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.
A hard Days Night
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.”
The Beatles
“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)
Hard Days Night Chord
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.
Here is a PDF of Jason’s findings, and here’s a prize you can give someone for getting it right 
Here is a really good discussion of the chord, what people thought it was, and what it really is. Its a great article and a very interesting read.
Someone has also figured out the mystery behind Stevie Wonder’s Clavinet parts on Superstition. Check it out.
36 Comments Received
November 8th, 2008 @12:26 pm
Nice use of the FFT - and kudos for your functional OCD.
November 8th, 2008 @12:50 pm
Great! I was reading about famous chords in Wikipedia. There’s the “Hendrix” “Electra”, “So What” and other chords that are important. This one sounds too complicated to be in the same set!
November 8th, 2008 @1:11 pm
Ummm George Harrison himself said he plays an Fadd9 on his 12-string
That’s f3, f4, a3, a4, c3, c4, g3, and g4.
November 8th, 2008 @1:20 pm
sorry all except the first two f’s should be 4s and 5s.
And not only must Harrison be a liar, he also Harrison must have a really strangely tuned guitar to play what this mathematician apparently figured out with his computer.
November 8th, 2008 @6:47 pm
The FT generally has equally spaced bin-sizes. If you are interested in musical notes, then you just shift the poles on the unit circle to be logarithmically placed, they are linearly placed usually, and line one bin up with A=440 Hz, based on your sample rate. Then, you have bins centered on the standard notes… You can then subtract the known harmonics from the lowest notes in proportion to the instrument type and ID the rest… There is more to do, but you get the drift… Very easy from the definition of the FT and knowledge of what it really is…
November 8th, 2008 @9:27 pm
I think I could have told them it was a piano, but as for finding the notes to be played, I have no clue. There is a hint of that piano hammer “hit” and vibration that a guitar doesn’t make.
I’m not a trained musician, but have noticed that I can pick up fairly obvious things in music that trained musicians can’t. I have seen musicians say there is no similarity between songs because it’s in the wrong chord, or key or whatever. It’s either too high or too low, but my ear and several other untrained ears can pick up a similarity. It seems that a lot of musicians get hung up in notes, chords, etc. and lose the ability to see the forest for the trees.
They would probably say “Well that note can’t be made on a 12 string guitar… what is it?, they only had a certain number of instruments in there.” Give the song to a lay person and they can just say it “sounds like” a piano.
November 8th, 2008 @10:09 pm
“Music and math are not really that far apart,”…….
They are even closer than that! Music is the language of maths, everything in Music is based on numbers…
November 8th, 2008 @10:21 pm
Steinberger has a guitar which with the tremolo bar can shift all in tune the key of the chord up and down I just saw.
BYTE once had a BASIC “pseudo FT” program I used as my boss had taken soil resistivity readings down in Florida, perpendicular to the shore, but had moved the four electrodes in the ground in the wrong order consistently. So I was able to take the pattern of readings and turn them from hills and valleys into a trend which fit with the underlying geology, more moisture more conductivity or “susceptibility” of electrical current and no anomaly.
November 8th, 2008 @10:55 pm
Very cool that the chord A Hard Day’s Night finally has been successfully
reproduced. Never expected mathematics
would be the tool used to solve it.
thanks from tony
November 9th, 2008 @12:31 am
It’s such a rich sound. Whenever I’m playing the CD in my car and the last song ends, it loops and the beginning always catches me off guard and scares me a little.
November 9th, 2008 @3:32 am
So no one has ever realised before that there was a piano in it? I can’t believe it. And then I seriously doubt Lennon played a single note. I really don’t think so.
November 9th, 2008 @8:58 am
It’s a Dmin7 chord with a 9 and 11 tensions! It would be a way “weirder” chord is George Martin didn’t play that F. D9sus4
November 9th, 2008 @12:53 pm
i’m sure i’m not alone in asking,what the hell is ” a2, a3, d3, d4, g3, g4, c4, and another c4 “….come on…i’ve been playing for 30 years and don’t know what this mans…more over i’m dead positive the freakin beatles don’t know what it means either…how bout some HELP !!!
November 9th, 2008 @4:33 pm
Wayne - The link to the PDF at the bottom of the article answers your questions.
November 9th, 2008 @5:19 pm
A D11 chord played on a 12 string (Rickenbacker). I knew it when I was 15 (I’m 52 now).
November 10th, 2008 @2:41 am
OMG…it’s Charlie Epps from Numb3rs for guitar players!
November 10th, 2008 @8:42 am
Mathematics - language of the universe, core of everything…including music now.
November 10th, 2008 @9:55 am
hahahahahahahahahahahahaha wayne. oh my god, seriously.
November 10th, 2008 @11:43 am
I’d say I definitively played the right chord when I was 16 in 1967 when I was figuring everything out. Yes, the chord is elusive, but I think I had it “sussed”. It’s the G in the left hand of the piano that makes it sound like more of a polychord. Treated as a Dominant V chord, where D would be the bass note, it’s a D7Sus.4. With a G in the bass, the chord becomes a G6Sus.4.
The Sus.4 needs to be resolved whether you look at it as a I chord or a V chord. If Lennon is hitting a hard C,
(which I don’t believe to be the case.
I agree he’s not present, and it sound like Paul hits a D and they slowly raise the volume of his note), it just emphasizes the Suspension. And on the ending the D7Sus.4 is resolved to Minor7 on George’s riff. Great stuff!
