Beatles Unknown "A Hard Day's Night" Chord Mystery Solved Using Fourier Transform
    By News Staff | October 29th 2008 12:00 AM | 91 comments | Print | E-mail | Track Comments
    It’s the most famous chord in rock 'n' roll, an instantly recognizable twang rolling through the open strings on George Harrison’s 12-string Rickenbacker. It evokes a Pavlovian response from music fans as they sing along to the refrain that follows:
    "It’s been a hard day’s night
    And I’ve been working like a dog"

    The opening chord to "A Hard Day’s Night" is also famous because, for 40 years, no one quite knew exactly what chord Harrison was playing.

    There were theories aplenty and musicians, scholars and amateur guitar players all gave it a try, but it took a Dalhousie mathematician to figure out the exact formula.

    Four years ago, inspired by reading news coverage about the song’s 40th anniversary, Jason Brown of Dalhousie’s Department of Mathematics 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 decompose the sound into its original frequencies using computer software and parse out which notes were on the record.

    It worked, to a point: the frequencies he found didn’t match the known instrumentation on the song. “George played a 12-string Rickenbacker, Lennon had his six string, Paul had his bass…none of them quite fit what I found,” he explains. “Then the solution hit me: it wasn’t just those instruments. There was a piano in there as well, and that accounted for the problematic frequencies.”

    Dalhousie University math professor Jason Brown and his Ibanez guitar.  Photo: Danny Abriel

    “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.”

    Dr. Brown deduces that another George—George Martin, the Beatles producer—also played on the chord, adding 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 the literature about the song to date, 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.”


    I am a Taylor man myself but Doc Brown did all right here, even with an Ibanez.

    What's so special about the custom 814CE?  No CE!  That's right, real men don't need electronics.   What's so special about that custom 714?  No pickguard!   That's right, real men don't need ...

    ... well, you can finish it.
    You're a tool.

    Totally wrong here. Randy Bachman gives us the actual guitar notes played after listening to the original multi track. Here it is. George plays an F chord with a G on top and a G on the low E string and a C on the 5th, on the 12 string. John plays a D sus 4 and Paul plays a D on the bass. Thats it. Heres the link wherein Randy explaines it all.

    WELL SO WHAT'S THE CHORD!?!?!?!? I've been playing G7sus4...

    That's it! The guitars play a G7sus4 & the bass plays a D

    Nice work Jason, but I believe I know the chord, or at least the combination of notes on a 6-string guitar - I don't know the name of the chord. The notes are ADACG. open A string, open D string, second fret G string (A) , first fret B string (C) and third fret e string (G). Try it; you'll like it. G7sus4 is definitely not the chord, nor is the variation of moving the index finger to the third fret E string (G). All of these have been on YouTube, and I believe the one I defined is the one. George Harrison said he played a "G over F" and Paul played a "D".

    Gerhard Adam
    Yours is a D7sus4.
    Mundus vult decipi
    you forgot to write what chord it is dummies.

    Take a look here:

    Mon May 02 2005 at 20:14:02
    ...But we're still lacking much of the serious punch that the opening chord. This is due to "the fifth Beatle", George Martin, playing a chord on a Steinway Grand piano, overdubbed on the final mix of the record. I myself was surprised to learn that there was a piano chord at the beginning of the track. But there is...

    Interestingly Hal Leonard's 'The Beatles Complete Scores' shows this chord as being Gsus4/D (xx0013) which always sounded perfectly good to me! Not to mention *really* satisfying to play :-)

    No mention of the piano chord in that score though!

    So what is the chord?? Tell me exactly what every instrument is playing for that chord!!

    the link above tells you what the chord is.

    It says you have to add an F note, but as all 6 strings of your guitar are already used in the chord it is impossible without a 7th string to play the chord correctly. Try trilling b/w the sus7 and the adjacent F note, see how that sounds.

    Here is a very non mathematical response:
    Has no-one thought about contacting the existing Beatles and asking them for the answer?

    Hank Campbell,

    Your completely irrelevant comment posted as an excuse to show your $5,000 worth of guitars on a cheesy leather couch makes you look like a douche.

