January 1, 2005

A Hard Day's Mystery

The opening chord to "A Hard Day's Night" is one of the most memorable in rock history. In The Complete Beatles Recording Sessions, author Mark Lewisohn quotes Beatles' producer George Martin as saying, "We knew it would open both the film and the soundtrack album, so we wanted a particularly strong and effective beginning. The strident guitar chord was the perfect match." But what exactly was that mysterious chord?

The two most common transcriptions are G, D, F, C, D, G (which appears on many Web sites) and the one given in The Beatles Complete Scores: G, D, G, C, D, G (George Harrison's 12-string), plus D, G, C, G (John Lennon), and D on bass (Paul McCartney). After 40 years, is there any way to tell whether either of these versions is correct?

A type of mathematics called Fourier Transforms can be used to reconstruct the original frequencies from a list of numbers, once the values have been calculated using software to analyze a digital recording of the sound. I selected a segment of approximately one second of the opening chord, and ran the Fourier Transform on the data. Then, I rounded each of the 48 loudest frequencies to their closest semitone, and these are the notes that comprise that marvelous chord (middle C is written as C4): A2, D3, D3, D3, D3, F3, F3, F3, G3, A3, C4, C4, D4, G4, A4, C5, D5, D5, D5, G5, G5, G5, B5, B5, C6, D6, E6, E6, E6, E6, F#6, G#6, A6, D7, D7, D7, D7, D7, D7, D7, E7, E7, F7, F7, G7, G7, G7, G7.

We see now why the most popular versions of the chord must be wrong: Each shows a low G2 being played, but this note is definitely not included in the frequency analysis. Examining the frequencies, I found that one D3 is louder than the others-which suggests it is a bass note played by McCartney-but it was impossible to match the other low notes to Harrison's 12-string, even taking into account the notes played on Lennon's 6-string.

Some music scholars and authors have previously suggested that a piano was included in the sonic layer, and Harrison allegedly offered differing versions of the guitar voicings himself in various interviews. But, how can we be sure that rock and roll's most famous guitar chord is part piano, and what the most likely guitar voicings were? With a bit more deductive work, I found the presence of the piano did indeed solve the frequency problem, and the voicings I deduced (along with likely positioning on the guitars) are shown in the diagram. The important point is that the piano is there because the math says it is. So, while the opening to A Hard Day's Night may no longer be the greatest guitar chord in rock and roll, the introduction's thrilling tonal layers still deliver one of rock's most transcendent chord voicings!

-Dr. Jason I. Brown, Professor of Mathematics and Computer Science at Dalhousie University in Halifax, Canada. Visit www.mathstat.dal.ca/~brown for additional details.  

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