◴ Artificial Wasteland · the physical seam
A pitch that rises forever and arrives nowhere — the auditory Escher staircase. You will hear it climb without end. Then watch the one number that gives the trick away: while the note seems to ascend through octave after octave, its true height never moves a hair. Press play; let your ear be fooled; then catch the lie in the spectrum.
Some tricks of the eye have an exact twin in the ear. The Penrose stairs that climb back to where they began; the barber's pole that rises endlessly while staying still — both have a sound.
Press play. The tone climbs, step after step, octave after octave. Wait. It is still climbing — and it has not gone anywhere. It cannot run off the top of your hearing because it never actually leaves the middle. This is a real signal, not a recording looped behind your back: it is being built right now in your browser from a stack of pure tones, and you can watch it being built in the next panel.
↳ headphones or decent speakers help — the illusion lives in the low and high partials at once. The sound is user-started and never autoplays.
Stepped is the classic Shepard scale: discrete semitone steps, like a staircase. Gliding is Jean-Claude Risset's continuous version (1969) — the same trick with the steps filed off, a single tone sliding up a banister with no end. Set it descending and it falls forever instead, a useful thing to do to a room.
Here is the whole machine. A Shepard tone is not one frequency — it is a comb of pure tones spaced exactly one octave apart (20 Hz, 40, 80, 160, … each double the last). Over that comb sits a fixed bell-shaped envelope — the glowing curve below — that decides how loud each partial is: loudest in the middle of your hearing, fading to silence at the top and bottom.
When the tone "rises," every partial slides up together (watch the bars drift right while the bell stays put). A partial that climbs past the top of the bell fades to nothing exactly as a new one fades in at the bottom. The comb is forever sliding; the bell never moves.
The number on the right is the catch. Pitch height — what your brain reports as "how high" — is the loudness-weighted average frequency of the whole comb (its spectral centroid). Because the bell is fixed and the partials are evenly spaced an octave apart, that average is a constant. The page measures it live: it does not move. The pitch you hear "climbing" has a height pinned to within a ten-billionth of a cent — far below anything an ear could resolve. You are hearing rise, and there is no rise. The verifier proves the centroid is constant ↗ over a full cycle.
Shepard's insight (1964) was that pitch is not one thing but two, and they can be pulled apart. There is height — the plain "low-to-high" dimension, a straight line. And there is chroma — pitch class, the quality that makes every C sound like a C whether it is a rumble or a shriek. Chroma is a circle: walk up twelve semitones and you are back where you started, one octave on, the same note again.
Put them together and pitch is a helix — a spiral staircase, climbing (height) as it turns (chroma). Ordinary notes move along the helix, so the two cues agree: turn and climb together. A Shepard tone flattens the helix into its circle. By spreading the energy across every octave under a fixed bell, it erases the height cue and leaves only the turning. And a circle has no top. Your ear, given only "which way round the circle," reports endless ascent — because going round is the only motion left, and round always looks like up when up is all you are asked about.
the helix of pitch — climb (height) while turning (chroma); flatten it and only the turning is left
Now the strangest turn. Play two Shepard tones in a row, a tritone apart — exactly half an octave, six semitones, the interval old theorists called diabolus in musica. On the chroma circle the two tones sit at opposite poles. Neither is "higher": they have identical height (the verifier confirms the pair is level to a trillionth of a cent). So which way does the pair move — up, or down?
Your ear will answer with total confidence. The catch, found by Diana Deutsch in 1986: different listeners hear it differently, and each is consistent — and which way you hear it correlates with the language and dialect you grew up speaking (Deutsch, 1991). The signal contains no answer. The answer is built into you.
Run it a few times. If you are like most listeners you will keep hearing the same direction even though each pair is a fresh, randomly chosen tritone — that consistency is your own internal map of pitch classes showing through. The page is not withholding the right answer. There isn't one. That is the paradox.
The illusion is not a lab curiosity. The endless-rising tone is a working tool of dread: Hans Zimmer built it through the whole score of Christopher Nolan's Dunkirk (2017), fusing it to a ticking watch so the music seems to tighten without ever resolving — Zimmer has described the device explicitly in interviews, and the same trick threads his earlier Nolan scores. Game composers have used the rising-forever tone for staircases that can't be climbed; sound designers reach for the falling version when something must seem to drop without end.