A mathematician at Dalhousie University has used an operation called a Fourier transform to pick apart the opening chord to the Beatles' "A Hard Day's Night." It's kind of a big deal because non-Beatles musicians have been trying for decades to figure out the chord, which happens to be impossible to play on a guitar. (According to the Chicago Independent Radio Project blog, Harrison let the secret out years ago, but I guess it's possible to be a huge Beatles fan and still not have heard that news.)
Turns out that producer George Martin snuck in a piano underneath the guitars, which accounts for the chord's phantom F note. I don't know if it's just my imagination or if it's an effect like how once you see the arrow in the FedEx logo you can't unsee it, but I've listened to that opening chord a dozen times today and I swear I can hear the piano clear as day now.
To give you an idea of the extent to which people have obsessed over this, here's an excerpt from The Beatles, a theory-intensive book by New York Times critic Allan Kozinn, describing just that one chord:
"A Hard Day's Night," the title track of both the album and the film, begins with a perfect attention-grabbing flourish, a stark, bright-edged, slightly dissonant guitar chord that lingers defiantly for a few seconds before the song begins. It took several tries to find the right chord, and the right colorations: they tried it distorted and plain, more dissonant and less, and even with tremolo. In the end, Lennon and Harrison settled on an intriguingly ambiguous configuration. Harrison, playing a twelve-string guitar, and Lennon playing a six-string standard instrument, played different voicings of a G suspended fourth chord--G major with an added C--while McCartney played a D on his bass. The bright, open sound they settled on was perfect for the gesture.