This first chord that starts A Hard Day’s Night is one of the most recognizable and famous opening chords in rock & roll. It’s played by George Harrison on his 12 string Rickenbacker.

The other reason that it’s famous is because for 40 years nobody knew for sure what it was. Many guitar players have tried in vain to recreate the sound but have usually failed miserably.

Well, someone has figured it out definitively – not a musician, but a Dalhousie mathematician.

Four years ago, Jason Brown was inspired by reading news coverage about the song’s 40th anniversary – so much so that he decided to try and see if he could apply a mathematical calculation known as Fourier transform to solve the Beatles’ riddle. The process allowed him to break the sound into distinct frequencies using computer software to find out exactly which notes were on the record.

What he found was interesting: the frequencies he found didn’t match theinstruments on the song. George played a 12-string Rickenbacker, John Lennon played his 6 string, Paul had his bass – none of them quite fit what he found. He then realized what was missing – the 5th Beatle. George Martin was also on the record, playing a piano in the opening chord, which accounted for the problematic frequencies.”

“I started playing guitar because I heard a Beatles record—that was it for my piano lessons,” says Brown. “I had tried to play the first chord of the song many takes over the years. It sounds outlandish that someone could create a mystery around a chord from a time where artists used such simple recording techniques. It’s quite remarkable.”

The Beatles producer added 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 songbooks and scores for the song, 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.

The original PDF published by Dr. Brown is online here.

Part of the problem is that a lot of people didn’t pay attention in their high-school science classes — they never learned what a scientific theory is.  Read how Brian Denning explains the concept of a theory from his Skeptoid essays and podcast:

Evolution is just a theory, not a fact. [argues the creationist]  This is an easily digestible sound bite intended to show that evolution is just an unproven hypothesis, like any other, and thus should not be taught in schools as if it were fact. Actually, evolution is both a theory and a fact. A fact is something we observe in the world, and a theory is our best explanation for it. Stephen Jay Gould famously addressed this argument by pointing out that the fact of gravity is that things fall, and our theory of gravity began with Isaac Newton and was later replaced by Einstein’s improved theory. The current state of our theory to explain gravity does not affect the fact that things fall. Similarly, Darwin’s original theory of evolution was highly incomplete and had plenty of errors. Today’s theory is still incomplete but it’s a thousand times better than it was in Darwin’s day. But the state of our explanation does not affect the observed fact that species evolve over time.

You, dear reader, are one in a thousand.

So begins an article at space.com

The fact that you’re confronting this column on a web site devoted to space science and astronomy makes you roughly as rare as technetium.  Despite the fact that astronomy is one of the two most popular science subjects in American schools (the other is biology), it’s really not that popular.

The overwhelming majority of the citizenry has other interests, and looming large among them are the peccadilloes and personal intrigues of the rich and famous.  Consider the contrast: in the past week the Space Telescope Science Institute released a startlingly detailed photo of a distant cluster of galaxies, a picture that gives even the non-expert a good idea of the structure of these, the largest entities in the universe.  The photo of cluster Abell S0740–an image that would have bedazed every previous generation of humans–probably didn’t even make it to the front section of your local newspaper.

However, what did garner front-page ink last week, not to mention huge dollops of chatter on talk radio, was the unexpected death of Anna Nicole Smith, a former Playboy Playmate and reality TV star.

I’m amazed at not just the apathy toward science, but the outright antagonism toward it.  In past centuries, the population thought the sun revolved around the earth.  We all accept now that the earth revolves around the sun, but it took drastic measures to convince the population of that fact.  Other significant discoveries have also been initially rejected by the people, then accepted.  Why then, especially in the United States do we still have debates about teaching evolution in science classes?  Why do we respect a blastocyst (a group of 15-60 cells) as more “sacred” than a soldier’s life?  Why do people still deny (vehemently!!!) that global climate change is a reality?  A couple of generations ago, the US was proud to send the “best and brightest” into leadership positions.  Now, with notable exceptions, we seem to be sending the “mediocre and beholden” to leadership.  (We can’t blame them, the people we elect are simply reflections of ourselves.)  Worse, the general population seems to be losing interest in maintaining the US’s technical and visionary leadership of the world.  Who cares???  Just gimmie my National Enquirer!  How do we reconcile a written “Thou shalt not kill.” with a whispered “Go to war in Iraq”?  How do abortion clinic bombers justify killing?  Aren’t they “pro-life?”

I’m a firm believer in education — “You shall know the truth and the truth shall set you free.”  Please, dear reader, don’t simply follow the crowd; inform yourself!  If that information along with a rational evaluation lead to you follow the crowd, then fine.  Keep an open mind! Read!  Discuss!  Debate!  Choose Wisely!  Every now and then, visit Barnes & Noble and browse the books on the shelves.  You might find interesting discoveries.  Every now and then, read a book that is counter to your own beliefs.  You might find surprising common ground.  Above all, try to lift yourself out of ignorance — and bring a few others along with you.

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