Advanced Mathematics Applied to “A Hard Day’s Night”

Simplified Spectrum from Fourier Analysis

After years of trying to figure out the first chord of “A Hard Day’s Night,” Jason Brown of Dalhousie’s Department of Mathematics decided to throw a little math at the problem and ran a Fourier analysis. You remember from your mechanical vibrations, mechanical controls, and digital signal processing courses that a Fourier analysis can be used to translate a signal from the time domain to the frequency domain. It’s basically a really accurate EQ.

It worked, to a point: the frequencies he found didn’t match the known instrumentation on the song. “George played a 12-string Rickenbacker, Lennon had his six string, Paul had his bass…none of them quite fit what I found,” he explains. “Then the solution hit me: it wasn’t just those instruments. There was a piano in there as well, and that accounted for the problematic frequencies.”

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Dr. Brown deduces that another George—George Martin, the Beatles producer—also played on the chord, adding a piano chord that included an F note impossible to play with the other notes on the guitar. The resulting chord was completely different than anything found in the literature about the song to date, which is one reason why Dr. Brown’s findings garnered international attention. He laughs that he may be the only mathematician ever to be published in Guitar Player magazine.

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16 November 2008 / mathematics, music, science / View Comments