A staircase that never ends
In 1964 the psychologist Roger Shepard built a curious sound on a computer. Each tone was made of many pure tones exactly one octave apart: for a C, the Cs of every octave sounded at once. Their loudness followed a fixed, bell-shaped curve, so the middle components were strong and the lowest and highest ones too faint to hear.
When Shepard played these tones one after another in semitone steps, listeners heard a scale that kept rising. Yet after 12 steps the sound was exactly the same as where it started. Looped, the staircase seemed to climb forever. A few years later Jean-Claude Risset (1969) applied the same principle to a sound that glides continuously instead of in steps. Round 2 of this experiment is a copy of Shepard's staircase.
Note name and octave: two kinds of height
A musical note has two separate properties. One is its name: C, D, E and so on. This is called the pitch class, and the 12 classes form a circle like a clock face: after B comes C again. The other is its height: the same C can be sung by a deep bass voice or played on a violin's highest string. In everyday sounds the two change together and we simply hear a 'higher' or 'lower' sound.
Shepard's tones separate them. Because the components always stay under the same envelope, the sound never really gets thinner or deeper; only its name changes. Step by step, the ear picks the shorter path between neighboring tones each time: from C to C♯ is one step up, and from B to C is also one step up. Nothing tells the ear that it has dropped an octave on the way from B to C. That is why the staircase never ends.
The ambiguity of half an octave
If the ear judges the direction between two Shepard tones by the shorter path around the circle, a curious gap remains. Two notes facing each other across the circle, such as C and F♯, are six semitones apart both ways. This interval is called the tritone, or half an octave. Clockwise and counterclockwise are equally far, so the shorter-path cue says nothing.
A reasonable guess is that such pairs would be heard at random: sometimes rising, sometimes falling. In 1986 Diana Deutsch showed that this is not what happens.
The tritone paradox: one pair, two opposite answers
Deutsch's listeners did not hear tritone pairs at random. Each listener answered consistently depending on which notes made up the pair: some pitch classes always sounded higher, and those on the opposite side of the circle always sounded lower. It was as if the pitch circle in their head had a peak. More surprising still, the peak differed from person to person: the C–F♯ pair could sound like it rose to one listener and fell to the next.
Round 1 of this experiment measures exactly that. Each pitch class is played twice as the first tone. On the result screen you see your personal circle, showing which notes you heard as higher, and the peak of that circle. If you heard complementary pairs, C–F♯ and F♯–C, in opposite directions, your orientation is consistent.
Does where you grew up shape your ear?
In 1991 Deutsch compared listeners who grew up in California with listeners from the south of England and reported that the two groups often heard the same pairs in opposite directions. In 2004 Deutsch, Henthorn and Dolson found that native speakers of Vietnamese heard the pattern differently from Californian English speakers. Deutsch suggests that people may acquire a template based on the pitch range of the speech they heard as children and interpret ambiguous pairs according to it.
This claim is contested. In 1994 Bruno Repp published a detailed critique that found the link between the pitch range of the speaking voice and the tritone paradox dubious; Deutsch replied in the same issue. Regional and language differences are intriguing, but they are correlational findings from small samples. In the crowd results we show players on the Turkish and English pages separately, but this reflects only the page language, not where anyone grew up.
The ear does not forget what it just heard
A listener's internal circle is not the only thing that decides how an ambiguous pair is heard. In 2017 Chambers and colleagues showed that when a few context tones are played before a pair whose direction is ambiguous, the context has a large, rapid and long-lasting effect on which way the pair is heard. The ear tries to read successive sounds as parts of a single source. Malek and Sperschneider (2018) also found that after listening to a rising or falling scale, tritone pairs were heard more often in the opposite direction: a kind of auditory aftereffect.
That is why we ask about the tritone pairs first, before the endless staircase; we play them in a shuffled order with silence between them and test each pitch class under two envelope positions. Still, remember that your result is a snapshot: on another day, with other headphones, your peak may move a step or two. This is not a test of musical ability; there is no right or wrong direction here.