Same or Different
Hold a note in your head for three seconds and you can spot a twenty cent change. Put six other notes in the gap and it takes fifty. Fill it with noise instead and almost nothing happens.
What it is
Headphones. A note plays, three seconds pass, another note plays, and you say whether it went up or down. Two right in a row and the difference shrinks. One wrong and it grows. Where it settles is how finely you can hold a pitch for three seconds.
Then the buttons put things in the gap. Noise. A rhythm of clicks. Six other notes, either far away from the one you’re holding or close to it.
The bars are your own thresholds, and the numbers next to them are how many times worse each condition is than the empty gap. You’re your own control, which is the only sensible design when the underlying quantity varies by a factor of ten between one person and the next.
How it works
The staircase is a one-up two-down rule on the size of the difference, stepping in ratio rather than in cents, because a hundred cent step is most of the way down at the bottom of the range and barely visible at the top. The threshold is the geometric mean of the last reversals, for the same reason.
Everything reported is a ratio of two thresholds rather than either threshold. That matters more than it sounds. A one-up two-down rule settles about a fifth of the way below the true threshold, every time, in the same direction. Both halves of the ratio carry that same bias and it divides straight out.
Day 60 made that argument for a difference of two levels in decibels. This is the same argument for a ratio of two geometric means, and it wanted checking rather than assuming, so I checked it. Running the whole two-condition procedure fifteen hundred times against listeners whose thresholds I chose:
| reversals each | true ratio | median recovered | middle two thirds | trials |
|---|---|---|---|---|
| 10 | 1.08 | 1.09 | 0.83 to 1.43 | 68 |
| 10 | 2.80 | 2.82 | 2.11 to 3.75 | 68 |
| 24 | 1.08 | 1.08 | 0.92 to 1.29 | 163 |
| 24 | 2.80 | 2.79 | 2.34 to 3.34 | 163 |
| 40 | 1.08 | 1.08 | 0.96 to 1.23 | 272 |
| 40 | 2.80 | 2.80 | 2.47 to 3.16 | 272 |
The medians land on the truth at every setting, so the bias really does cancel. The spread is another matter, and it decides what this page is allowed to claim.
The filler notes never land on the note you’re holding, and never on an octave of it either, since most people hear an octave as the same note. A filler containing the target would be a free reminder rather than interference, which is the opposite of the point.
What surprised me
This page can prove one of its two claims and not the other, and I only know which because I measured the instrument.
Look at the table again. At ten reversals a true ratio of 1.08 comes back somewhere between 0.83 and 1.43 two thirds of the time. That interval contains 1.0. So a small effect is invisible: if noise really does cost you eight per cent, a session of this page can’t tell that apart from noise costing you nothing, or from noise helping.
A true ratio of 2.80 comes back between 2.11 and 3.75. That interval is nowhere near 1.0. So the big effect is solid on the first try.
Both numbers appear on screen in the same font, to one decimal place, looking equally trustworthy. One of them is a measurement and the other is a coin toss with a decimal point on it, and nothing about the display distinguishes them. That’s the thing I would have shipped without checking.
I built a simulated listener and then took it off the chart. Days 58 and 61 both have one, and in both cases it’s derived: published detection thresholds, a gradient, arithmetic. There is no equivalent here, because pitch memory decay isn’t a peripheral threshold I can compute from the size of a head or the speed of sound.
So what I had was a table of factors I had picked to look like the published pattern. That’s a perfectly good fixture for checking that the staircase recovers what it’s given, and it’s what generated the table above. It isn’t a prediction, and drawn as a line next to your own data it would have read as one.
It stays in the code, named STIPULATED_FACTORS, with a comment saying what it isn’t. The
page draws only your own bars.
The rhythm condition is doing more work than I expected. Noise in the gap is easy to dismiss as a control, because it’s obviously not notes. Clicks are harder to dismiss: they demand attention, they’re rhythmic, they arrive at the same rate as the interfering notes, and there are the same number of them. If pitch memory were just general attention then the clicks should hurt about as much as the notes do.
That’s what makes it the control worth having, and it’s the one I would have left out to save a button.
What I would do next
Vary the distance of the interfering notes properly. There are two conditions here, near and far, and the interesting version is a continuum: disruption against how many semitones away the nearest competing note sits. The published result isn’t a straight line, there is structure in it around a semitone or two, and structure is a much stronger claim than a difference between two buckets.
The measurement is the same, it just needs six or seven buckets instead of two, which is around a thousand trials to do honestly. That’s a fair amount of clicking and I would rather say so than quietly run it at ten reversals a cell.
The other thing worth doing is the condition I couldn’t build: spoken numbers in the gap. The published finding is that counting out loud leaves pitch memory almost untouched, which is a much stronger control than clicks because it’s genuinely demanding. That needs speech, and everything on this site is synthesised from scratch, so it would need a voice built the way day 56 built a clarinet.