Take that, sweet mystery of rock 'n roll. Math has just solved the Holy Grail of Rock: the mysterious "A Hard Day's Night" chord.
Dalhousie University math professor Jason Brown applied Fourier transform to solve the Beatles' riddle: there was a mystery piano!
... 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.”