Dr. Brandon Konoval is a UBC music theorist shedding light on the role math plays in our favourite songs.
From a basic understanding of ratios to complex musical analysis, music and mathematics share a centuries-old connection. Konoval, an associate professor of teaching for the UBC School of Music, discussed this deep relationship between math and music with The Ubyssey, from his PhD thesis to his modern works.
An ancient tradition
Knowledge of the connections between mathematics and music is nothing new — many concepts used in music theory date back hundreds of years.
“Music actually had played a rather significant role in what we now refer to as early modern science,” said Konoval.
Konoval has discussed the complex relationship between Pythagorean ideas about music and more modern music theorists like Vincenzo Galilei, father of Galileo Galilei, and Marin Mersenne in his research. His work delves into how mathematical paradigms in music have been shaped over the centuries.
Mathematicians from around the world have contributed to our understanding of music theory.
A famous example is the inception of the twelve-tone equal temperament, which separates an octave into 12 parts that, when placed on a logarithmic scale, wind up being equal with a ratio of the 12th root of 2.
Music theorists have long debated who first conceptualized this signature since it was “mathematically formulated” at around the same time in China’s Ming dynasty and in Europe’s 16th century, according to an article published in Music Theory Spectrum. Recent literature suggested that Zhu Zaiyu, a Ming dynasty mathematician and music theorist developed the temperament first.
Grasping the basics
Mathematical tools give scholars insight into some of the more complicated aspects of music.
One of these tools is called pitch-class set theory, which uses ratios to categorize different components of music and find relationships between them. Pitch-class set theory organizes groups of related pitches to more complex musical operations and can be conceptualized using geometry.
When referring to his doctoral dissertation, Konoval touched on how pitch-class set theory informed his research.
“[Mathematical tools were] really actually helping me to understand what was going on in music by a composer whose music I was deeply drawn to, but often really quite perplexed by,” he said.
Multiple published studies apply mathematical principles to our understanding of rhythm, pitch, timing and much more.
Music and math ability
Students with musical training have appeared to perform better in mathematics than those without training, but the connection is not well established in the literature.
Math scores and confidence in music theory have been used as predictors of scores on music theory tests for university-level music students, as seen in one study in Applied Cognitive Psychology. However, more research needs to be conducted to further define those connections.
Test scores aside, according to Konoval, the connection between math and music runs deep, with stellar implications.
“[The connection between math and music] becomes the basis for a pretty deep engagement with the possibility that the entire cosmos is fundamentally structured in mathematical ways and that in many respects that might be perceived in musical terms.”