Stack notes exactly an octave apart and fade the top and bottom under a fixed loudness curtain. Slide them all up together and the pitch seems to climb — but the whole pattern is the same every octave, so it climbs FOREVER without ever getting higher (the audio version of Escher’s endless staircase, and the ‘dun-dun-dun’ tension in film scores). Slide the step and watch the partials loop.
A Shepard tone is a set of sinusoids spaced one octave apart (frequencies f·2ⁿ) whose amplitudes follow a FIXED bell-shaped spectral envelope. Shift every partial up by a semitone and each rises, but a new one fades in at the bottom and the top one fades out — after 12 semitone steps (one octave) the set of frequencies is identical to the start. So the spectrum is periodic in octaves while the ear, tracking the moving partials, hears an endless rise. A fail-loud self-check throws unless the partial set at step 0 equals the set at step 12. ◆ real psychoacoustics/physics, node-verified.
The spectral construction is exact (octave-spaced partials under a fixed envelope, periodic mod 12); the ‘forever rising’ is a perceptual reading of that periodic spectrum — the illusion, honestly a figure over exact physics. (Silent here: the geometry is shown, not synthesized.)