    Taylor 714CE player

    If you're really a guitar player, you know there is no way such important work can be allowed on an Ibanez.   And you think those two guitars are worth $5000?   Are you in Taylor marketing or something?  

    Calling a man a douche is fine.   Ridiculing a man's couch is a bit offsides, though.
    lol, Your joke about the couch has redeemed you.

    A guy that gigs NEEDS those electronics though, buddy... Ya gotta admit that. My Taylor 714 is a bitch to mic properly because of that mid-range boominess, let alone in a live sound environment. Plug and Play!

    - Taylor 714CE Player

    No, he's still a douche. A good musician can make good music with any old instrument. We don't care what guitar you play.

    Yes mr Hank Campbell, you are a total loser !

    People who niggle over pissy little things like elctronics n shit need to go play their guitars and stfu. Pickups in acoustics are no good to me, I play way too heavy handed, they just distort the fuck out. Point the mic towards the neck so just out the way of the sound-hole to remove boom. Fuck your taylors, both of you. I bet they're beautiful to play, and sound great, but I play a $700 Takamine and it's how you play the thing not how reputable the guitar is. I'll play my takamine against anyone, any day. It's how you play, not how much money is sitting in your lap. I usually end up with blood pissing out my rhythm hand after a decent beatles or elvis jam. New strings, and good control over your instrument are what's needed. I'd love me some expensive guitars, but only for love of the instrument itself, not because I think it could make me play better.

     I usually end up with blood pissing out my rhythm hand after a decent beatles or elvis jam
    I don't think anyone disputes skill trumps an instrument but as I said, someone like Eric Johnson, who even obsesses over the batteries he uses in his effects because he can hear the difference, is on another level.  I played 'better' on a $35 guitar before I had kids but there is no question my better guitars have a better sound.  Saying an instrument makes no difference is not valid, but it sure can't make a bad player into a good one.  I have seen plenty of rich kids with a PRS and just shake my head.
    Now please apply this same stuff to King Crimson's "Schizoid Man" on that distorted chord being strummed over and over again! :P

    Nobody can get that same punch that KC got with it.

    just hit all the open strings, no one will notice the difference

    Um, this is not any big revelation. That Martin added piano to the mix has been known for quite a while.
    Notation for the song included guitar tablature that indicated merging the Fchord with Gvoicing on both low and high E string.

    Listen to their Hollywood Bowl live recording to hear a reasonable interpretation of how they played it live. Without the piano. :)

    You mean to tell me that someone who quotes a part in tabulature can actually name the notes he is playing? Unheard of! (I'm only busitng chops, so don't kill me)

    Actually, a G7sus4 chord with an F in the bass is not so unusual, afterall, the f is simply the minor 7th interval of the chord. it's just that the low f is played on the piano giving it an unusual characteristic sonically.

    It's G7sus7. Just plug your guitar into a decent chorus pedal and mess with the settings. You can get it to sound pretty darn close.

    I'm far more impressed with the guitar strumming throughout the song than the single chord in the beginning.

    Uhhh... G7sus7??? Okay, I may not be a music theory genius, but I don't think you can have a sus7. It's either sus4 or sus2, right???

    Try these, frets in order, strings 6-1 with x being not sounded and 0 being open:

    1) x 0 0 0 1 1
    2) 3 0 0 0 11


    I don't know if you realize that every Beatles fan in the world knows that there is a piano on that intro. Outtakes have been circulated in bootleg land featuring takes made before the piano was overdubbed. So you can hear Harrisons chord clearly.

    It is an F add 9: Forth string, third fret - third string, second fret - second string, first fret - first string, third fret. The same chord he arpegiates at the end of the song. With that, Paul plays an open D, and the piano slams on a D as well, thus making the complete chord nothing more than a Dm7sus4.

    Silly. Use your ears.

    apart from their extensive bar band employment, thus learning the pop music vocabulary very well, i dont think the Beatles knew formal music theory in great detail, but they were musically gifted and had great intuition. to me the fact that things like the intro chord to "hard days night" is so easy to play yet sounds so great is genius.

