Fourier and McCartney

Here’s a long but fascinating post on deciphering the opening chord in A Hard Day’s Night. Along the way it gives a good explanation of Fourier transforms for the non-mathematician.

It also gives a really good example of why it’s important to look at the overall reasonableness of a result, rather than blindly relying on the maths. Summary of this bit: somebody ran a Fourier analysis on the chord, assumed that the loudest frequencies were the fundamentals, and came up with the following notes:

  • Harrison (electric 12 string guitar): A2 A3, D3 D4, G3 G4, C4 C4
  • McCartney (electric bass guitar): D3
  • Lennon (acoustic 6 string guitar): C5
  • Martin (piano): D3 F3 D5 G5 E6

But why would Lennon play only one note? It was meant to be a dramatic opening, give it all you’ve got. Single notes just don’t cut it.

This observation led to a realisation that the assumption that the loudest frequencies were the fundamentals was flawed. Record producers often fiddle with the frequencies, and in this case it appears that the bass frequencies were turned down.

There’s lots of other interesting stuff in the post about how the author went about his detective work, and what really hits home to me is the variety of techniques he used. The moral of the story is to use all the information at your disposal, not just the maths.

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