What do you need to make a hit song? It's all in the numbers, according to听a听Dal mathematician who created a pop song using fractals, the听Cantor set and all things听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听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听was trying to figure out what he was doing,听and听realized听he was doing these patterns of threes against the patterns of fours," says Dr. Brown,听a听professor and chair听of the听Department of Mathematics and Statistics听at Dal.
"Berry听found it so cool听鈥� even though he didn't know what the mathematics听was听鈥� that he would do his duck walk and go across the stage because the mathematics听moved him emotionally!"
For Dr. Brown听鈥� an avid musician and songwriter himself 鈥� math is essential to the composition of both lyrics and music, yet isn't widely recognized as a critical ingredient in the听song-writing听process.
So, he and a colleague at the University of Texas听set out to compose a pop song听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
听
The result听is听,听a folk-rock song about losing one's identity in a relationship听that听runs听4:53听and is based on听mathematics听鈥� both musically and lyrically.听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.听Dr. Brown describes the听Cantor set听as听a very abstract thing known to mathematicians听in which听you take all the numbers between 0听and听1 and听cut out听the middle parts.听You're left with smaller intervals and for each of those smaller intervals you keep cutting out the middle thirds.听In听the end you're left with infinitely many points that survive the cuttings and yet they cover no area.
Underlying mathematical metaphor
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"This could be a metaphor for a relationship when someone loses more and more of themselves into a relationship," says听Dr. Brown, who sings and听plays听everything but the drums on听the song.
The song also uses words that reflect mathematical ideas. For example,听lightening is听another听example of a听fractal听and that word appears in the bridge听of the song.
"These听things are small references that came to us because we had the underlying mathematical metaphor and we knew the properties of it,听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 for example, is characterized bygroupings of three against background groupings of听four, creating听a听sense of听anticipation听for listeners attuned to the song's pattern.
Read also: John, Paul and Jason: How a Dal mathematician is helping sort out Beatles songwriting disputes (August 2018)
Most people are听comfortable with the idea that music 鈥� from classical to jazz to rock to pop and everything in between听鈥� is a form听of art.听Yet听when people wonder about the听tools听that听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
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Dr. Brown wants to make clear that one of those tools听may听be found听in the elegance of math.
But what about musicians? Do they think about math when writing songs?
"No!听But their brain is mathematical.听Any musician is mathematical even if听they hated math,听and I've gotten a lot of hate mail over the years when I say music is all about math.听People听think it takes all the creativity out听and that听mathematicsis simply like being an accountant. But听it's an integral part of the creative process!"