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A Mathematician Solves A Mystery in The Beatles’ Music

McCartney should know!


It certainly says a lot about the genius of the Beatles that there is still a mystery about their music, more than 50 years after it was composed. I had no idea you could tell so much from a note and I certainly had no clue there was still a mystery surrounding the opening chord of their famous song ‘A Hard Day’s Night’, made super famous because of the film of the same title. This is actually more than a note, it’s a complex and layered sound and until now, nobody knew how it was made? I had never really paid attention to this opening 2 seconds of the famous song, I honestly thought it was made by a guitar chord, but I couldn’t have been more wrong.

The mystery was solved by Jason Brown, a professor of mathematics at Dalhousie University in Canada, and also musician. He talked to ABC Australia admitting ‘It’s hard to tell exactly what is being played,’ and further explaining the physics behind his discovery: ‘When a string is plucked, you not only get the main frequency, but you get harmonics, which are higher multiples of that original frequency.’

But why was this still a mystery? After all, Paul McCartney or another Beatle should know? According to ABC, someone tried to ask George Harrison in 2001, but he could only vaguely remember his own part. ‘In the absence of having anyone there transcribe what actually was being played, it is a mystery’, said Dr Brown.

Since the song ‘A Hard Day’s Night was recorded in one day, during a chaotic and busy time for the Fab Four, nobody could remember exactly how this was recorded. Brown had also doubts regarding the original source tapes because ‘the drums, bass and two guitars were all recorded onto the same track’. So he decided to use a very scientific approach, and reading about math and sound, he decided to solve the mystery: ‘I thought of combining the music with the mathematics, and whether there’d be a scientific way to decide how the chord was being played — as opposed to just using your ears.’

In particular, a chapter in the book he was reading taught him how to break a musical chord into its component parts. ‘I could decompose the opening chord into a bunch of these fundamental notes. I got in the order of 30,000 of them,’ he explained, ‘I realized that the notes that were actually being played in the chord would be amongst the loudest ones,… This allowed me to start making some mathematical deductions from the data that I got.’

He matched the loud frequencies to the corresponding instruments but there was still ‘things missing’, the ‘ghost notes’, and at the end, there were frequencies for a certain F note that couldn’t be attributed to any of the guitars.

‘Later on in the song, you can clearly hear a piano doubling George Harrison’s lead guitar solo. So I thought, maybe there is a piano in the song,’ he continued, ‘A piano typically has three strings tuned identically corresponding to each note, and a hammer hits them. So perhaps those three frequencies could come from a single note on the piano.’ Finally Brown concluded that the missing F frequencies ‘came from a single note played on a mid-sized grand piano.’

‘It was extraordinarily exciting. The chord was a mystery for such a long time, and people still talk about it,’ he said.

Listen to this first note, the first 2 seconds… can you tell there is a piano in the mix? I couldn’t and still can’t!

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