AbilityBench48 s of rise, zero net octaves
Shepard tone illusion — a scale that climbs and gets nowhere
A scale that appears to rise without limit, synthesized in this tab from sine voices spaced exactly an octave apart whose loudness is read off a fixed spectral envelope. Free, no signup, 48 seconds per pass at the default speed, and the construction is on screen beside it: the voices move, the envelope does not, and each voice has faded to silence by the time it wraps back to the bottom. Nothing about the illusion can be scored — everyone with ordinary hearing hears the rise — so the measured half of the page is the tritone paradox, 24 pairs built from the same complexes where the direction has no physical answer and listeners genuinely disagree.
- 100% free
- No signup
- 5, 7 or 9 voices
- 24 tritone pairs
- No correct answer
The endless scale
8 octaves of apparent rise, 48 seconds, ending exactly where it started. Mark the moment it stops convincing you, or let it run out.
Voices
Seconds per octave
Envelope width
7 voices centered on 440 Hz span 38.9 Hz to 4978 Hz. The envelope is 1.00 octaves wide, which puts the ends of that span -53 dB down. At that depth the moment a voice jumps from the top back to the bottom is inaudible, which is the whole trick.
How the stack is built — open this only when you are ready to stop being fooled
- 39 Hz-61 dB
- 78 Hz-35 dB
- 156 Hz-18 dB
- 311 Hz-9 dB
- 622 Hz-9 dB
- 1.24 kHz-18 dB
- 2.49 kHz-35 dB
That is the whole mechanism at rest. 7 sine voices sit exactly an octave apart, so they fuse into one timbre instead of a chord — an octave is the interval the ear is least able to hear as two things. Each voice slides upward at one octave per 6 seconds, and its level is not its own: it is read off the shape drawn behind them, which stays still. A voice fades in from silence at the bottom, is loudest crossing 440 Hz, and has faded to nothing by the top, where it jumps back to the bottom -53 dB below anything you can hear. Because the voices are evenly spaced and the shape does not move, the set of levels is identical at every instant. Pitch class keeps climbing; the spectrum never changes; the ear believes the pitch class.
The tritone paradox — the part with a result
24 pairs of those complexes, six semitones apart, 500 ms each. Say whether each pair went up or down. There is no correct answer for any of them: both tones occupy the same span under the same envelope, so the physical direction is genuinely undefined and what gets measured is which pitch classes you hear as low.
Hearings per pitch class
Two hearings is the setting worth quoting, because it is the only one that can check itself: the same pitch class comes round twice, separated by other pairs, and how often the two agree is the one figure here that was fixed before the run. One hearing is 12 seconds of sound plus however long you take over it, and shows the shape without confirming it.
Up and down arrows answer, R replays. Nothing is timed and nothing is graded, so take as long as you like over a pair — but answer what you heard first, because the second listen to an ambiguous stimulus is a different question.
How to hear the illusion and then measure the part that varies
Set the level, mark where the rise stops working, then answer the ambiguous pairs.
Set a level, then check the bottom of the stack
One motionless complex plays first: six sine components an octave apart, which should fuse into a single organ-like note rather than a chord you can pick notes out of. A second button plays its lowest component alone at 65.4 Hz. If that one is inaudible, your output is rolling off the bottom of the stack — a laptop or phone speaker often does — and everything after it is a thinner sound than the page describes, which matters here because the judgments in the second half move with the spectrum rather than with the notes.
Play the scale and mark the moment it stops working
Eight octaves of apparent rise are scheduled on the audio hardware clock in one call, so nothing in it depends on a browser timer. While it plays, each voice is drawn at its own frequency with its own level in decibels, climbing through the envelope shape behind them. Press the marker when the rise stops convincing you and the page records the elapsed audio time — that is an observation about where your attention moved, not a score, and there is no number to beat.