    Too funkin' cool, daddy-o.
    You hipsters really make the scene.

    Stay on groovin' safari,
    Tor Hershman

    So what is the chord? It supposed to be solve but where is it?

    musicobsession, read the other comments!

    I always played it as a +9 chord. Turns out I was right.

    Who are the Beatles?

    Have you been in a coma for the past 50 years or something? Or are you just a complete moron?

    So it turns out all that time I spent as a pimply youth trying to figure it out over my crappy guitar was wasted. If only I'd know I'd have needed to mash at a apiano to get there as well, I'd have been rich I tells yer! RICH!

    Actually someone did ask George Harrison in an online chat. Pretty much spells it all out on Wikipedia

    Ya'all don't know a sweet guitar when you see it. This is a 1979 Ibanez Artist 2330, semi-hollow body with 2" chunk of solid maple under the pickups and a coil tap to allow 5 different pickup combinations: a copy of a Gibson ES-335. Workmanship and materials are excellent. The guitar is awesome - the tones, finish, inlays, electronics - look at the quilted maple top on this one. I had one in high school (1979) and sniped another one (1978) one off of eBay 3 years ago.
    Ibanez was sued by Gibson for making these and similar guitars (look up "Ibanez lawsuit guitars). Their Les Paul copies are especially desired. I think Gibson builders went over there in the late 1970's to check out their processes and came back to initiate the lawsuit. From Wiki: "The artist series established the company as manufacturers of high quality original instruments."
    As for me, I learned how to play from Beatles albums on another Japanese Gibson copy of an acoustic (called a "Conqueror") and this guitar which allowed a decent replication of the many electric sounds on the albums over the years. Not everyone has the cash to buy American when you are 14.
    If you love and appreciate electric guitars, you won't be a snob about them (excepting the mass produced guitars from China, Korea and Mexico which are obviously sub standard). The Ibanez Japanese builders, much like the Fender Japanese builders used good materials and had good workmanship for the most part.

    Andy Summers (The Police) plays the same exact chord in the song "Walking On The Moon"...

    Well Delhousie, spell out the damn chord -- so the rest of us can play it.

    Taylor grips like a sissy. And sounds inferior to a Larivee in a studio. So do yer math, big boy.

    Are we here to talk about math and music or are we here to make jokes?   You can't even spell Larrivee so I'm having a hard time believing you have done the research.   

    I have Taylors but my every day guitar is a Martin.  Go figure.

    P.S.  If I buy another classical, I bet it will be a Larrivee.  He's been doing it for 40 years so clearly he knows his stuff.
    Kimberly Crandell
    We're here to talk about S-C-I-E-N-C-E.  Sheesh, it's like you're not even aware of which website we're on.
    Gotta love gear snobs. Stevie Ray on a Danelectro is still Stevie Ray.

    Way to go journalist! Way to go! What is the chord??????

    Its not a single chord. It is several chords stacked, being played by at lest two guitars, a Bass and a piano simultaneously. To play it on a single guitar you would need an insturment that has some classical strings, some low bass notes and some doubled strings. and the strings would need several different types of amplification. Or you could build the chord with a synth or multitrack.
    >>So, all in all, what do we have?

    George Harrison: Fadd9 in 1st position on 12-string electric guitar
    John Lennon: Fadd9 in 1st position on a 6-string acoustic guitar
    Paul McCartney: high D played on the D-string, 12th fret on electric bass
    George Martin: D2-G2-D3 played on a Steinway Grand Piano
    Ringo Starr: Subtle snare drum and ride cymbal

    This gives the notes:

    G-B-D-F-A-C (the B is a harmonic).

    As for what to actually call this chord. Well...that's anyone's guess!<<

    See this link:

    Ok, here is a way to write this out.
    There are actually a few different methods.

