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| Math prof Jason Brown and his Ibanez guitar.(Danny Abriel Photo) |
It鈥檚 the most famous chord in rock聽'n' roll, an instantly recognizable twang rolling through the open strings on George Harrison鈥檚 12-string Rickenbacker. It evokes a Pavlovian response from music fans as they sing along to the refrain that follows:
It鈥檚 been a hard day鈥檚 night
And I鈥檝e been working like a dog
The opening chord to A Hard Day鈥檚 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 黑料吃瓜网mathematician to figure out the exact formula.
鈥淚 started playing guitar because I heard a Beatles record鈥攖hat was it for my piano lessons,鈥� says Jason Brown of Dalhousie鈥檚 Department of Mathematics and Statistics with a good laugh.聽 鈥淚 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鈥檚 quite remarkable.鈥�
Four years ago, inspired by reading news coverage about the song鈥檚 40th anniversary, Dr. Brown decided to try and see if he could apply a mathematical calculation known as Fourier transform to solve the Beatles鈥� 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鈥檛 match the known instrumentation on the song. 鈥淕eorge played a 12-string Rickenbacker, Lennon had his six string, Paul had his bass鈥one of them quite fit what I found,鈥� he explains. 鈥淭hen the solution hit me: it wasn鈥檛 just those instruments. There was a piano in there as well, and that accounted for the problematic frequencies.鈥�
Dr. Brown deduces that another George鈥擥eorge Martin, the Beatles producer鈥攁lso 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鈥檚 findings garnered international attention. He laughs that he may be the only mathematician ever to be published in Guitar Player magazine.
鈥淢usic and math are not really that far apart,鈥� he says. 鈥淭hey鈥檝e 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.鈥