Shepard Tone — Endless Illusion
Hear the Shepard tone endless pitch illusion rise or fall forever with octave-stacked glides. Famous film-tension effect. Free in your browser, no download.
Protect your hearing. Start at a low volume. Never raise the volume to make a tone audible. Levels are shown in dBFS, relative to full scale — not SPL.
How it works
Octave-spaced sinusoidal oscillators glide continuously while shaped by a fixed raised-cosine spectral envelope. As top partials fade into silence at high frequencies, sub-bass partials smoothly fade in at the bottom, creating an unbroken ascending or descending pitch illusion.
The Shepard Tone is the acoustic equivalent of the visual Barberpole illusion or M.C. Escher’s infinite staircase (Ascending and Descending).
How the Psychoacoustic Illusion Works
Human pitch perception relies on two distinct dimensions:
- Tone Chroma (Pitch Class): The position of a note within an octave (e.g. C, D, E, F, G, A, B).
- Tone Height (Octave Register): The absolute frequency altitude (e.g. C1 vs C4 vs C8).
In natural musical instruments, as a note goes up in chroma, its absolute pitch height simultaneously rises.
A Shepard tone breaks this link:
$$\text{Gain}(f) = 0.5 \left(1 - \cos\left(2\pi \cdot \frac{\log_2(f / f_{min})}{\log_2(f_{max} / f_{min})}\right)\right)$$
By simultaneously sounding 6 to 9 octaves beneath a stationary bell-shaped raised-cosine spectral envelope, the tone chroma clearly glides continuously (e.g. +1 semitone per second), but the aggregate spectral centroid of the sound remains perfectly stationary at the center frequency (~500–800 Hz).
When any high harmonic reaches 18–20 kHz, its amplitude is already zeroed out by the spectral envelope. At the exact same time, a new sub-bass harmonic at 20–30 Hz smoothly rises above silence. Because your auditory cortex tracks the prominent mid-frequency motion, your brain perceives continuous, uninterrupted ascent.
Frequently asked questions
What is a Shepard tone?
A Shepard tone, invented by cognitive scientist Roger Shepard in 1964, is an auditory illusion created by superimposing octave-separated sine waves whose overall spectral amplitudes are shaped by a fixed bell-shaped envelope. As the pitch glides upward or downward, higher components fade out into inaudibility while lower components quietly emerge, creating the psychoacoustic impression of an endless scale.
What is the difference between a Shepard scale and a Shepard-Risset glissando?
A Shepard scale shifts pitch in discrete musical semitones (like a keyboard stair-stepping upward indefinitely). The Shepard-Risset glissando, pioneered by French composer Jean-Claude Risset, glides frequencies continuously, generating an unbroken infinite glissando without audible discrete step boundaries.
Where is the Shepard tone used in cinema and popular culture?
Film composer Hans Zimmer famously used the Shepard-Risset glissando in Christopher Nolan's films 'Dunkirk' and 'The Dark Knight' to manufacture relentless psychological tension and an escalating sense of impending doom without the audio running out of pitch range. It is also famous as the infinite staircase theme in Super Mario 64.