    Very simple. G major triad plus the mixo 7th, 9th, and 11th all over D in the bass


    Dm13(no 9)
    You have the Dm triad with the 7th (C), the 11th (G), and the 13th (B)


    B half-dim b9, b13/D
    B-D-F-A, the b 9th(C), and the b 13th (G) all over D


    F #11 (no 7)/D ---OR--- F #4 (no 7)/D ---depending on the voicing
    F-A-C, the 9th is G, the #11th is B natural all over D


    C-F-G, the B is the Maj 7th, the D is the 9th, and the A is the 13th all over D


    Am9, b13(no 5th)/D
    A-C (no E), G is the 7th, B is the 9th, D is the 11th, and F is the b13

    Hope that helps!

    I meant
    F 9, #4(no 7)/D

    That would be a G11 chord. to jazz types. Voicing is everything, though - spreading the notes further apart is the magic.

    I think you could call it G13add11

    F flat demolished

    According to Wikipedia, "Harrison was playing the following notes on his 12 string guitar: a2, a3, d3, d4, g3, g4, c4, and another c4; 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."

    Hey, George Martin is still alive. Couldn't someone have just asked him to explain it?

    That's positively unscientific!  And a memory from 40 years ago.  I can't remember what I had for dinner yesterday so how will he remember that?
    Hatice Cullingford
    A hard day's night

    Large or small might

    "Still, the funniest" though

    Hank Campbell runs hydrogen-tight.
    I will never understand why people have been pissing about the "mystery chord" for so many years, YEARS! Its clearly been a piano all along, you don't need a masters in mathematics or theory. All thats required is an attentive set of ears to clearly hear that its a piano. I have been trying to tell people that its a piano for a LONG time and I think that the clue to the "riddle" of the chord has more to do with blind adoration than anything to do with harmony.

    "Hey, George Martin is still alive. Couldn't someone have just asked him to explain it?"

    Martin, or someone else who was also in the studio, commented that when they had a problem while recording, that is a wrong or sour note, they would just "splash" a piano note, the correct one, over the recording in the proper place.

    I don't know if this was peculiar to Martin's recording technique, or an industry commonality.

    I read this in an article probably 35+ years ago.

    Whereas a problem could be fixed by doing this, I imagine other areas, like the chord, could be enhanced.

    Whereas a problem could be fixed by doing this, I imagine other areas, like the chord, could be enhanced.
    It's often you can take a defect and make it a feature.   The entire mult-billion dollar MEMS industry was created because magnetic fields deformed metal at the small scale - so they made that deformation into sensors.
    Very interesting.

    Btw, for all you "use your ears' people, try
    and have a go !

    (It is Prokofieff .. Romeo and Juliet, scene "the Montagues and Capulets".

    Good luck !

    Dunno bout da chords,but is sure great to read all ur love to one of history's biggest happening;)))

    Interesting site!! it seems really important. music technology in the news, The best music is analytical and pattern-filled and mathematics. give a thumbs up on su !!!

    Great and very useful site for music technology!! Give a thumbs up on SU!!

    idiots! that chord was photoshopped!

    The answer is sitting on the original tapes.  If George Martin and Paul McCartney don't remember, someone (e.g., Geoff Emerick) can go back to the individual recorded tracks and listen to them.  Using a Fourier transform to figure this out is silly and non-musical.  Any musician knows, you're better off using your ears to hear into the chord, rather than doing a Fourier analysis.  And, there's nothing special about this chord in particular.  You can take many parts of rock/pop recordings and be challenged to hear what the precise voicings were.  This is a result of the mixing, treatment of the various parts by effects/compression, etc.  It's especially challenging for guitars, which may be in alternate tunings (not that this was necessarily the case in this instance).
      Using a Fourier transform to figure this out is silly and non-musical. 
    Egads, do you know where you are?!?     :) 

    We know plants grow too but we still want to know how and why.
    Yes.  But a Fourier transform is simply not the right tool to figure out the structure of a chord.  Your ears are.  
    How many suggestions of different chords have been made by people who probably have alot better level of hearing than me, using 'your ears' as you call them???
    Some are wrong,
    but most of the suggestions are related harmonically, and fit in some way.
    This proves that the fourier transform might not be the best but it is a much better tool than 'your ears' because our brains have the ability to hear what they want to hear. Ears only become good with not just expirience but more importantly, plenty of dialogue with other muscians, only these factors can over come the ability of the human brain to hear what it wants to hear. But that is not scientific is it?
    Some people get so offended when the magic of music is demystified, and some mostly amature musicians can behave with such superior attitude to what they think they know. I'm not saying that is you, just saying that our ears can be good yes, but the software that runs this high spec kit is not designed to work alone, nor did it evolve to be scientific, more of a social piece of kit, thats why we resist pioneers so much, keep up the good work Jason!

