Shepard Tone & Auditory Illusions — Pitch Without End

How the illusion is built

A Shepard tone isn't a single frequency — it's a stack of pure sine waves, each exactly an octave above the last (110 Hz, 220 Hz, 440 Hz, 880 Hz, and so on: fₖ = f₀·2ᵏ). The trick is in the amplitude envelope: rather than equal loudness, each partial is weighted by a fixed bell-shaped curve plotted against the logarithm of frequency, loud in the middle of the audible range and fading toward silence at both extremes. Because the envelope stays put while the partials slide through it, no single component ever dominates for long — as a rising partial drifts into the loud centre, another quietly vanishes at the top edge, and a fresh one materialises at the bottom. The spectrum keeps renewing itself while its overall shape stays fixed, which is the entire trick.

Partial frequency:  f_k = f_0 · 2^k
Amplitude envelope: A(f) = exp( −(log2(f) − μ)² / (2σ²) )
  μ = envelope centre (log-frequency), σ = envelope width

Why the brain is fooled: pitch height versus chroma

Human pitch perception isn't one-dimensional. Psychoacousticians split it into pitch height — the general sense of high or low — and chroma, the quality that makes every note called "C" sound related regardless of octave. A Shepard tone deliberately keeps chroma in motion while holding the spectral centre of gravity fixed, so the ear tracks the shifting chroma and reports "rising" with no fixed anchor to notice that absolute spectral energy never actually moved. Picture pitch as a helix: height climbs the central axis while chroma is angular position around it — going once around returns you to the same chroma an octave higher. A Shepard tone keeps you circling the helix without ever climbing the axis, so perpetual rotation is perceived as perpetual ascent, and because octave-related tones sound strongly similar, the substitution of a vanishing top partial for a reappearing bottom one is seamless.

From the lab to the cinema

Named after cognitive scientist Roger Shepard, who described the effect in 1964, the tone has a continuously gliding cousin — the Shepard-Risset glissando, created by composer Jean-Claude Risset using a smooth frequency sweep instead of discrete steps. Film composers use the never-ending rise to sustain dread and momentum (the technique is closely associated with Christopher Nolan's scores), video-game designers deploy it during chase sequences to imply endless escalation, and psychoacoustics courses use it as a standard demonstration that pitch height and chroma are processed separately. A related effect, the tritone paradox studied by Diana Deutsch, plays two Shepard-tone-style sounds a tritone apart — whether a given listener hears the pair as rising or falling differs from person to person, apparently tied to their native language and regional speech patterns, showing that perceived pitch direction is partly an inference the brain makes, not a fact read directly off the air.

Frequently asked questions

Try it live

Everything above runs in your browser — open Shepard Tone, press play, and watch octave-spaced partials slide endlessly under a Gaussian envelope while the pitch seems to climb forever. Nothing is installed, nothing is uploaded.