The opening chord from the Beatles’ tune A Hard Days Night has been infamously difficult to transcribe by fans wanting to recreate the sound. I have a book of complete Beatles transcriptions that lists this chord as a Gsus4/D. In 2008 a mathematician, Jason Brown, used a Fourier analysis to accurately transcribe the opening chord.
What he found was interesting: the frequencies he found didn’t match the instruments on the song. George played a 12-string Rickenbacker, John Lennon played his 6 string, Paul had his bass – none of them quite fit what he found. He then realized what was missing – the 5th Beatle. George Martin was also on the record, playing a piano in the opening chord, which accounted for the problematic frequencies.
What did he find the chord to be?
George Harrison was playing the following notes on his 12 string guitar: a2, a3, d3, d4, g3, g4, c4, and another c4; Paul McCartney played a d3 on his bass; producer George Martin was playing d3, f3, d5, g5, and e6 on the piano, while Lennon played a loud c5 on his six-string guitar.
For fun I took the pitches in this chord and used them to compose a melody and then wrote a short fugue using that melody as a subject (because composing fugues are what I do for fun). It’s in the style of Hindemith, not a baroque style fugue, so I had some fun with dissonance. Here’s a MIDI realization of it. Listen for the Beatles quote near the end.