IRA FLATOW: If you had a number one hit song, I bet you would remember writing it, right? John Lennon and Paul McCartney wrote over 200 songs together. That was over 50 years ago though, so it’s no surprise that memories have gotten a little fuzzy when it comes to who wrote which Beatles song. Let me give you an example. Take the 1965 song, In My Life.

[MUSIC – THE BEATLES, “IN MY LIFE”]

(SINGING) All these places have their moments with lovers and friends I still can recall. Some are dead and some are living. In my life I’ve loved them all.

John claims to have written that tune, but Paul remembers it differently. The two Beatles agreed to disagree, but die-hard fans remain curious. Was there a way to get closer to the truth? True Beatle fans will tell you that they are more partial to songs written by Paul or by John. There’s something in the songs themselves that make them unique to the songwriter.

My next guest is one such curious fan, as well as a Harvard statistician. He has developed an algorithm to determine the authorship of In My Life and several other contested Beatles songs by identifying what makes a song as a John song or a Paul song. Dr. Mark Glickman, senior lecturer on statistics in the Department of Statistics at Harvard. He’s here with his guitar. Welcome to Science Friday.

DR. MARK GLICKMAN: Thank you very much for having me.

IRA FLATOW: So how do you break down a song in a way that will tell who wrote it?

DR. MARK GLICKMAN: Well there are lots of ways to take a song and break it down into its constituent parts. And the way that we did it was to borrow from some ideas that are used in analysis of text documents. There’s a long history of analyzing sequences of words to be able to distinguish different authors. And we applied the same kind of idea to musical content of songs.

So for example, in an individual song there’s a melody line and there’s also a chord sequence. So if you treat the melody line, the notes in a melody line, almost as if that’s the words in the document, as well as having the chord sequence, which can also be viewed as like another dictionary of words that are in a document, you can use the same kind of analysis, which basically is examining the frequencies of certain kinds of words and certain kinds of chords or certain notes sequences or chord sequences as the way of establishing the fingerprint for a songwriter.

IRA FLATOW: All right, let’s go down to brass tacks here. Let’s talk about McCartney versus– what makes a Paul McCartney song a Paul song.

DR. MARK GLICKMAN: So there are a bunch of little things that came out of our model. I suppose some of these ideas are somewhat known, others maybe not so much. One thing that is actually sort of known among maybe hardcore Beatles fans is that with the melody line Paul tended to take a lot more liberties and tended to jump around a lot.

And just as an example, there are exactly two songs, two Lennon-McCartney songs over the period of songs that we incorporated into our work, which was basically songs from 1962 to ’66, which is all the songs in the years that the Beatles were touring and didn’t enter the studio yet full time. There are two songs in that period where the melodic jump is more than an octave. So in other words, they’re– I mean, I’m happy to demonstrate.

IRA FLATOW: Yeah, play them for us. Yeah, go ahead.

DR. MARK GLICKMAN: OK, sure.

IRA FLATOW: Go ahead, please, please.

DR. MARK GLICKMAN: So all right, so the very first song that Paul McCartney ever recorded for the Beatles is the song Love Me Do. I’m going to embarrass myself by playing a little bit of– well, I’m going to sing a little bit of it, but I’ll very quickly move to the part of the song where there’s the octave jump. But just to remind your listeners, Love Me Do is like–

[GUITAR PLAYING – “LOVE ME DO”]

(SINGING) Love, love me do. You know I love you.

And then you fast forwards to the bridge, where it goes

(SINGING) Someone to love. Someone like you.

And so that jump from someone to love, love, where is it? Love. And then it jumps to some. So that jump from–

[CHORD STRUM]

–to–

[CHORD STRUM]

–is an octave and a semi-tone.

[INTERPOSING VOICES]

IRA FLATOW: And that’s a signature then of his work.

DR. MARK GLICKMAN: And so that’s a distinguishing feature of Paul’s song. And so it just as another quick example, your listeners may know the song Eleanor Rigby, which is another Paul song. So that goes–

[GUITAR PLAYING – “ELEANOR RIGBY”]

(SINGING) Eleanor Rigby picks up the rice in her–

Where does she pick it up?

(SINGING) Picks up the rice in a church where blah, blah, blah, blah.

So the part where it jumps more than an octave, which is an even bigger jump than in Love Me Do, is–

(SINGING) All the lonely people, where do they all belong?

So that jump from where–

IRA FLATOW: Yeah.

DR. MARK GLICKMAN: Where do they all belong is an octave and a third. So that’s huge. And there are no John songs that have jumps that big.

IRA FLATOW: So what is it John–

DR. MARK GLICKMAN: Just as an example.

IRA FLATOW: What is John’s signature then?

DR. MARK GLICKMAN: So John, so interestingly, John songs tend to be using more standard– more standard musical motifs. So as I can give one example would be we discovered that there’s a particular chord change which is a pretty common one in probably most of pop music. And just to play the example, it goes from the tonic to the minor six.

Now that sounds all very complicated, but in fact for those of you who are listening, it’s basically going from the major key to the relative minor. So it might sound like this. This is just the two chords. So it goes from, say–

[CHORD STRUM]

–this chord to–

[CHORD STRUM]

–this chord. So those two in sequence sound very natural. It’s a very natural progression. And that particular chord sequence occurs with much, much greater frequency in John’s songs than in Paul’s songs.