    The presence of the piano has been documented before. Plus, there are interviews with George Harrison where he says that he played an F with a G on top on his Rickenbacker 12 (as did John on his Gibson J-160e) while Paul played a D on the bass. George Martin plays DGDFC (first D below middle C) on the piano.

    The F with the G on top is played xx3213 low to high in standard tuning (EADGBE).

    No, that's incorrect. The F with a G on top that Mr. Harrison is referring to is played XX3563, a shape which later becomes part of the arpeggiated coda.

    Here's another discussion that's pretty accurate of the chord--

    Are you kidding me? What brainiac seriously thinks this is worthy of internationaly aclaim? what? couldnt find a serious problem to work on? whatever. i know its just internet rambelings about one of the few original things in this world, but come on now, this is a guitar and a piano... whoop'd doo dah

    Yes, I can hear how the Guitar, Bass and Piano define this famous chord... but i just can't help thinking

    I figured it out myself, with a little help from youtube. It's a live performance in 1964. You can here the intro chord and there is no doubt about George playing th G7sus4 on the 3rd position on his 12-string rickenbacker. But right after that you can see John, holding the chord F9 (1st postion, 4 strings) which is, with a little fantasy, also a G9 with a double sus4. I can't see what Paul is playing, but the mathematic did it's work. Maybe that George Martin played an additional chord on the piano in the studio, but the live performance sounds pretty authentical. I think that all the notes are in it. The other mystery is also soved, the solo of George Harrison. It is played on postion 10 and it sounds lik in the studio. All the rumours as should it be dubbed or played on half speed is not true. Allthough it could be that in the studio George has played it an octave lower. George was more a genious than a virtuous player. I found out the way he play his solo. It's even for me (amateur) easy to do. the magic is en push pul end playing another note in between it. I'll work it out for youj some day.
    This is why I enjoy Scientific Blogging. Who would have thought "Mystery Chord" would show up on these pages?

    If we're going to be snobs about guitars, how about the non-import Bozo's for acoustic gear?

    "the frequencies he found didn’t match the known instrumentation on the song. “George played a 12-string Rickenbacker, Lennon had his six string, Paul had his bass…none of them quite fit what I found,” he explains. “Then the solution hit me: it wasn’t just those instruments. There was a piano in there as well, and that accounted for the problematic frequencies.”

    Put away the pocket protector. Here are your problematic frequencies: All Rickenbacker 12 String Guitars, in this case, George's 360/12 Deluxe, are strung differently than any other 12 string guitar so that the low tones on all string-sets strike first. This is what accounts for the Rick's unique bassy jangle. John's Rickenbacker 325 has a 3/4 short scale neck and does not produce the same tonal qualities of a full scale 6-string. Determining what FRET (yeesh) Paul played on would depend if he was using his flat wound steel stringed 4001S Rickenbacker (which he used in the studio) or his Nylon Stringed Mud Puddle Poorly Intonated 500/1 Hofner (which he used on stage and for the movie scenes). You will rarely see Paul playing past the 7th fret on the Hofner because the intonation is so bad. You don't need to "mathematically" decide if George Martin played on it.. Just ask the man for the sake of Jeebis! And in general, The Beatles tuned to A=435, not the traditional A=440. I didn't read where ANY of these factors were used in the study. I am now wondering what chord was used on the "Chipmunks Sing The Beatles" album, though.

    George was asked. He told us he played "an F with a G on top (Fadd9)" This video proves that at time index 0:25. George's hand is clearly positioned for a 1st Position Fadd9, just like he said it was:

    John plays the same chord on his 325. See his fingering at time index 0:22 of this one:

    If you want to duplicate that chord exactly, first you will need to spend $6000+ on a Rick 360/12 and a Rick 325.

