According to this article a mathematician uncovered the secret to the opening chord on Hard Day’s Night.
Dr. Brown deduces that another George—George Martin, the Beatles producer—also 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’s findings garnered international attention. He laughs that he may be the only mathematician ever to be published in Guitar Player magazine.
Apparently the Science Daily editors did not check out the Wikipedia entry for Hard Day's Night, because - WAIT – someone else had pointed to George Martin (everyone’s favorite 5th Beatle) before the Mathematician in the Science Daily article. Hmmm:
Dominic Pedler has also provided an interpretation of the famous chord, with the Beatles and George Martin playing the following:
• George Harrison: Fadd9 in 1st position on Rickenbacker 360/12 12-string electric guitar
• John Lennon: Fadd9 in 1st position on a Gibson J-160E 6-string acoustic guitar
• Paul McCartney: high D played on the D-string, 12th fret on Hofner 500/1 electric bass
• George Martin: D2-G2-D3 played on a Steinway Grand Piano
• Ringo Starr: Subtle snare drum and ride cymbal
This gives the notes: G-B-D-F-A-C (the B is a harmonic). One of the interesting things about this chord (as described by Pedler) is how McCartney's high bass note reverberates inside the soundbox of Lennon's acoustic guitar and begins to be picked up on Lennon's microphone or pick-up during the sounding of the chord. This gives the chord its special "wavy" and unstable quality. Pedler describes the effect as a "virtual pull-off".
Yikes – at least you can’t accuse the Beatles of being one of those rock-bands that only knows three chords.