Mathematics unmasks the fifth Beatle.
Unmasking the Fifth Beatle! With math!
This is Sandra Tsing Loh with The Loh Down on Science and ... one of the most famous--and mysterious--chords in rock and roll:
Yep, that's the lead-in to "A Hard Day's Night."
For forty years, rock bands have struggled to reproduce its rich complexities.
Why so hard? Because it seems like more than four musicians are playing: John, Paul, George, Ringo ... and someone else.
Jason Brown of Canada's Dalhousie University has finally deconstructed this auditory mess. Brown used a mathematical technique called Fourier analysis to split the killer chord into its thousands of constituent tones.
He crossed off the tones corresponding to guitars, bass, and drums. But several tones were left behind. Where did they come from?
A piano, it turns out! In need of slight tuning, in fact. Probably played by Beatles producer George Martin.
Using similar techniques, Brown found that the guitar solo from that same song ...
. . . was most likely recorded at half-speed.
Now if only he could tell us whether Paul is dead!