How Math Shapes Music (From Bach to Taylor Swift)

Even though you can't always notice it, math permeates almost every aspect of society. Even music! An article I came across, published in February 2024, explains how recent research revealed mathematical patterns in Bach's music.

As a violinist since 6 years old, with a passion for mathematics, when I read about this intersection between the two subjects, I knewI had to share it!

The Research - Math's Presence in Music

Johann Sebastian Bach, a German composer, created the most renowned pieces of his time as the most influential Baroque composer. 

Published In Physical Review Research, physicists replaced common musical notation with a series of dots and lines, aiming to discover mathematical patterns of musical tones and networks. Often, these patterns may help create a better listening experience.

The researchers calculated the amount of information entropy in a piece, which explains how random a certain pattern is (or isn't) in any score. This concept closely relates to thermodynamic entropy, a concept taught in chemistry and physics that outlines molecular disorder as it relates to energy (don't worry, that might sound complicated, but it isn't important to understand right now). 

The article explains that in the human mind, as a piece of music is played, a "mental model" is formed in our head andpredicts what sound may come next based on past patterns. 

The research identified that chorales, a hymn, had little "information" but still had an apparent structure. On the other hand, toccatas and preludes, a style normally associated with keyboard instruments, had more randomness or entropy. This entropy provides the listener with more of a sense of surprise. 

The Conclusion

Using information theory and vast network analysis, the research showed how mathematics may alter someone's interpretation of music, possibly opening up a new opportunity for more research in music and its relationship with math and psychology. 

Importantly, even though music, on its surface, doesn't appear to relate to the complex equations and theorems of mathematics, math lies in the foundation of all music.

From Bach to Taylor Swift, math shapes music.