Like pals Paul McCartney or John Lennon, Harvard statistician Mark Glickman and felllow researcher and Beatles fan Jason Brown came together to solve a question many loyal listeners have asked over the years: who wrote the melody to one of the band's biggest hits?
While the famous duo typically wrote and produced tunes together, Glickman said some of their popular songs, particularly "In My Life," have disputed authorship. So, to prove who most likely influenced the songs, Glickman and Brown, a mathematics professor at Dalhousie University in Nova Scotia, turned to an algorithm.
"We wondered whether you could use data analysis techniques to try to figure out what was going on in the song to distinguish whether it was by one or the other," Glickman said in an online statement Friday.
The pair recruited Harvard statistics student Ryan Song to assist them in "decomposing" every Beatles song from 1962 to 1966 into five categories: frequencies of common played chords, melodic notes, chord transitions, frequencies of continuous melodic note pairs and whether melodic sequences were considered "ups," "downs" or "the same."
In total, they divided Beatles songs into 149 "constituent components."
"Think of decomposing a color into its constituent components of red, green and blue with different weights attached," Glickman explained.
The group came up with the various components based on what they already knew about Lennon and McCartney's writing styles. Lennon generally stuck to one pitch, while McCartney's varied.
"Consider the Lennon song, 'Help!'" Glickman said. "It basically goes, 'When I was younger, so much younger than today,' where the pitch doesn't change very much. It stays at the same note repeatedly, and only changes in short steps. Whereas with Paul McCartney, you take a song like 'Michelle,' and it goes, 'Michelle, ma belle. Sont les mots qui vont très bien ensemble.' In terms of pitch, it's all over the place."
The researchers then created an additional three-step tool to create an algorithm to determine the probability Lennon wrote a song over McCartney, or vice-versa.
They studied the frequencies of the 149 musical components, used the Bayes' theorem — a statistics law that determines the likelihood of an event based on previous knowledge — to examine Lennon or McCartney-labeled songs and then the "results of [the] model were applied to Lennon-McCartney songs and song portions in which the authorship was disputed," a news release detailing the project states.
According to their calculations, the probability McCartney authored the 1965 hit "In My Life" — a song he has long claimed to have written, despite Lennon's name being attributed to it — was only .018.
"Those were the words John wrote, and I wrote the tune to it. That was a great one," McCartney told broadcaster Paul Gambaccini a decade after it was released, according to The Telegraph.
The algorithm, however, suggests McCartney "misremembers."
While the group is confident their model is accurate, Glickman said he's not trying to paint McCartney as a liar.
"We don't claim that we think Paul was mistaken - rather, our model merely suggests that the patterns of musical idioms in 'In My Life' matches more with Lennon's writing style, relative to the patterns we recorded," Glickman told Business Insider.