The secret chord (?)

In short, this is the story: do you remember the opening klang of A Hard Day's Night? (Beatles, 1964). If the answer is no, start the video below: it's the very first thing you hear.

The problem was that it was impossible to precisely determine the composition of this chord, and it was impossible to accurately reproduce it with two guitars (one 12-string) and a bass (the instrumentation on the recording). In practice, it seemed impossible to achieve that exact sound with the aforementioned instrumentation. Although the notes had been identified, their distribution among the instruments was impossible to account for.

In his thoughtful analysis, Alan Pollack, who analyzed the four's entire output, says:

I’ve seen better people than myself argue (and in public, no less) about the exact guitar voicing of this chord and I’ll stay out of that question for now (what a cop-out, Alan!), and merely state that its sonority is akin to a superimposition of the chords of d-minor, F-Major, and G-Major; i.e. it contains the notes D, F, A, C, and G – to my ears, only the B is missing. Even if you don’t know a thing about harmony or musical dictation, you can at least hear the G as a suspended fourth over the D on the bottom. Hullaballoo aside, this chord functions as a surrogate dominant (i.e. V) with respect to the chord on G which begins the first verse.
[A. Pollack – Notes on “A Hard Day’s Night”]

But finally, Dr. Jason I. Brown of Dalhousie University saw fit to perform an FFT analysis of the chord, listing all the frequencies it contains. The analysis allowed him to determine the exact composition of the chord, highlighting the fact that the notes involved could not have been produced with just two guitars and a bass (and there is no trace of overdubs, which were a bit problematic in 1964).

The final hypothesis, therefore, is that George Martin's piano is also present in the "klang," which, moreover, later doubles George's solo. You can see the chord in the figure (click here to enlarge). The 8th-note doublings of A, D, and G that you see in the G-string part are due to the 12th string. Here you can find Jason Brown's article (pdf) with all his deductions.

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