One Stream Or Two
High, low, high, rest. Either a galloping rhythm or two separate beeping lines, and near the boundary, both.
What it is
A repeating pattern: high tone, low tone, high tone, rest. Drag across to change the speed and up and down to change the pitch gap.
With a small gap you hear a gallop, one rhythm, tri-plet tri-plet. With a large gap the same recording becomes two things: a high tone beeping steadily and a low tone beeping half as often, no gallop anywhere. Nothing about the audio changed except how far apart two frequencies are.
In the purple region it’s genuinely both, and if you keep listening it’ll flip without warning.
How it works
The diagram is van Noorden’s, from 1975. Two boundaries, not one.
Below the fission boundary, about five semitones, you can’t hear two streams however hard you try. Above the temporal coherence boundary you can’t hear one. Between them the percept is bistable and depends on attention. Listen for the gallop and you get it, listen for the high tone alone and it detaches.
The half that surprises people is the shape. Fission is roughly flat with tempo while coherence falls steeply as the sequence speeds up. So a gap that gallops comfortably at two tones per second splits into two streams at sixteen, with no note changing pitch at all. Speed alone reorganises it.
The tones are scheduled against the audio clock a fraction of a second ahead, never on animation frames. A sequence timed by frames audibly stutters, and here the rhythm is the experiment.
What surprised me
That the ambiguous region is a genuinely different thing from a measurement error.
Everything else in this series has had a right answer I could put in a test. The notches are at those frequencies, the pendulums diverge at that rate, the threshold is that number. Here the model’s middle case is the same input having two valid outputs, and the correct behaviour of the code is to say so rather than to pick.
So the test asserts the structure instead of the outcome. That the two boundaries are correctly ordered, that a region exists between them, that it narrows as the tempo rises, and that below fission nothing is ever two streams. It never asserts what you’ll hear at nine semitones and four tones per second, because that isn’t a property of the signal.
That’s a clean line between the two kinds of claim this blog keeps making. Most days the ear is a measuring instrument with a quirk to characterise. This one, the ear is choosing.
What I would do next
Fix the pitch gap in the bistable region, add a button to log each flip, and see how long a percept survives before it switches.