through sound, going up exponentially fast or decaying,” Pilgrim said. “That's actually quite common. When you're teaching kids' math, you want to make the problems and the activities accessible to people with a variety of backgrounds. And you do that through using multiple representations, visual clues, stories, rather than only symbols.”
