"Hard Day's Night" Mystery cchord solved using math

[Dave Monroe]

Chaaaaaang!……
"It's been a hard day's night
And I've been working like a dog"

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.

 "Music and math are not really that far apart," he says. "They've
found that children that listen to music do better at math, because
math and music both use the brain in similar ways. The best music is
analytical and pattern-filled and mathematics has a lot of aesthetics
to it. They complement each other well." (comic courtesy of xkcd.com)

So how was the chord played you ask?  George Harrison was playing the
following notes on his 12 string guitar: a2, a3, d3, d4, g3, g4, c4,
and another c4; Paul McCartney played a d3 on his bass; producer
George Martin was playing d3, f3, d5, g5, and e6 on the piano, while
Lennon played a loud c5 on his six-string guitar.

http://www.noiseaddicts.com/2008/11/beatles-hard-days-night-mystery-chord-solved/

Jason I. Brown, "Mathematics, Physics and A Hard Day's Night"

http://www.mscs.dal.ca/~brown/n-oct04-harddayjib.pdf

Cf. ...

   ... "you'll think I'm crazy, Oed. But I can do the same thing in
reverse. Listen to anything and take it apart again. Spectrum
analysis, in my head. I can break down chords, and timbres, and words
too into all the basic frequencies and harmonics, with all their
different loudnesses, and listen to them, each pure tone, but all at
once."
   "How can you do that?"
   "It's like I have a separate channel for each one," Mucho said,
excited, "and if I need more I just expand. Add on what I need. I
don't know how it works, but lately I can do it with people talking
too. Say 'rich, chocolaty goodness.'"
   "Rich, chocolaty, goodness," said Oedipa. "Yes," said Mucho, and
fell silent. "Well, what?" Oedipa asked after a couple minutes, with
an edge to her voice.
   "I noticed it the other night hearing Rabbit do a commercial. No
matter who's talking, the different power spectra are the same, give
or take a small percentage. So you and Rabbit have something in common
now. More than that. Everybody who says the same words is the same
person if the spectra are the same only they happen differently in
time, you dig? But the time is arbitrary. You pick your zero point
anywhere you want, that way you can shuffle each person's time line
sideways till they all coincide. Then you'd have this big, God, maybe
a couple hundred million chorus saying 'rich, chocolaty goodness'
together, and it would all be the same voice."
   "Mucho," she said, impatient but also flirting with a wild
suspicion. "Is this what Punch means when he says you're coming on
like a whole roomful of people?" "That's what I am," said Mucho,
"right. Everybody is." He gazed at her, perhaps having had his vision
of consensus as others do orgasms, face now smooth, amiable, at peace.
   She didn't know him. Panic started to climb out of a dark region in
her head. "Whenever I put the headset on now," he'd continued, "I
really do understand what I find there. When those kids sing about
'She loves you,' yeah well, you know, she does, she's any number of
people, all over the world, back through time, different colors,
sizes, ages, shapes, distances from death, but she loves. And the
'you' is everybody. And herself. Oedipa, the human voice, you know,
it's a flipping miracle." His eyes brimming, reflecting the color of
beer.
   "Baby," she said, helpless, knowing of nothing she could do for
this, and afraid for him.... (Lot 49, p. 116-7)

http://www.innternet.de/~peter.patti/thomaspynchon-thecryingoflot49.htm

   "Suddenly what sounded like a whole kennelful of dogs began to bark
furiously.  'Pugnax,' explained Darby, noting Chick's alarmed
expression.
   "'Him and what else?'
   "'Just ol' Pugnax.  One of his many talents. Guess we'd better go
and have a look.'" (AtD, Pt. I, Ch. 2, p. 17)

http://waste.org/mail/?list=pynchon-l&month=0701&msg=114457