Archive for the ‘Beatles’ tag
It’s been a Hard Days Night
How can technology aid scientific discovery? We’ve covered on Bench Press examples such as providing the computing power needed to simulate particle physics and using cosmic muons to scan Mayan temples. But what about something closer to home – like figuring out what the “infamous” opening chord in the Beatles classic “A Hard Days Night” is?
As you probably guessed from the fact that I’m writing this, the answer is yes.
Professor Jason Brown of Dalhousie University applied a technique called Fourier analysis to the problem at hand. Fourier analysis is useful for decomposing a particular waveform into the fundamental frequencies which make it up. Or, to put it more commonly, it lets you take a waveform (like a particular sound) and figure out what all the underlying frequencies are which make it up.
The concept of Fourier analysis has been around at least as early as the 1800s when Jean Baptiste Joseph Fourier used the concept to explore heat propagation. However, the lack of computers made the technique unwieldy for exploring real world analog data. This problem was addressed with the development of programs and integrated circuits adept at deploying a numerical approximation of Fourier analysis called the Fast Fourier Transform (oftentimes abbreviated FFT) which has made an entire realm of sophisticated analyses possible and relatively simple to do.
What Brown did was very elementary. Using a digital recording of the Beatles classic and the widely available program Mathematica, he broke down the opening “twang” into the 29375 frequencies that made it up. He then applied a filter (to filter out harmonics and background noise) to pick out the 48 most important frequencies and compared them to popular “estimates” of what was played.
What Brown found was that most popular guesses of the opening were wrong as they assumed the Beatles had played the G2 note (where C4 is “middle C”) which didn’t show up at all in his Fourier analysis. But, using information about what instruments the Beatles played (which gives you information like knowing that pianos make 3 distinct frequencies due to the hammer hitting 3 strings simultaneously), Brown deduced what countless enthusiasts have guessed at for over 40 years. Without further ado, the opening sound to “It’s a Hard Day’s Night”:
Awesome.