IRA FLATOW: For example? Can we get an example?

DR. MARK GLICKMAN: So as an example–

IRA FLATOW: Yeah?

DR. MARK GLICKMAN: Yeah, so the John Lennon song It’s Only Love actually starts exactly with that alternation. So it’s–

[GUITAR PLAYING “IT’S ONLY LOVE”]

[HUMMING “IT’S ONLY LOVE”]

So those two chords just go in sequence. And that’s characteristic of John. He ends up using common chord changes. And he also ends up using notes on the diatonic scale much more often than Paul McCartney does. Paul McCartney tends to do– he tended to do more unusual things musically–

IRA FLATOW: Let me–

DR. MARK GLICKMAN: –than John Lennon did.

IRA FLATOW: Let me just remind our listeners that this is Science Friday from WNYC Studios. Talking with the very musical Mark Glickman, who is a stat– so you’ve taken a statistical analysis of this.

DR. MARK GLICKMAN: Yeah, yeah, so–

IRA FLATOW: So you– so who then wrote In My Life?

DR. MARK GLICKMAN: Well, I personally came into this not being entirely sure. I guess I probably would have thought originally it sounded like it was a John Lennon song based on the lyrics. It sounds kind of like John, because it’s sort of reflective and Paul McCartney tended to write much more love-focused lyrics. And this one tended to be a little bit more recollections.

But what came out of our model, if you believe the way we constructed the model, there’s a 98.2% chance that this was written by John Lennon, and only a 1.8% chance that it was written by Paul McCartney. And I think there’s no dispute that John Lennon actually wrote the lyrics. I think Paul McCartney’s side of the story was that John wrote the lyrics and then just kind of handed it to him and say here, you figure this out.

And that’s how Paul remembers it. But John basically said this is pretty much my song with Paul McCartney helping on the bridge. But according to our model, the song is pretty solidly a John Lennon song.

IRA FLATOW: Has this news gotten back to Paul? Do you know? And the reaction?

DR. MARK GLICKMAN: Well I read that there were some reporters that heard about this story and knocked on his door. And apparently he said no comment. Or at least that it didn’t get past his entourage who would particularly ask him. But just as well. I don’t want to go to my dying day with Paul McCartney hating me.

IRA FLATOW: Yeah. And well, speaking of hating you, I mean, not that other people do hate you–

DR. MARK GLICKMAN: Great.

IRA FLATOW: No, but there are going to be lawyers, right, who are listening to your statistics? And we always hear of controversies about hey, somebody stole my musical type or song or phrase or something.

DR. MARK GLICKMAN: Right, right, right.

IRA FLATOW: Have they been knocking on your door?

DR. MARK GLICKMAN: No, fortunately no lawyers. I mean, we’re not trying to set all this in cement. We’re being very careful in saying that we’re making certain assumptions in our model. We identify what amounts to 149 different musical features. And it’s entirely possible that we’re missing some crucial ones. So to the extent that you believe that the 149 features captures most of the signature of a song, then it’s probably worth, to some degree, believing the results of our model. But that said, every good statistician is careful to point out that probability prediction is only as good as the assumptions in a model.

IRA FLATOW: Yeah.

DR. MARK GLICKMAN: If the model assumptions aren’t quite right, then there’s certainly a dose of healthy skepticism. But we think we did a decent job capturing the main features. So–

IRA FLATOW: Two million people will be listening to this. And I think some record producer is going to knock on your door now to give you–

DR. MARK GLICKMAN: Great.

[LAUGHTER]

Can’t wait.

IRA FLATOW: Give you a new career as a recording artist.

DR. MARK GLICKMAN: I’m changing my phone number.

IRA FLATOW: OK. Thank you very much, Mark. Mark Glickman.

DR. MARK GLICKMAN: My pleasure.

IRA FLATOW: Any relation to Marty Glickman? You know Marty, the sports caster?

DR. MARK GLICKMAN: No, no, no. I’ve been asked that for many years.

IRA FLATOW: Decades.

DR. MARK GLICKMAN: No, no. Nope.

IRA FLATOW: All right.

DR. MARK GLICKMAN: No relation.

IRA FLATOW: Mark Glickman, senior lecturer on statistics in the Department of Statistics at Harvard University. Good luck to you. Thank you for taking time to be with us today.

DR. MARK GLICKMAN: Thanks for having me on your show.

IRA FLATOW: One last thing before we go. Anna and Ella have been busy working on season two of our podcast, Undiscovered. And it’s coming out next month. But if you can’t wait that long, Undiscovered co-host Annie Minoff will be joining authors David Kwame and Sy Montgomery for a celebration of great science writing.

That’s going to be at the American Writers Museum in Chicago next Thursday, August 6th. That’s next week, August 16th. I said six. 16th, Thursday, August 16th.

Tickets and information are available at sciencefriday.com/events. Chicago, August 16th, Undiscovered. Charles Bergquist is our director. Senior producer, Christopher Intagliata.

Our producers are Alexa Lim, Christy Taylor, Katie Heiler. Our intern is Lucy Wong. We had technical engineering help from Rich, Rich [? Cayman ?] and Sarah Fishman in New York.

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