The opening chord of the Beatles song “A Hard Day’s Night” has been something of a mystery. Guitarists have tried to reproduce the chord with limited success. Turns out there’s a good reason why they haven’t figured it out: the chord cannot be played on a guitar alone.

Jason Brown has digitally analyzed the chord using Fourier analysis and determined that there must have been a piano in the recording studio playing along with the guitars. Brown has determined what notes each member of the Beatles were playing.

I heard Jason Brown’s story on the Mathematical Moments podcast. In addition to the chord discussed above, Brown talks about other things he has discovered about the Beatles and about the relationship between music and math in general. Unfortunately, Mathematical Moments does not make it easy to link to individual episodes. Here is a link to a PDF file of show notes with the audio embedded. The file is slow to download, and your PDF viewer may not support it. Here’s a link directly to just the MP3 audio file.

The Mathematical Moments podcast also does not make it obvious that you can subscribe to the podcast; they only provide links to individual episodes with fat PDF files. However, you can subscribe by using the URL http://www.ams.org/rss/mathmoments.rss.

**Update**: Here’s a paper that goes into some details.

Thanks a million for the podcast :)

By the way, there are plenty of interesting math talks on iTunes U (U for the University). For example:

Infinity – Mathematics

Maths as others see it

Maths Challenges

The Rainbow analysed

The sound of silence

Sounds Harmonious

Spotlight – Public Lectures (not entirely about the math, but there is one talk about “Structure and Randomness in the Prime Numbers”)

MaJJ, thanks for the list of math podcasts. Here’s another math podcast: Peter Rowlett’s Travels in a Mathematical World.

It’s imtresting that Jason should go to all that trouble, and he may be right about the piano, but what I reckon is being played is indeed not one instrument but THREE. I always played the opening chord as a sort of F9, but listening back on the new stereo remaster version, I hear a Gsus (probably open, on John’s Gibson acoustic, an F9 on what sounds like a Rickenbacker 12-string as used in the film, and Paul’s bass plays a D to confuse things even more. That first chord is hit really hard, which would lead to a piano-like envelope. So add another theory to the mix.

A really interesting set of posts. Keep ’em coming!

I am surprised to learn that such a prominent chord in a top song from the most famous pop group ever has resisted analysis until now. The Boys have managed to intrigue and puzzle us for more than four decades.

Sounds like someone slapping a spring reverb to me. You could get all sorts of harmonics, subharmonics and intermodulation distortion out of that.

You needn’t “put up” with poorly-portable PDFs. If desired, I’ll happily re-render the documents so that they look the same on a wider range of viewers.