The Dunkirk Soundtrack is Way Cleverer Than You Think.

(Contains spoilers.)

I went into Dunkirk with high expectations for the score. Whenever Christopher Nolan and Hans Zimmer collaborate you know you can expect big things, and this time in particular everyone had been raving about Zimmer’s use of something called the Shepard tone, a way of ratcheting up tension seemingly endlessly. Given the incredible intricacy behind the music in the their previous work together like Inception (more on that later), I doubted the hype was unjustified.

But it turns out the score for Dunkirk is on a totally different level – and, though its genius starts with the Shepard tone, it goes way, way beyond it.

What is the Shepard tone?

The Shepard tone, or Shepard scale*, is a way of making it sound like a musical pitch is perpetually rising. The way you achieve this is by stacking several ascending scales on top of each other, each separated by an octave, and, as the scales progress, fading the higher notes out and the lower notes in. This way, you can make it sound like you’re endlessly rising up the scale, without the listener noticing the shifts in octave. (It works because our brains perceive notes an octave apart as versions of the same pitch.)

A visualisation of a Shepard scale: the green and yellow notes are louder than the purple notes.

Given that an ascending scale is a good way of building tension, and the Shepard scale gives you an endlessly ascending scale, you can see why Nolan and Zimmer decided to use it in Dunkirk. And we know they did because Nolan revealed as much in an interview.

However, he didn’t provide any details as to how exactly they’d used it. Which it turns out is an easter egg of vast proportions.

Nolan and Zimmer have a history of depicting time musically.

These two like their scores to be woven into the fabric of their narratives much more than is traditional. And Inception is — or was — the prime example of this.

One of the central conceits of Inception is that time passes more slowly in dreams, getting progressively slower as you descend ‘dream levels’ — that is, as you enter dreams within dreams.

There are two bits of music in Inception that, on first listen, sound entirely unrelated: the Edith Piaf song Non, Je Ne Regrette Rien, and a doom-laden theme in the trombones that has all the hallmarks of Zimmer’s orchestral writing.

It was pretty astounding, then, when people realised that Zimmer had captured the idea of time passing more slowly in dreams in his music: the trombone theme is the passage from the Edith Piaf song, just played much slower (which also serves to shift its pitch down to the bass register). They’re one and the same piece of music, on different timescales.

The music, then, is far more intricately bound up with the narrative than you initially thought, or than any regular composer would settle for.

But this was just a warm-up for what was to come in Dunkirk.

Zimmer’s Shepard Scale

The way people had been talking about the Shepard scale in Dunkirk, I was expecting a continuous rising pitch, pretty much permeating the entire score — think an ever-rising siren. It turns out its use is much more limited, and the pitches Zimmer uses are, for the most part, discrete: a rising diminished scale.

The rising diminished scale used in Dunkirk

This rising diminished scale is used in various places throughout the score, and adds to the rising intensity of the film even before it’s stacked on top of itself and turned into a Shepard scale.

But the stacking — the Shepard scale — isn’t the clever bit.

Three stories, on three different timescales, building to the same point.

One of the most surprising — and, I think, effective — features of Dunkirk is its structure: three separate stories, following three different groups of people, on three different timescales, all building to a single, simultaneous climax. As a reminder:

  1. The soldiers escaping the beach (spans 1 week)
  2. The men on the boat (spans 1 day)
  3. The pilots (spans 1 hour)

These stories are interspersed so that you’re constantly jumping around in time, with the jumps getting smaller and smaller as the film approaches its ending, building to a climax where all three groups, and stories, meet.

We know from Inception that Zimmer likes to represent structural aspects of a film, particularly those that relate to time, in his music. And that’s exactly what he does in Dunkirk.

Three Shepard scales, on three different timescales, building to the same point.

At the film’s climax — the meeting of the soldiers, the boat and the pilots out at sea in a fiery wash of oil — it’s not just that Zimmer uses a Shepard scale to build tension. He uses three of them, on three different timescales but playing at the same time, to represent the three stories portrayed in the film, all building to a climax at the same point.

Here’s a simplified transcription of what’s going on:

- The Oil, from 3:40

He loops this structure throughout the scene, doubling octaves to get the Shepard scale effect. The bottom part is playing the rising scale really slowly; the middle part is playing the same scale at double speed; and the top part is playing the same scale at quadruple speed.

So Zimmer isn’t just using the Shepard scale to build tension. He’s using three simultaneous Shepard scales, on three different timescales, to build tension in three storylines that are moving at different paces. The bottom part represents the week of the soldiers; the middle part the day of the men on the boat; and the top part the hour of the pilots. All start in different places, but build in intensity to the same point.

In short, he’s taken the idea of the Shepard scale, and applied it to the unique structure of Dunkirk. And the result is amazing.

Have a listen from 3:40.

* The Shepard tone and Shepard scale are actually different things, but I thought it would make this post easier to follow if I treated the two concepts as one. If you’re interested in the difference between them, here you go:

  • A Shepard tone is a tone in which all the frequencies present are separated by an octave, unlike the kinds of tones we’re used to, which have more complex frequency relationships. This aspect of Shepard tones makes it hard to tell which octave is the tone’s fundamental frequency (ie. what its pitch is). The volume of the frequencies are centred around a middle frequency, tapering off at the high and low ends of the spectrum.
  • A Shepard scale is what you get when you make an ascending (or descending) scale of these Shepard tones. Because of the difficulty in identifying the precise pitch of each Shepard tone, and the fact that the frequency around which the volumes are centred is kept constant, it sounds like the scale is constantly rising (or falling).