The Beatles’ Magical Mystery Chord

On the 16th April 1964 the Beatles, George Harrison, Paul McCartney, John Lennon and Ringo Starr, were on the cusp between stardom and mega-stardom. Groundbreaking albums, hit films, cartoons, royal honours, Sgt. Pepper, Indian mysticism, and an acrimonious break up all lay in their future as did the murder of Lennon and attempted murder of Harrison by separate mentally disturbed fans. That was all to come. Their task that night was to record an impressive opening track for their forthcoming debut film and the album to accompany it. Their producer, George Martin, wanted something spectacular: ‘We were looking for something big to open it with, an introduction. It needed a strong chord, a dramatic thing’ (p487 of Dominic Pedler, The Songwriting Secrets of the Beatles, Omnibus Press, 2003). Those present in the Abbey Road studio to record Lennon’s song A Hard Day’s Night could not have imagined that 50 years later the events would still be analyzed and dissected. Particularly since the focus of the analysis is almost not a piece of music, it’s a short sound, less than 3 seconds long, a crashing, ringing, chiming sound that has caused arguments and discussions between Beatles’ fans and musicologists ever since it was recorded. The noise is impossible to describe accurately in words – the famous quote ‘writing about music is like dancing about architecture’ comes to mind. The sound can be heard here: http://www.kevinhouston.net/blog/wp-content/uploads/2014/12/original-chord3.wav The central question is simple: What is it? That is, what notes are played and who is playing them? Many versions have been suggested. In his massive Beatles book, The Songwriting Secrets of the Beatles, Dominic Pedler collects twenty one educated guesses from various sources and devotes over 40 pages to discussion, including his own theory. It is not difficult to produce a chord that is close – strumming a guitar without fretting produces a similar sound. It’s close. But close is not exact, right? So, what is it really? In 2004 a mathematician claimed to have discovered this musical holy grail by applying mathematics. Once and for all, the riddle was solved because, after all, mathematics is not wrong and you can’t beat the scientists with their fancy abstract toys. Except there was a problem. He got it horribly wrong. Here, for the honour of all mathematicians, I would like to put the record straight — or at least straighter. The mathematical tale of the Beatles’ Magical Mystery Chord is a tale of 18th century mathematicians, the study of heat, Karaoke tricks and a measure of luck. The quest begins I am a mathematics lecturer who enjoys promoting mathematics to school children and the general public. My introduction to the mystery of the chord came not from a love of the Beatles music but a desire to show off in front of my parents. My mathematics promotion involves giving talks all over the country but as I live in the north of England and my parents live in a secluded part of the north east of Scotland, they would under normal circumstances be unable to see their second son on a stage explaining mathematics. Back in 2011 I heard that the British Science Festival would be held the following year in Aberdeen which is close to where my parents live. The festival is held in a different city in the UK each year and aims to engage the general public in science. Hundreds of events take place over a week in September with debates, demonstrations and hands-on exhibitions at the local university as well as theatres and even, like maths busking, in the street. (Maths busking is as it sounds. Mathematicians go out in the street and do mathematics to entertain passers-by. I’ve tried it and it is hard. See my report here.) All I had to do was offer to give a talk, get accepted and I would get my chance to impress...