Friday math Movie - How Math Unraveled the “Hard Day’s Night” Mystery

By Murray Bourne, 21 May 2010


This week's movie is for those of you with an interest in music and math.

There's been a mystery about the chord you hear at the beginning of the Beatle's song, "A Hard Day's Night". It turns out it's not possible to play all the notes in that chord with only 3 musicians (George Harrison and John Lennon on guitar, and Paul McCartney on bass).

Here's the chord we are talking about at the beginning of the song:

[Music source:]

The original story, at, How Math Unraveled the "Hard Day's Night" Mystery, is unfortunately no longer available.

Professor Jason Brown from Dalhousie University used Fourier Series to figure out the notes that couldn't be accounted for, and suggested the solution to the mystery. The extra notes must have been played by someone (probably George Martin, the producer), on piano.

Fourier Series are used to encode the MP3s that you listen to all the time. You can read an overview of the process: Application - The Fast Fourier Transform

Now to this week's video. The Melodyne products allow you to split a piece of music into its component parts and change those parts, either by changing speed - known as "tempo" in music - or pitch, or to change the melody itself. This would mean a musician would only need to record a piece of music once and thousands of other pieces of music could be derived from that one recording.

The developer of the Melodyne explains with examples how the software works. This is how they analyzed the Beatles' song and realized notes exist in the chord that were not actually possible with 3 players only.

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