Occasional Observations

I love it when I find an article that brings together multiple of my favorite topics.  So when I saw this article on the Noise Addicts blog about a mathematician who used numerical analysis to finally solve a problem plagueing the music world about a Beatles song;  well, I just had to publish it!

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.

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Why is it that only evolution is under attack?  There are other scientific theories…..

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.
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