Perception · about 3 minutes
The Shepard Staircase
A sound that rises. Keeps rising. Goes on rising for as long as you are willing to stand there, without ever arriving anywhere, and without -- this is the part your ears will refuse -- ever actually getting higher.
Before we start. This room plays a continuous synthesised tone at moderate volume; set yours low first. It is genuinely unsettling to some people after a while -- that is the effect working, not a fault -- and there is a stop button that always works. If sound isn't available to you, the picture below tells the same story silently and the explanation needs no ears.
Press play and listen for at least twenty seconds. Try to hear where it stops rising, or where it jumps back down to start again. Neither of those things happens.
Silent
The trick, which does not help
The picture above is now labelled. There is not one tone climbing -- there are six, spaced an octave apart, all sliding upward together. And there is a fixed loudness window sitting over the whole range: quiet at the bottom, loud in the middle, quiet at the top.
As the highest tone slides up into the top of the window it fades to nothing and is gone. At the same moment a new tone fades in at the bottom, an octave below everything else, where you cannot hear it well enough to notice it arriving. The pattern of pitches is exactly the same as it was one octave-crossing ago -- the whole thing has looped -- and no part of your hearing is willing to report that.
It is the barber's pole. Stripes going round a cylinder, read by your visual system as stripes going up forever, because the place where the truth is revealed has been carefully hidden at both ends.
Now play it again, knowing all of that.
Pitch is two things pretending to be one
The illusion works by prising apart something you have always experienced as a single quantity. Musical pitch has height -- how shrill a sound is overall -- and it has chroma, its position in the twelve-note cycle: every C is a C, whether it is played by a piccolo or a tuba.
Ordinarily those two rise together, so you never notice they are separate. Roger Shepard's tones, from 1964, hold the height constant -- that is what the fixed loudness window does -- while letting the chroma cycle upward forever. Your hearing has no procedure for that situation, because in the world that made your hearing it never once came up. So it reports the thing it always reports when chroma climbs: higher.
Jean-Claude Risset later did it with a continuous glide instead of steps, and then did it again with tempo, producing a rhythm that accelerates permanently. If you have watched a Christopher Nolan film you have heard both, holding a scene at a tension that never resolves because it structurally cannot.
Why the explanation changed nothing
You now know precisely how the trick works, and it still rises. That is the interesting bit, and it is a feature of a whole class of illusions: they are cognitively impenetrable. What you know sits in one part of the system; what constructs your experience sits in another, and it is not taking notes from you.
Compare the room you just left. In Exhibit № 4 you also could not override your perception by deciding to -- the cube flipped when it wanted. And in Exhibit № 31 you will meet the opposite case: a sound that changes permanently the moment you are told one fact about it. Some doors open to knowledge and some are welded shut, and there is no way to tell which from the inside.
That asymmetry is worth carrying around. It means "I know better" is not a reliable defence against a misperception -- sometimes it is a complete one, and sometimes, as here, you can hold the truth clearly in mind and go on hearing the lie for as long as you care to listen.
Take it further
Roger Shepard published the tones in 1964; Jean-Claude Risset made the continuous version and the accelerating-rhythm cousin. Diana Deutsch's work on auditory illusions is the best onward reading and includes the tritone paradox, where the same pair of Shepard tones rises for one listener and falls for another, apparently depending on the language they grew up speaking -- which is a rather large thing for a pair of notes to know about you.
One honest note about ours: real Shepard tones are usually built from carefully weighted harmonic stacks. Ours is six plain sine waves under a Gaussian window, synthesised live because this museum ships no audio files. It is a slightly cruder staircase than the classic recordings -- if the climb feels weak, try headphones, or the versions on Diana Deutsch's site.