It’s the most famous chord in rock 'n' roll, an instantly recognizable twang rolling through the open strings on George Harrison’s 12-string Rickenbacker. It evokes a Pavlovian response from music fans as they sing along to the refrain that follows:
It’s been a hard day’s night
And I’ve been working like a dog
The opening chord to A Hard Day’s Night is also famous because for 40 years, no one quite knew exactly what chord Harrison was playing. Musicians, scholars and amateur guitar players alike had all come up with their own theories, but it took a Dalhousie mathematician to figure out the exact formula.
“I started playing guitar because I heard a Beatles record—that was it for my piano lessons,” says Jason Brown of Dalhousie’s Department of Mathematics and Statistics with a good laugh. “I had tried to play the first chord of the song many takes over the years. It sounds outlandish that someone could create a mystery around a chord from a time where artists used such simple recording techniques. It’s quite remarkable.”
Four years ago, inspired by reading news coverage about the song’s 40th anniversary, Dr. Brown decided to try and see if he could apply a mathematical calculation known as Fourier transform to solve the Beatles’ riddle. The process allowed him to decompose the sound into its original frequencies using computer software and parse out which notes were on the record.
It worked, up until a point: the frequencies he found didn’t match the known instrumentation on the song. “George played a 12-string Rickenbacker, Lennon had his six string, Paul had his bass…none of them quite fit what I found,” he explains. “Then the solution hit me: it wasn’t just those instruments. There was a piano in there as well, and that accounted for the problematic frequencies.”
Dr. Brown deduces that another George—George Martin, the Beatles producer—also played on the chord, adding a piano chord that included an F note impossible to play with the other notes on the guitar. The resulting chord was completely different than anything found in the literature about the song to date, which is one reason why Dr. Brown’s findings garnered international attention. He laughs that he may be the only mathematician ever to be published in Guitar Player magazine.
“Music and math are not really that far apart,” he says. “They’ve found that children that listen to music do better at math, because math and music both use the brain in similar ways. The best music is analytical and pattern-filled and mathematics has a lot of aesthetics to it. They complement each other well.”
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