Music is often portrayed as being at the crossroads of mathematics and artistic emotion. Many would argue that there’s an inherent tension between the calculated nature of math and the spirited talent of an artist. One team of researchers is looking to change this conversation.
In a study published Tuesday by the American Institute of Physics, scientists at The University of Tokyo proposed a new “nonlinear time series method” for analyzing irregularities in global music structures. This method was developed to overcome the limitations of past tools, and it aims to visualize musical features such as rhythm and tone through two-dimensional graphs and models.
Some musicians, particularly those with a background in mathematics, recognize the subtle calculations involved in composing or performing a piece. Terry Everson, the director of undergraduate studies at the School of Music in Boston University’s College of Fine Arts, said professionals in the two fields often share a common mission.
“There are a lot of musicians who have at least some propensity that seems to resonate and relate well back and forth,” Everson said. “I think mathematics, pure mathematics, is something of a search for order, and I think music often times … is a very ordered kind of expression.”
This sense of order is often genre-specific, said Michael Reynolds, a CFA professor and the cellist in the Muir String Quartet. While many pieces of the 20th century embrace irregularities in rhythm, Reynolds noted that older genres share structural similarities, to a certain extent.
“There’s always a certain amount of symmetry, particularly in classical and romantic and early contemporary composers,” Reynolds said, “in terms of how they structure a piece so that there is always one climactic moment and some sub-climactic moments and some little hills on the way to those moments.”
The scientists’ proposed model is able to dive deeper into the mathematics behind such climaxes and sub-climaxes, which Reynolds said would help listeners understand the narrative behind certain pieces.
“Every good piece has a storyline of some sort, and I think this can help a listener … come away and say, ‘Oh I kind of understood what that story was about, what the structure was, where the emotional highs and lows were,’” Reynolds said. “Anything that increases awareness is always a good thing.”
Sam Headrick, a professor of music composition and theory in CFA, agreed with Reynolds in championing a broader understanding of musical structure. He also drew attention to the similarly broad array of emotions brought forth by music.
“The different aspects of rhythm are going to create a different emotional palette,” he said. “If you have a piece with very jagged, asymmetrical meters and so forth, that might create a different emotional response than something that is more repetitive and predictable … Any type of input that helps one understand the overall shape or communicate some aspect of the drama, that’s going to be helpful.”
The potentially problematic nature of the study comes into play with analyzing the visualization, according to Marié Abe, an ethnomusicologist and professor in CFA. Abe said Western culture practices “ocularcentrism,” or favoring vision over the other senses, which poses a threat to the auditory side of music.
“I think the impulse to want to decode sound by visualizing it in a way comes from it,” Abe said. “I think there are a lot of positives, but I also feel that there’s an importance to paying attention to just the act of practicing and sound itself.”
Abe credited the culturally specific potential of the scientists’ method, but also warned against universalizing emotional reactions to certain pieces of music, as the AIP did in its Tuesday press release.
“I think that’s kind of a dangerous assumption, that there’s this universal relationship that you can decode by visualizing sound,” she said. “Each culture becomes socialized to hear sounds in a certain way … I would definitely resist the narrative of this being the key to answering the mystery between human emotion and music.”
A possible solution would be to use the new technology as a mere means to understand and strengthen composition and performing skills rather than as a way to analyze global emotions, both Headrick and Everson said. This would make the method a positive resource for music professionals.
“All research is good because there are going to be some people that think something about this research stimulates them and makes them successful, whereas someone else may not be interested and may not use this new technology,” Headrick said.
Everson, who also instructs CFA students on trumpet performance, said a simplified visualization could be helpful while communicating difficult techniques to his students. However, he added that the quantifiable element of the research shouldn’t distract from artistry.
“I hope we never get rid of the art,” he said. “I don’t think we will. I tend to believe that there’s something in the human spirit and soul that’s more intangible … There are elements of this that I would think there could be some pedagogical use for.”