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..