There's a tone that seems to climb endlessly, like a staircase that loops back on itself — the audio version of a Penrose staircase. It's why the Dunkirk score makes your chest tighten, why Super Mario 64's endless stairs never end, and it fools nearly everyone who hears it.
The foundation: a stack of sine waves spaced an octave apart, first described by cognitive scientist Roger Shepard in 1964. As the top notes fade out and new bass notes fade in, the pitch seems to rise without end.
A guided tour of where you've already heard it without knowing — The Dark Knight, Dunkirk, the Joker's cello, and the infinite staircase in Super Mario 64.
The producer's-eye view: exactly how the octave layers and amplitude envelopes are stacked so the ear never catches the loop point. You can build one yourself.
Vox's classic explainer on why Christopher Nolan is obsessed with Shepard tones — and how Hans Zimmer built a whole score around a trick played on time itself.
Hear it isolated: the rising diminished scale threaded through the Dunkirk score, so you can catch the illusion doing its work in real time.
How Zimmer wove the illusion through the film: 'It's the idea of eternity and endlessness... the idea of playing a trick on time itself.'
The science of why it unsettles you: a study finds the endless glissando triggers a 'feeling of falling,' with 87.6% of listeners rating the loss of equilibrium as unpleasant.