Shepard Tone (Auditory Barber Pole)

A scale that never arrives

Before you start, please turn your volume down a little; headphones work best. Press play in the demo and a scale starts climbing. You'll expect it to run out of room and either stop or drop back down, as any real scale has to. It doesn't. It keeps rising, step after step, with no point where it obviously starts again, and if you leave it looping the climb goes on for as long as you care to listen.

No single tone could do that, because pitch can't rise forever. The trick is that you aren't hearing one tone at all, and the chart I've added to the demo shows you the parts.

Many tones under a fixed spotlight

A Shepard tone is a stack of pure tones, each one an octave above the next (exactly double its frequency), all rising together. What makes it work is the loudness. A fixed bell curve sets how loud each tone is allowed to be depending on its pitch: tones in the middle of the range are loud, and those near the top and bottom are almost silent. As the stack rises, each tone climbs out of the loud middle towards the quiet top and fades away, while a new one fades in at the quiet bottom and begins its own climb.

Your ear doesn't follow each tone separately. It hears the combined sound, which always has its loudest part somewhere in the middle and always moving upwards. The hand-over between a tone leaving at the top and a new one arriving at the bottom happens where both are too quiet to notice. In the stepped version, after twelve steps every tone is back exactly where it began, so the sound is literally identical to where it started, and yet each step along the way sounded like a step up.

The Penrose stairs do the same thing in pictures. Each step is believable on its own, and the impossible part is spread around the whole loop, so there's no single place you could point to.

Why it's called the auditory barber pole

The nickname compares it with the barber pole illusion, where the stripes on a spinning cylinder seem to travel endlessly upwards. In both cases, something that goes round in a cycle (a turning pole, or a bank of tones fading in and out) is perceived as continuous movement in one direction, because perception follows the local motion and misses the fact that the structure loops back on itself.

Pitch has two dimensions

Roger Shepard described the effect in 1964 while he was working at Bell Labs. He used it to show that musical pitch has two separate components: chroma, which note it is (C, D, E and so on, repeating every octave), and height, how high or low it sounds overall. A Shepard scale keeps the chroma moving while removing any stable sense of height, so you hear the note changing in one direction without it ever getting anywhere.

The composer Jean-Claude Risset later made a continuous version that glides instead of stepping, now known as the Shepard-Risset glissando. You can choose either one in the demo, and set it rising or falling. The psychologist Diana Deutsch went on to find related pitch illusions that different listeners hear differently, depending partly on the language or dialect they grew up with.