Dmitri Tymoczko, professor of music at Princeton, analyzed the connection between math and music Tuesday in a lecture titled “Musical Geometry, Games and Multimedia Art” as part of the Institute for Computational and Experimental Research in Mathematics’ public lecture series. Tymoczko is a musician by training, but his work involves many high-level mathematical concepts, drawing parallels between complex mathematical structures and Western music pieces.
Tymoczko’s work is only the latest development in a long history of exploration at the intersection of math and music. In Ancient Greece, Pythagoras drew connections between certain ratios and harmonies, and, in renaissance Italy, Vincenzo Galilei — the father of Galileo — found relationships between math and music as well, Tymoczko said in an interview with The Herald.
Brendan Hassett, director of ICERM, introduced Tymoczko and praised his work, pointing out that he is the only musician published in the research publication Science. In his lecture, Tymoczko analyzed various classical pieces of music using higher dimensional objects, such as Frederic Chopin’s “Prelude in E-Minor” and several pieces from Dmitri Shostakovich. He found that several classical pieces are very closely related to tesseracts, a type of four-dimensional object. Tymoczko has recently expanded his work to encompass rock music as well, observing that many rock songs abide by a mathematical model, albeit a different one than classical music follows. Tymoczko said that his findings refute the idea that modern rock musicians are not properly trained, a notion often put forth by classical musicians.
Though a non-mathematician may have a difficult time understanding Tymoczko’s work, he has created a number of visual animations and programs to illustrate his ideas, including a program that rethinks the way notes are arranged and an animation of a song’s chords highlighted on a mathematical object. One of his pieces is currently on display at the Museum of Mathematics in New York, helping everyday viewers draw parallels between math and music.
While music is obviously closely connected to mathematics, there is a limit to which theories can be applied, Tymoczko told The Herald. Not all branches of math are connected to music, and Tymoczko thinks it is unlikely that new areas of math will reveal a connection either. “Math done at universities today is much more complicated than anything you will ever need in music,” Tymoczko said.
Tymoczko originally separated his music from his research, hesitating to make pieces based off a mathematical concept. “A lot of composers got lost in theoretical ideas that weren’t that helpful. I wanted my music to be beautiful,” Tymoczko said. But, in recent years, he has composed a piece titled “The Thousand Faces of Form,” which implements various complex geometrical theories, seeking to strike a balance between math and music. The piece is accompanied by a visual component created by Nathan Selikoff, which depicts the geometry in action.
Tymoczko’s lecture was interesting to both the mathematicians and non-mathematicians in the audience alike. Many mathematically-oriented attendees questioned and praised the mathematical side of Tymoczko’s work during the question-and-answer session, while non-mathematicians inquired about the general applicability of his work beyond mathematics. Maddy Adams ’21 said she greatly enjoyed the lecture, particularly Tymoczko’s visualizations of chord progressions. Math and music are seemingly different on the surface, but Tymoczko’s lecture showed the deep intersection between the two, she said.
