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No Longer a Hard Day's Night Puzzle

For some, it is the most famous chord in rock 'n' roll, an instantly recognizable twang rolling through the open strings on George Harrison’s 12-string Rickenbacker. Then, this refrain follows:

It’s been a hard day’s night
And I’ve been working like a dog

For 40 years, no one has been able to determine the exact chord being played by Harrison. Though musicians, scholars, and fans all had their theories, Jason Brown, a Dalhousie University mathematician, was the first to figure out the exact formula using mathematics.


Inspired by news about the song’s 40th anniversary, Brown tried to use Fourier transforms to solve the Beatles’ riddle. Essentially, he would use computer software to decompose the sound into its original frequencies, then parse out and identify the desired notes.

But, he had only partial success: the frequencies found did not match the song's instrumentation. Brown wrote: “George played a 12-string Rickenbacker, Lennon had his six string, Paul had his bass…none of them quite fit what I found...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.”

The final conclusion: George Martin, the Beatles producer, played a a piano chord that included an F note impossible to play with the other notes on the guitar. The resulting chord was differed significantly from anything known about the song. As his resolution of the puzzle brought international fame, Brown merely laughs and claims "he may be the only mathematician ever to be published in Guitar Player magazine.

Brown adds: “Music and math are not really that far apart. 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.”

Source: ScienceDaily, October 31, 2008