    This chord has always troubled me, but it makes more sense now! I never realized there was a piano but having now listened to it again knowing there is, it’s actually quite easy to notice it :)
    legal steroids

    What do you mean no one knew what it was? A friend of mine has been playing that chord for decades, lol. Anyone with a good enough ear could've worked that out. I can't believe there's a page this size for something so simple. I mean it's not that difficult to work out, trust me!!!

    Is the opening chord of the song Here Comes Your Man by The Pixies the same?

    We'll have to ask one of the five people who still listen to the Pixies.
    Hank, you are a funny guy.

    Ouch... The Pixies are/were a great band.

    How stupid can you get? the intro chord is a G7 sus4, which is a dominant 5th, the intro chord for all western music. Contrary to an F note being impossible to play in the chord as stated in the article, the opposite is true- you can't play a G7 on the guitar without including an F on the 3rd (D) string. This dummie "solved" a mystery that any 15 year old in a garage band could figure out.

    I'm a linguist. As back-translations check language understanding, let's feed the Fourier transformation to a synthesiser. If nobody can tell the difference between the original track and the output synthesised from the Fourier analysis, then we have a new, quite complicated, way of recording. If Jason Brown will release his work then we have a new industry,

    I have a "Harmony" ukelele made in the People's Republic of China in 1955. Made of lacquered wood, except for the strings, it has its original box. It is worth $50,000 and I would accept offers.

    As someone who was a sound engineer for quite a few years, and remember George Martin and the equipment of that era, I find that many of the comments here fail to take account of natural vibrational beat frequencies
    You are discussing musical notes as if they are pitch perfect invariates!
    Fourier analysis fails miserably at anything except pitch dependent matched frequencies, which rarely, if ever, occur
    The mere fact that most stringed instruments vary in pitch during the duration of one song, and several instruments were involved, is further complicated by the slight beat frequencies which the Beatles themselves would have created in tuning up before the song was recorded - its a harmony thing, which gives pleasure to those playing and is much more a feeling than a Science
    Anyone who has played a stringed instrument with others may intuitively, if not technically know this to be so
    The equipment used for amplifying is also relevant, as valve amplifiers of the day produced more even harmonic distortion than later solid state equipment, [including hum], and including effects, mixing desk and final tape transport mechanism there is yet more tonal variance
    I would say it is impossible to 're-create' those chords, as played by the is musical history
    Try subtracting a stringed sound from a recording of a stringed sound, by anti-phasing it....rarely will there be absolute silence, or a full nullity, but, had the guitar chords progressively been removed as played, the piano would be obvious, without 'Fourier mathemagic'

    Make new music, as they did - it cannot be 'copied' tonally, even if you play the same notes,

    ...... merely imitated

    Music is to be enjoyed, not analysed, and I speak from experience, having analysed the enjoyment out of it, whilst designing a high quality hifi setup many years ago

    If you apply a little music theory to this you'll find the proper name of this. I prefer the guitar voicing 100213 FADACG which is either a F6/9 chord or a G7sus4/F chord or a Dm7/11. Being the song is in G, I would call it G7sus4/F. If a chord is suspended it's neither major nor minor.

    Gerhard Adam
    How do you get a G7sus4/F out of that?  It's a G9sus4.  G9 = G-B-D-F-A.  Moving the B to a C makes it the sus4. 
    Mundus vult decipi
    My bad. G9sus4/F is correct. Thanks for pointing that out!

    Gerhard Adam
    Wow ... we have agreement on a post. :)  Good job!
    Mundus vult decipi
    The chord that George Harrison played at the start of the song on his12 string Rickenbacker was definitely as follows - 6 string G (thumb), A string muted, 4 th string F, 3rd string A, 2nd string C and 1st string G. It sounds wrong on a regular 6 string guitar but rings true on the 12 string with the octave strings. It would be a G9 sus 4, or G7 sus 4 add 9 (as there is no third in the chord.) Remember that Rickenbackers have the octave string in each course the other way up to virtually all other 12 strings and so you hit the lower note of the pair first on a downstroke.

    Who is Dan Electro??? :)