Chaaaaaang!…“It’s been a hard day’s night, And I’ve been working like a dog”.  40 years of trying to figure out that first chaaaaaang and the mystery is finally solved not by a musician, but by a mathmetician.  Dr. Jason Brown used a mathematical calculation known as Fourier transform to solve the Beatles’ riddle.

This first chord that starts A Hard Day’s Night is one of the most recognizable and famous opening chords in rock & roll. It’s played by George Harrison on his 12 string Rickenbacker.

George played a 12-string Rickenbacker, John Lennon played his 6 string, Paul had his bass -- none of them quite fit what he found. He then realized what was missing -- the 5th Beatle. George Martin was also on the record, playing a piano in the opening chord, which accounted for the problematic frequencies.”

Here’s how the chord was actually played:

George Harrison was playing the following notes on his 12 string guitar: a2, a3, d3, d4, g3, g4, c4, and another c4; Paul McCartney played a d3 on his bass; producer George Martin was playing d3, f3, d5, g5, and e6 on the piano, while Lennon played a loud c5 on his six-string guitar.

Hello London!  Are you ready to solve an ordinary differential equation?!  Chaaaaaang!

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