Stop me if you’ve heard this one. Two statisticians walk into a conference and become fast friends thanks to their shared love of mathematics — and The Beatles.
"He had done some work previously applying something called Fourier analysis to figure out what the first chord was of 'A Hard Day’s Night,'" explained Harvard’s Mark Glickman, a senior lecturer in statistics.
The “he” is Dalhousie University math professor Jason Brown.
Brown, it turns out, has a knack for turning songs into data in all sorts of interesting ways.
"He'd been doing some subsequent work where he was trying to come up with some representations of Beatles songs using graphs," explained Glickman. "And it's not the type of graph that you'd typically see ... it's a mathematical representation."
A favorite debate among Beatles fans is 'who wrote which song, John Lennon or Paul McCartney?' There are any number of tunes in the Fab Four's catalog where that answer is still unclear, and Lennon and McCartney often had differing memories about who wrote what. As the two scientists engaged in friendly banter on the topic, Glickman began thinking about stylology — a statistical technique that’s been used for decades to determine probability of authorship of everything from sacred texts to Shakespeare’s plays. It’s essentially a complex way of spotting and counting how often certain words and phrases are used by an author.
"And that, in a way, is almost like a fingerprint of style," said Glickman.
The two scientists began to wonder if Brown's methods could allow them to treat individual notes in song melodies and individual chords in the backing music as words; and treat pairs of notes and pairs of chords as phrases. Could they then run an experiment, borrowing stylological techniques, to distinguish between Beatles songs written by John Lennon and those written by Paul McCartney?
So they tried. First, they looked for each writer’s fingerprint. They hand-coded and computer-analyzed 70 Beatles songs — or song fragments — that were known to have been written by either Lennon or McCartney.
When it came to melody lines, they found that Lennon tended to be limited in his range, while McCartney was more likely to take big leaps in pitch up and down the scale from note to note.
Glickman pointed out the moment in Eleanor Rigby, a McCartney-penned song where Paul sings, "Where do they all come from?"
"The 'Where do' is an octave jump," he said. "There are no John Lennon songs where there's an octave jump on the diatonic scale of the song."
When it came to chord progressions under the melody, they found that John had a predilection for moving from what’s called the tonic chord to the minor sixth. You can hear this in his song, "It’s Only Love." Conversely, they discovered a chord change that is very particular to Paul McCartney — the “fourth” to the "minor second," as McCartney does on “I’m Looking Through You.”
Next came the fun part. Armed with a fingerprint for each songwriter, Glickman and Brown applied their model to 17 songs, which were known only as collaborations, or for which Lennon and McCartney had conflicting memories.
Glickman said he always suspected the "Rubber Soul" track "The Word" was a Lennon tune, but the analysis skewed heavily in McCartney’s favor. And then there is "In My Life," a song Lennon said he wrote with a little input from McCartney, but McCartney remembers as one that he wrote to a lyric sheet from Lennon. So?
"Our model says it’s pretty likely that John wrote the song," said Glickman.
Of course — like any good statistician — Glickman was quick to point out the limits of the work. They aren’t taking into account plenty of variables, like lyrics, tempos, and instrumentation. Still, the team is already discussing how to refine their techniques for more complex analysis.
All they’ll need is love. Well, love and probably some more time and computing power.