November 10th, 2008 @1:21 pm
If you watch live clips you’ll see Paul playing a G on the bass on the third string & John an F9 chord in the first position. I haven’t seen any clips where you can see George’s chord.
November 10th, 2008 @4:10 pm
I think its wonderful that your mathematical skills can dissect such an iconic sound of our generation! The instrumentation (including credit to our beloved 5th Beatle) is spelled out in BEATLESONGS by William J. Dowling. For any fan, this is the definitive book - and I am not a sales person or involved with it in any way. I bought it for my son, he never puts it down (cheap too!)
Great job - Thanks!
November 10th, 2008 @4:32 pm
“Mathematics - language of the universe, core of everything…including music now”
Yeah, and for the last 2.5 thousand years if you know anything about Pythagoras, musical intervals and ratios.
November 11th, 2008 @8:25 am
The article linked above on everthing2.com has the following from George Harrison:
Q: Mr Harrison, what is the opening chord you used for “A Hard Day’s Night”?
A: It is F with a G on top (on the 12-string), but you’ll have to ask Paul about the bass note to get the proper story.
…which negates the “correct” math answer. GH should know, they played the song live about 100 times. Overtones and reverb can create lots of extra tones; I suspect this is where the math went wrong.
November 11th, 2008 @8:57 am
this is pretty cool, but all of you who think music IS math, you are completely missing the point. music is not math, any more than architecture is math, or painting.
if you listen to music and hear numbers, i feel very sorry for you.
November 11th, 2008 @3:48 pm
“if you listen to music and hear numbers, i feel very sorry for you.”
You don’t know very much about math, do you?
November 13th, 2008 @6:07 am
There are some really poor assumptions made in the research, which is why the answer that the analysis gives is flawed.
First, he arbitrarily selects one seconds’ worth from the middle of the chord, then imposes an arbitrary threshold on the fourier amplitudes. That’s why he didn’t see the F4 he expected to find from the 12-string guitar (it IS there, almost as strong as other nearby frequencies). This leads to incorrect conclusions about which notes are played by which instrument.
What he should have done was to take a few FFT slices of the chord, and look at how the amplitudes change over time. He should also have been more careful about losing valuable information by applying a threshold. This may provide much more reliable evidence to link groups of notes to specific instruments.
He also missed some of the lowest notes played on the piano (low D minor triad), and made some dodgy assumptions about tuning (he shouldn’t expect harmonics on stringed instruments to be integer multiples!).
Good idea to the do the work, but disappointing execution.
November 15th, 2008 @2:50 am
It’s an E11 Chord. Use your ears!
November 15th, 2008 @5:08 am
You should all get out more…
November 17th, 2008 @8:32 am
This is the best thing ever! Thanks so much for sharing these findings. I’m going to show this to
1) my music appreciation students, who will now have it cemented in their brains that I am a lunatic;
2) my private students, to whom I always stress the connection between math and music (and physics); and
3) my brother, who’s a crazy musician/theory nerd/math enthusiast like me!
November 29th, 2008 @6:55 pm
i do not agree with these findings, though one has to be impressed with the lengths that were gone to in order to reach them.
i have heard other recordings of this song from the same sessions that clearly illustrate what this is - 6 and 12 string guitars playing f major add 9 (with the open A string on the 12 string, at least, also present) and the bass guitar playing a D3.
i know this because i can hear it. perhaps that seems less certified than this study, but i’m telling you, that’s what it is.
January 17th, 2009 @9:57 pm
What can you say about a researcher who says he was “surprised” that there was a piano in the chord? The piano is about 75 per cent of the sound of this chord, which is why the end chord of the song (it is a bookend, same chord) sounds different….there’s no piano at the end.
The volume is not gradually being raised as the chord rings out, there is a large amount of compression on the mix and you are hearing the compressor slowly release as the chord rings out.
George plays what he has said he plays. The piano is basically hitting a G sus with 2 “d” notes (in octaves) with the left hand. Those D notes are HUGE in the chord. The Ricky 12 is basically the highs you are hearing in the chord, the piano all the mids’ and lows. Paul doubles the D’s of the piano. It’s not the mystery everyone makes of it. You want mystery, start figuring out the polychords Nelson Riddle used in the string arrangements of Frank Sinatra recordings;)
TH
February 9th, 2009 @7:08 pm
I had no idea that this topic would show itself for discussion. So when I “Stumbled” over it, I had to comment.
“I remember the first time I heard these notes and recall the magic of that time. What is stranger is that, a new time is upon us. We can receive and understand more frequencies than we had previously realized. But the magic of “Beatles” will resonate forever in our universe along with us.”
February 26th, 2009 @1:08 pm
this is a piece of cake. If you want a real challenge tell me what the last chord is of “Because” by the Dave Clark Five.
March 5th, 2009 @5:27 am
It’s interesting but surely the point is here that it is a great song by a great band. The fact that the opening chord is causing debate forty-five years after the release only reinforces the genuis of the band.
March 6th, 2009 @1:15 am
I don’t think it’s ever been a “mystery” that there’s a piano in there played by George Martin. Sounds pretty obvious to me.
And what about the snare drum hit? It’s a little surprising to see no mention of it in the analysis. Interesting discussion though.
March 6th, 2009 @1:16 am
The question I’d like to know is “How did they come up with that chord?” Pretty amazing…whatever it is.
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