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The Mathematics of Music - Part 3 / 3

The final part of this article - we take a look at Interpol with "pattern overlapping"!

Example 2 - Interpol - Take You on a Cruise

Let's talk about another example. This one comes from Interpol's album "Antics". It's track 4 - called "Take you on a Cruise". The best Interpol song ever, and you're about to find out why! Please listen to the song from 3:25 onward until the end of the video:

Again - I've provided another video of sheet music I put together for this section by ear. Please give it a watch and then continue reading!

Now, this one is a bit more simple to talk about. Everything that you see on the stave is aligned to the 4x4 rhythm of the song - except for one instrument - the second guitar playing the long, almost mournful, notes.

The first guitar that plays these notes starts at point 00:19 in the playback video. The second guitar starts at 00:29. (They are both marked as "Violin", but that's only so I could get the most appropriate midi sound from the playback device!)

Now then, I have marked the first guitar (at the very bottom of the stave) with yellow highlights. You will see that each of the yellow highlights represents 4 bars. These 4-bar highlights match precisely with the 4 bar rhythm of the song, without any overlap. The same 4 notes repeat over and over again. The second guitar (above the first one) is marked with lines and hand-written comments. These lines actually represent 5 bars, instead of 4. The same 5 notes repeat over and over again.

So we now obviously have a similar situation to Radiohead's Let Down. Both guitars start playing together at bar 13. Because one is playing 4 notes in 4 bars and the other is playing 5 notes in 5 bars, we need to wait 20 bars of music (5 x 4) before they re-align again. The guitar that plays 5 notes in 5 bars starts becoming out of sync with the rest of the music - the result is that you hear a different pairing of guitar notes for 20 bars of music... That's almost the entire length of this final section of music! By the time they have re-aligned again, the rest of the music (mainly the bass and vocals) have developed so much since then that it still feels completely fresh, as the song comes to a climax.

It's so simple to execute, yet incredibly effective! You have the constant feeling that you're hearing the same notes over again, but they somehow always sound different. This contributes to that feeling of being on a cruise, out in the great wide open sea. Did you ever go on a Ferry, and simply stand out on the front or back and watch the endless open stretch out in front of you? That's this song. It's a lonely almost despondant feeling. No sight of when the journey will end or repeat - just embracing the journey that you're on, wondering what's next. That's what a slight lack of structure can do. That's why pattern overlapping works!

To be fair, I think the playing style and the sound of the long guitar notes (which don't sound too dissimilar from the foghorn on a cruise ship) is actually what's mainly providing that feeling. But the lack of synchronisation in the guitars (and therefore the variation in paired notes) is definitely a strong contributing factor.


At it's very core, music is certainly mathematical. But that concept is so often masked away from us, the listeners. Generally, what we understand is that it sounds good or bad! There are endless techniques and variations / combinations of techniques that make us feel emotional about the music we listen to. My hope is that this article has enlightened you to one quite rare, very simple and very effective technique - "pattern overlapping". It's important to note though... like with the example of the Star Trek episode "Human Error" that I discussed earlier - that the mathematics and techniques alone are simply not enough! What truly makes the music special is the soul and our own unique interpretations.

As a music enthusiast and composer, I tend to naturally be drawn to try picking these things out of most music I listen to. If you've taken the time to read this entire article (geez! good job!), then you might even like doing the same. Just take care that it doesn't detract you from the overall enjoyment of music - perhaps the mystery of why something is so good is better than trying to understand why :) I guess the same thing could be said for analysing paintings.

But! If you do like what you've read and find it interesting - see if you can pick it out in other songs! Let me know what you've found - I'd love to hear about it.

This is Thomas - signing out.

Posted on April 29th, 2017

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Comments (1)
Very interesting read, Thomas, thanks for sharing I still know nothing about music but I guess I learned a thing or two
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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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