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The Mathematics of Music - Part 2 / 3

I personally coin this technique "pattern overlapping". Let's take a look at how Radiohead use it!

Example One - Radiohead - Let Down

Let's take a look at the first minute of a Radiohead song from their album "OK Computer". This is track 5 - the song is called "Let Down". Please take a listen to the first 60 seconds and then continue reading:

So how can we describe this music? Let's forget about the lyrics and focus solely on the instrumentation. Well it instantly sounds very melancholic - it gives you a feeling of hopelessness and despair. There is just something about that endless guitar riff in the background that makes you feel that... you don't have control and you'll never win. It's very difficult to explain why that repeating pattern in the background is so effective, don't you think?

There is actually a very simple and clever musical technique that's being used in this case, and I absolutely love it. I like to call it "pattern overlapping". I'll also point out another piece of music later on where a very similar thing is done.

Well what on earth is this lunatic dribbling about, I hear you ask?! How best to explain... Well... The very high majority of western music uses a simple time signature in music where 4 beats forms what's known as a "bar" and between 4 to 16 "bars" form what's known as a "phrase". A "phrase" marks the point of repetition - the point where the different chords have been played, and are ready to loop around again. A phrase-ending is also usually the point where the music is ready to transition from a verse to a bridge or from a bridge to a chorus. And very often your melody, harmonies and riffs fit into that structure as well. They repeat (perhaps albeit with slight variety) when the phrase repeats.

Pattern overlapping is a technique where the musical pattern or riff doesn't quite match the time signature of the piece - meaning that it takes many iterations of the piece's rhythm before the riff fully re-aligns again. So when those bars and phrases are ending and repeating, the riff is not ready to do the same. So it simply just carries on and ignores everthing else, and eventually by the laws of mathematics it will align again at some point! This technique is so powerful in a song such as Let Down, because it's combined with the sound of the atmospheric guitar and the minor tone of the notes. So the pattern just completely washes over you, and your mind never gets that standard, structured sense of when it will end and how it will align with the music. That's how the feeling of hopelessness is magnified!

Allow me to graphically represent what I mean here. By ear, I have put together my own interpretation of the sheet music. Firstly, watch this video to see the playback of my sheet music. This will help to understand what notes play when! I've also annotated it to re-assert the things I will be talking about:

Now, take a look at the music for the bass (bottom stave) at the time that the bass-line kicks in (point 00:16 in the playback video). We can see here that the bass riff fits into 4 bars and repeats, for the purpose of introducing the bass-line. After the bass-line introduction, the bassline becomes instrumental (no pun intended!) in defining the chord progression for the verse.

Now, see point 00:45 in the playback video. 4 bars for the first chord, 4 for the 2nd, 4 for the 3rd and 4 for the 4th - making 16 bars in total that repeat, providing the structure of the music. As I've mentioned, having things fit into 4s and 16s is very standard and common in western music - and we would usually expect the melodies and harmonies to conform to this as well... but do they in this case?

Well from the graphic above (and by listening), we can hear the melody (vocals, 3rd Stave from the top) does match-up with the bassline. The pattern of the melody stays in sync. Standard. So now let's take a look at the main guitar riff in the background (2nd Stave from the top). This is the riff that repeats from the very beginning of the song. Let's check it out at the start of the video.

Well... This riff takes up FIVE bars of music (not 4!) And it simply just repeats over and over again. So every time you hear that bass-line and the melody starting a new "4" pattern, you're going to be hearing a different starting note of the guitar riff. After 20 bars have elapsed (5 x 4), you'll hear them start together once more before they start to mis-align again. To make matters more confusing, that main driving bassline (after the initial introduction - so from 00:45 onwards) actually begins at bar 20. It would need to start at bar 21 to actually start at the same time as the guitar riff. So it starts 1 bar before the main guitar riff has actually finished... So it's always 1 bar out as well!!

Hopefully watching the video a few times helps to clear up what I'm talking about. That mis-alignment is so critical to the feeling that you get from listening to the song :)

I hope you've enjoyed Part 2 / 3 of this article! Please keep your eyes open for Part 3 coming soon, where we'll take a look at how this technique is used similarly. Of course, we will be looking at Interpol :)

Thomas.

See also:

Posted on April 22nd, 2017

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Thomas

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Comments (1)
Decl
I don't understand anything about music nor the science behind it, but it was a nice read nonetheless Thumbs up for actually creating a video and analyzing a song so closely!
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With a name inspired by walking through the autumn countryside, Underneath the Sycamore generally represents artists that express themselves through calm and introspective music.

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