December 08, 2004

The Opening Chord to "A Hard Day's Night" Revealed! "The opening chord to “A Hard Day’s Night” is one of the most memorable in rock history. . . But what exactly was that mysterious chord? . . . A type of mathematics called Fourier Transforms can be used to reconstruct the original frequencies from a list of numbers . . " Ya know, I never would have guessed that particular arrangement. Warning: Beatle geekery inside!

The important point is that the piano is there because the math says it is. Nifty! Only now how do I rationalize purchasing a 12-string?? Ooh ooh! A MIDI 12 string!

posted by petebest 20 years ago
  • This is really, really cool.
  • Cool article! Anyone know where I can find an mp3 of that opening chord?
  • Ah, but what can science tell us about the opening chords of this recording of the song? (Via Clay's Oddities) Or this one? (Via April Winchell) There's also a great alternate recording of the song by Cathy Berberian, but all I can find online is this version of her singing I Wanna Hold Your Hand.
  • I heard the dude talking about this on the radio a while back; he was the biggest nerd ever. But, he was a nerd about the Beatles, so it was cool. I still think the fact he used fourier transforms is hilarious, though. As a non-techie type, the first time I heard of fast fourier transforms I couldn't help but picture an extremely quick (fur) trapper. So combining that with the Beatles makes me laugh my ass off.
  • Oh, and I meant to say, BeatleFilter from pete_best! Awesome.
  • Terrific link! I love the chord but really couldn't care less how they did it. However, it pleases me enormously that someone, somewhere cares in such a delightfully focussed manner. The internet really belongs to people like this and their millions of virtual sub-netwoks.
  • I have a BS in Electrical & Computer Engineering, and am working towards a masters. Fourier Transforms are, as far as I'm concerned, one of the most profound, practical insights of mathematics. The idea isn't that hard to grasp, but it takes a little bit of imagination. If you remember back to your calc days, there was a theorm that said you can approx. a function by a polynomial (ie: 3x^2+(1/2)x+1) with as much accuracy as you desire (you just keep adding properly weighted terms of higher orders). And with some functions, given an infinit sum of polynomials, you can represent them exactly. Fourier came along and said "I don't have to use polynomials, I can use sines and cosines!" His idea for approx. a function was to use an infinit sum of sines and cosines, at different frequencies and different weights. This caused a bit of an uproar at the time, with various mathematicians screaming that he couldn't do that! And they were right, in general, but for most practical functions you can. Later, people began to wonder what would happen if you looked at simply the weights and frequencies (ie: 4sin(23x) -- 4 is the weight, 23 is the frequency) apart from the infinit sum. What you do is take some graph paper, and let the x-axis be the frequency and the y-axis the weight. As you plot more and more points in the infinit sum, you start to get another graph. The limit of this is called the Fourier Transform. The initeresting part is that the Fourier Transform is a bijection: every function you can transform has exactly one frequency representation, and the oposite is true also. So both a function and its transform are different views of the same thing. Two functions can't have the same frequency representation, and two frequency representations can't belong to the same function. How's this useful? Take AM radio for instance. If you were to graph the time domain representation of several stations together, you'd have a jumble of information almost no one could make sense of. But if you transform this data, in the frequency domain each station is seperated and obviously visible (because they each occur at different frequencies). Fourier transforms tell us how we can multiplex several signals together, over the same wire, and still seperate them at the end. It really makes modern communication possible (it, and packet switching). Anyhow, that't probably more information that you wanted to know. But that's why someone can transform a piece of music, and recover what the tones are. please excuse the spelling mistakes
  • Good post, thank you.
  • sbutler . . *snif* . . that was beautiful! Thank you )! And as to how they did it: making it a twelve-string, a bass, another 6 string, and a piano - that's a whole different thought process than just the 12 string alone. That wasn't a happy accident, that was freakin' floor-pounding genius!! Somebody pass the prellies! livii do you remember the show/station you heard that on?
  • petebest, it was on the CBC, 95% sure on DNTO (Definitely Not the Opera). It was quite some time ago though, but I don't remember the date, sorry.
  • This makes me happpppy.
  • If you remember back to your calc days ... and that's where you lost me. the idea that this can be done is really neat though. add that to the fact that they made a 4 instrument chord? whoa.
  • very well put, sbutler.
  • thanks for putting the time into the fourier explanation sbutler. I have come across it and all i recall is that it made gobbledygook graphs or chaos turn into order. magic! i thought. but i'd never looked for a simple explanation.
  • It just occurred to me today that the significance of this opening chord being a multi-instrumental element leads to the end of "A Day In the Life", where two (four?) pianos are used for the ending chord. Although the intent and sound are completely different, I think the idea is the same.