Are you a John person or a Paul person?
That鈥檚 the thing about the Beatles: despite being perhaps the most beloved rock band of all time, they鈥檙e as well known for their individual personalities as their collective work.
鈥淧eople have favourites: John or Paul, or perhaps George or Ringo,鈥� says Beatles fanatic and 新加坡六合彩开奖直播 Math professor Jason Brown. 鈥淎nd they cling strongly to what that person鈥檚 contribution was to the Beatles.鈥�
Which can get tricky at times, given that the vast majority of the band鈥檚 songs are credited to 鈥淟ennon-McCartney鈥� regardless of which of the two may have written it. As well, especially on earlier Beatles material, there was often a great deal of collaboration and editing done between the two songwriters 鈥斅燼nd many cases where the recollections of exactly who wrote what differ.
The question of authorship is one of the many Beatles-related ponderings that have tickled Dr. Brown鈥檚 mathematical mind over the years. Now, together with Harvard statistician Mark Glickman, he鈥檚 put together a study aiming to settle some long-standing Beatles debates 鈥� with math.
The math behind the music
The study, , is an exercise in stylometry: using statistical techniques to determine authorship. With the help of Harvard student Ryan Song, Drs. Brown and Glickman analyzed the entire Beatles catalogue up through 1966鈥檚 Revolver, going through the scores and recordings for every song. (鈥淭here seems to be a change in styles after Revolver,鈥� says Dr. Brown, noting as well that Lennon-McCartney songwriting partnership became a bit more disparate. 鈥淪o it seemed like a good breaking point.鈥�)
What the researchers were looking for were songwriting patterns that disguised McCartney or Lennon鈥檚 work: things that each of them did, consciously or unconsciously, that left fingerprints on the songs. The fact that there are about 70 or so Beatles songs (or portions of songs) from that era on which the authorship isn鈥檛 disputed, based on interviews over the years, gave the researchers a starting point to identify those patterns and, from there, analyze songs where there鈥檚 some debate.
Take, for example, a Beatles classic from Rubber Soul which ranks 23rd on . Sung by Lennon, 鈥淚n My Life鈥� is a song where the recollections of the two songwriters differ as to how it was written. Lennon (who was killed in 1980) credited McCartney with the song鈥檚 harmony part and the middle-eight, but McCartney has claimed in the past that he wrote the majority of the music himself.
The math sides with Lennon on this one: the analysis found just a 0.018 per cent probability that McCartney wrote the music for 鈥淚n My Life.鈥�
鈥淭hat particular song generates a bit of emotion on both sides because it鈥檚 considered such a great song,鈥� says Dr. Brown. 鈥淏ut there are other songs like where many believe it鈥檚 a Lennon song, but our study shows it to be almost certainly written by McCartney.鈥�
Finding the pattern
So what sort of patterns distinguish the two songwriters?
鈥淧aul, perhaps because of his larger vocal range, often has big skips in terms of melody notes,鈥� Dr. Brown says, offering one particular example. 鈥淔or instance, in 鈥楲ove Me Do鈥� 鈥斅爐he end of the chorus 鈥斅燩aul sings the top line and then jumps down an octave. In 鈥楨leanor Rigby鈥� he does the opposite thing. John doesn鈥檛 do that to the same degree.
鈥淥n the other hand, John liked, chord-wise, to go between what鈥檚 called the tonic 鈥� the base chord of the key 鈥斅爐o the relative minor. He does it in 鈥楻un for Your Life,鈥� 鈥業t鈥檚 Only Love鈥� 鈥� it鈥檚 a typical move for him. I think it鈥檚 a sense of ambiguity in the key:聽is it the major or the relative minor? He liked that sort of ambiguity in his songwriting.鈥�
This isn鈥檛 the first time Dr. Brown has applied his mathematical expertise to unlock long-argued Beatles lore. Ten years ago, he earned international attention for his work using a mathematical calculation called Fourier transform to try and identify how the oft-imitated, never-quite-duplicated opening chord of 鈥淎 Hard Day鈥檚 Night鈥� was played. (The answer, he found, was a piano note buried in the mix.) He also took to the pages of Guitar Player magazine to write about George Harrison鈥檚 solo on that same song, and how the math shows it was initially performed at half-speed and sped up to match the rest of the recording.
His newest project has been generating headlines around the world over the past week 鈥斅爄n , ., , and beyond. (The day he spoke with Dal News he had three other interviews lined up.) And if you think that all of this effort to unlock Beatles鈥� secrets takes some of the fun out of rock 鈥榥鈥� roll, Dr. Brown couldn鈥檛 disagree more: he finds, in the math, even more evidence of the band鈥檚 greatness.
鈥淔or a lot of people, the music is so eternal and so fresh that it鈥檚 like it鈥檚 just yesterday 鈥� to pardon the pun,鈥� he says with a laugh, when asked why his research on the Beatles seems to generate such attention. 鈥淭he Beatles hold a special place in people鈥檚 hearts and minds. I鈥檓 still captivated by the brilliance of their songwriting, like no other band. Even after all this analysis, it still excites me.鈥