Algorithm & blues: Dal prof's songwriting showcases the math behind the music

- July 23, 2024

Dal Mathematics and Statistics Professor Jason Brown. (File photo: Danny Abriel)

What do you need to make a hit song? It's all in the numbers, according to a Dal mathematician who created a pop song using fractals, the Cantor set and all things mathy.

When musician Chuck Berry used to bop across a stage doing his signature duck walk, most people marvelled at his ability to move so smoothly while strumming on a guitar strapped to his back.

Jason Brown, however, saw in Berry's rhythmic moves a love of the mathematics in the music and the specific patterns on which it was based.

"I was trying to figure out what he was doing, and realized he was doing these patterns of threes against the patterns of fours," says Dr. Brown, a professor and chair of the Department of Mathematics and Statistics at Dal.

"Berry found it so cool — even though he didn't know what the mathematics was — that he would do his duck walk and go across the stage because the mathematics moved him emotionally!"

For Dr. Brown — an avid musician and songwriter himself — math is essential to the composition of both lyrics and music, yet isn't widely recognized as a critical ingredient in the song-writing process.

So, he and a colleague at the University of Texas set out to compose a pop song inspired by and based on mathematics. He and co-writer Lawrence Lesser were intent on creating a piece of music that could stand alone as a pop song and be appreciated without people being conscious of any of the underlying mathematics that went into the process.

Cue the composition

The result is “One More Part of Me”, a folk-rock song about losing one's identity in a relationship that runs 4:53 and is based on mathematics — both musically and lyrically. They are presenting the song at the international Bridges conference in Virginia next month, along with a paper outlining their methods.

The pair started by discussing what mathematical concepts might form a basis for the lyrical content of the song. They settled on fractals, which are mathematical shapes that are infinitely complex and can repeat forever. They also used the Cantor set. Dr. Brown describes the Cantor set as a very abstract thing known to mathematicians in which you take all the numbers between 0 and 1 and cut out the middle parts. You're left with smaller intervals and for each of those smaller intervals you keep cutting out the middle thirds. In the end you're left with infinitely many points that survive the cuttings and yet they cover no area.

Underlying mathematical metaphor

"This could be a metaphor for a relationship when someone loses more and more of themselves into a relationship," says Dr. Brown, who sings and plays everything but the drums on the song.

The song also uses words that reflect mathematical ideas. For example, lightening is another example of a fractal and that word appears in the bridge of the song.

"These things are small references that came to us because we had the underlying mathematical metaphor and we knew the properties of it, but if you're a listener you would think that's just a part of the lyrics."

Dr. Brown, a Beatles devotee who has written extensively about the band, says you can identify math in most songs. Led Zeppelin's "Rock and Roll," for example, is characterized bygroupings of three against background groupings of four, creating a sense of anticipation for listeners attuned to the song's pattern.

Most people are comfortable with the idea that music — from classical to jazz to rock to pop and everything in between — is a form of art. Yet when people wonder about the tools that can accentuate the aesthetics, the emotion or the connection between the lyrics and the music, they don't often settle on mathematics.

Part of the creative process

Dr. Brown wants to make clear that one of those tools may be found in the elegance of math.

But what about musicians? Do they think about math when writing songs?

"No! But their brain is mathematical. Any musician is mathematical even if they hated math, and I've gotten a lot of hate mail over the years when I say music is all about math. People think it takes all the creativity out and that mathematicsis simply like being an accountant. But it's an integral part of the creative process!"