Up or Down Is Up to You
Two tones half an octave apart. Whether they went up or down is not in the signal, and you will still be sure.
What it is
Headphones. Two tones play in sequence, half an octave apart. Say whether the pair rose or fell. Another pair comes, keep going.
The circle fills in with your answers, amber where you said the pair rose, blue where you said it fell. After a dozen or so, look at it.
This is a reproduction of Diana Deutsch’s finding: the pattern is stable within a listener and different between listeners, and people are usually astonished the disagreement exists at all.
How it works
Each tone is an octave-complex, meaning the same pitch class at every octave, weighted by a raised-cosine envelope in log frequency that doesn’t move between tones. So no tone is in a register.
Asking whether C or F♯ is higher is like asking whether Tuesday is before Friday. True in some framing, and the framing is what the question is missing.
The pairs are always six semitones apart, which is the only interval that’s the same distance up the pitch-class circle as down it. On the circle, every pair is a diameter.
What surprised me
Not the illusion, which I already knew about. It’s how thoroughly empty of information the signal is. It isn’t finely balanced. There’s nothing there at all:
| pair | interval cue | spectral centroid cue | energy cue |
|---|---|---|---|
| C → F♯ | 0 | 0.52 semitones | 0.000 |
| C♯ → G | 0 | 0.45 | −0.010 |
| D → G♯ | 0 | 0.24 | −0.017 |
| D♯ → A | 0 | 0.00 | −0.020 |
| E → A♯ | 0 | −0.24 | −0.017 |
| F → B | 0 | −0.45 | −0.010 |
The interval cue is exactly zero by construction for every tritone, where a five-semitone pair scores 2. The spectral centroid is the one quantity that could smuggle in a direction, and it differs by at most half a semitone across the pair, against a six-semitone step the listener is being asked to judge. For D♯ → A it’s precisely zero, and the answer is still not “I can’t tell”.
So the percept isn’t being computed from the sound, it’s being supplied. Something in the listener holds a map from pitch class to height, that map differs between people, and it’s confident.
The interesting part isn’t that the illusion works. It’s that a question with no answer in its input doesn’t feel like one. There’s no sensation of ambiguity to report.
That makes this the third day where the instrument was the surprise. Day 35’s phase experiment needed the right measure before an obvious effect appeared. Day 46’s vowels showed a voice can’t transmit what it doesn’t sample. Here the instrument is the listener, and it returns a value for a measurement it hasn’t made.
What I would do next
Vary the envelope centre across trials. Deutsch found the orientation map holds steady as the envelope moves, which would mean the effect really is indexed by pitch class and not by absolute frequency. That’s a claim this page could test on whoever is reading it.