Do the Math, Get an F -- Note, That Is...

For a long time (about 40 years, in fact), nobody but those involved really knew just what that great opening chord was in the Beatles' "A Hard Day's Night." They could duplicate the Beatles' instruments and read the written sheet music but could never make it sound like it did when John, Paul, George and Ringo kicked off their story of a working fellow who felt very rewarded by the time he was able to spend with his lady love. Even when different Beatles would say what they played or film of the song played live was analyzed, the results didn't seem to match the sound from the record.

Leave it to a mathematician to figure it out. Jason Brown, a professor of mathematics at Dalhousie University in Nova Scotia, put the chord through what's called "Fourier analysis" in order to find what musical notes are being played. Fourier analysis, of course, shows how mathematical functions may be represented by the sums of simpler trigonometric functions (didn't you know that?)

What that means is that a mathematician doing a Fourier decomposition of a math function breaks it down into simpler functions that can be added together to make the function he or she had to start with. At least one kind of Fourier analysis involves something called a "sinusoid," which sounds like the kind of thing in a SyFy Original Movie somewhere and makes me think that math got a lot more interesting after I stopped being able to understand it. I would imagine that the sinusoids are either:

• A form of viral infection spread by aliens to disorient our communications in prepation for their invasion: "Do, Mibter Prebident! You bust bissen to be! I saib de abiens are inbading!"
• Elite, deadly warriors enslaved by the master villain who can devastate anything in their path: "Let's see how the humans cope with the Sneeze of Devastation! Attack, my sinusoids!"
• A heretofore undiscovered hibernating species of dinosaur awakened by an unscrupulous billionaire whose company was illegally fracking to obtain natural gas from a pristine wildlife reserve. Although their rampage will devastate the fracking rig and cause many deaths -- including, of course, the unscrupulous billionaire sometime during the last few minutes of the movie -- a handsome, unconventional scientist and a beautiful park ranger (or vice-versa) will discover a way to corral them and prevent the all-out bombing assault ordered by the closed-minded military leader. "No, general! You don't have to destroy them! We can contain them now that we know they eat through their noses!"

Actually, "sinusoids" are sine wave functions. You see them as the wavy lines on oscilloscopes used as props in some of those very SyFy Original Movies, in fact.

Anyway, Dr. Brown ran his Fourier analysis of the sounds in the chord, since music and mathematics are closely linked, and determined that another George, producer George Martin, had played a certain chord on the piano that added an "F" note to the mix, which created the unique opening sound of "A Hard Day's Night."

Many of the comments on the story suggest Dr. Brown is way off and that everyone has always known what the chord is. Rumors that those people have since disappeared, with the only known clue a suspicious sniffle heard just before they vanished, have yet to be disproven.