Elaine has pointed me to mathematician Jason I. Brown's analysis of the opening chord of The Beatles' "A Hard Day's Night":
"Mathematics, Physics, and 'A Hard Day's Night'" (.pdf download, 92KB)
The mysteries of this chord remind me of André Previn's observation re: Duke Ellington:
"Stan Kenton can stand in front of a thousand fiddles and a thousand brass and make a dramatic gesture and every studio arranger can nod his head and say, 'Oh, yes, that's done like this.' But Duke merely lifts his finger, three horns make a sound, and I don't know what it is!"Previn must have been thinking of "Mood Indigo."
[Quoted in Mimi Clar's "The Style of Duke Ellington" (1959), in The Duke Ellington Reader, ed. Mark Tucker (New York: Oxford University Press, 1993).]
YouTube bonus links
The Beatles, "A Hard Day's Night"
Duke Ellington, "Mood Indigo"
Peter Sellers, "A Hard Day's Night"