Dr. Jason Brown of Dalhousie University in Halifax, Nova Scotia, told the Halifax Chronicle-Herald in recent years he's used mathematics and computers to sort out debate on the effects. The first was the opening chord from "A Hard Day's Night," he said.

"I had an assumption that George Harrison played this on his 12-string guitar, but very quickly I could look at the frequencies and tell it wasn't playable on his guitar alone," he said. "So even when I tried to apportion the notes that I deduced to all of the instruments in the Beatles, to the two guitars and the bass, it still wasn't playable. And then I realized that the only solution was there must have been a piano in the mix."

Brown, who is writing a book called "Our Days Are Numbered," told the newspaper he also unraveled George Harrison's guitar solo on "A Hard Day's Night."

"He must have recorded it at half-speed and then they sped it up to match the rest of the band," he said. "People may say different things ... but the mathematics tells the truth."