God bless Joseph Fourier

I never would have expected to find a piece on mathematics and Beatles music in the WSJ, but here it is. Among other revelations, the opening 12-string guitar chord to "A Hard Day's Night" also contains a piano note. Graph theory also features in the article, as a tool to attempt to partition authorship of various songs in the Beatles' catalogue between John Lennon and Paul McCartney.

This piece reminds me about a famous critique of "Not A Second Time" that appeared in the London Times back in 1963:

William Mann: "...harmonic interest is typical of their quicker songs, too, and one gets the impression that they think simultaneously of harmony and melody, so firmly are the major tonic sevenths and ninths built into their tunes, and the flat submediant key switches, so natural is the Aeolian cadence at the end of 'Not a second time' (the chord progression which ends Mahler's Song of the Earth)..."

John Lennon: "To this day I haven't any idea what Aeolian cadences are. They sound like exotic birds."

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