Working It Out. Math solves a mystery about the opening of "A Hard Day's Night."

The music of most hit songs is pretty well known, but sometimes
there are mysteries. One question that remained unanswered for over
forty years is: What instrumentation and notes make up the opening
chord of the Beatles. "A Hard Day.s Night"? Mathematician Jason
Brown - a big Beatles fan - recently solved the puzzle using his
musical knowledge and discrete Fourier transforms, mathematical
transformations that help decompose signals into their basic parts.
These transformations simplify applications ranging from signal
processing to multiplying large numbers, so that a researcher
doesn.t have to be "working like a dog" to get an answer. Brown is
also using mathematics, specifically graph theory, to discover who
wrote "In My Life," which both Lennon and McCartney claimed to have
written. In his graphs, chords are represented by points that are
connected when one chord immediately follows another. When all
songs with known authorship are diagrammed, Brown will see which
collection of graphs - McCartney.s or Lennon.s - is a better fit
for "In My Life." Although it may seem a bit counterintuitive to
use mathematics to learn more about a revolutionary band, these
analytical methods identify and uncover compositional principles
inherent in some of the best Beatles. music. Thus it.s completely
natural and rewarding to apply mathematics to the Fab 4 For More
Information: Professor Uses Mathematics to Decode Beatles Tunes,
"The Wall Street Journal", January 30, 2009..