Open the construction, then answer 24 ambiguous pairs
The disclosure panel draws the stack at rest and explains why a voice can vanish at the top without a click, and the envelope-width control lets you break it deliberately: widen it and the ends of the span stop being silent, so you hear the reset and the scale becomes an obvious loop. Then the tritone block plays two complexes six semitones apart and asks whether the pair went up or down. Answer with the arrow keys or the buttons; the pattern across the twelve pitch classes is the result, and the same pitch class comes round twice so the page can check that pattern against itself.
Technical specifications
| The stack | 5, 7 or 9 sine voices exactly one octave apart, centered on 440 Hz. Seven span 38.9 Hz to 4978 Hz, five span 77.8 Hz to 2489 Hz, nine span 19.4 Hz to 9958 Hz. The octave is chosen because it is the interval the ear is least able to hear as two separate things, which is what makes the stack a timbre instead of a chord |
|---|---|
| The envelope | a Gaussian in log frequency, fixed in place, standard deviation one seventh of an octave per voice in the span — 1.00 octave at seven voices. It has to be fixed: an envelope that travels with the voices is a glissando, and one that does not reach silence at the ends of the span makes the wrap audible |
| One pass | 8 octaves of apparent movement, which is 32, 48 or 72 seconds at the three speeds. The whole schedule is placed on the audio hardware clock in a single call rather than fed from a timer, so a busy main thread cannot stretch the rise; the schedule is finite by construction and the page says so instead of pretending to loop |
| Disclosure control | the envelope width multiplies by 1, 2 or 3.5, which puts the ends of the span 53, 13 and 4 dB down. At 53 dB the jump from the top of the span back to the bottom is inaudible and the rise never ends; at 4 dB it is a plain descending step, and the illusion is simply gone |
| Tritone pairs | 12 or 24 pairs, six semitones apart. Each tone is 6 octave-spaced sine components — C2 to C7 at 65.4 to 2093 Hz for pitch class C — under one envelope fixed at 523.25 Hz with a standard deviation of 12 semitones, 500 ms per tone, the two played back to back with the component levels summing to 1 so neither tone is louder than the other by construction |
| What the block reports | the share of pairs heard as rising for each of the 12 pitch classes, the pitch class those judgments peak at from the phase of the first Fourier component, the two half-circle proportions with 95% Wilson intervals, and how many of the 12 pitch classes were answered the same way both times with the binomial probability of that agreement under coin flips |
| Voided pairs | a pair whose sound was scheduled while the tab was hidden is discarded, counted, and asked again at the end of the block. Nothing here is timed, so a slow answer is never penalized and a replay is allowed and counted rather than hidden |
| What is never reported | a percentile, a band, a pass mark, or any suggestion that hearing the rise says something about you. There is no reference distribution for either half of this page: the scale has no correct answer and the paradox has one different answer per listener, which is the finding rather than a shortfall |
Frequently asked questions
Is the tone really rising, or is my ear being fooled?
Both halves of that are true at once, which is the point. Pitch has two components: chroma, the note name that repeats every octave, and height, how far up the range a sound actually sits. In this stimulus the chroma really does rise continuously — measure any single voice and it is gliding upward — while the height, which is set by the spectral envelope, never changes at all. Your ear is not making a mistake about either quantity. It is choosing which of the two to report, and it reports chroma, because in every natural sound the two move together and there has never been a reason to keep them apart.
Why can I never hear it drop back down?
Because a voice is silent long before it gets to the point where it jumps. Each voice fades according to the envelope, and at the default width the two ends of the span sit 53 decibels below the middle — a gain of about 0.002. The wrap happens there, between two levels that are equal to each other and both inaudible, so the only discontinuity is in frequency and nothing you can hear changes across it. Widen the envelope to 3.5 times its designed width and you can hear the reset perfectly clearly, which is the fastest way to convince yourself the trick is exactly this and nothing more.
Can it be made to actually go on forever?
Not by this page, and the reason is a deliberate refusal rather than a limit. A schedule that never ends needs something to keep extending it while it plays, and a browser timer is the only thing available — the same timer that stalls behind layout, garbage collection and any other script on the page. Everything audible here is placed on the audio hardware clock up front, in one call, which is why the rise cannot stutter. Eight octaves is what fits in one pass; press play again for another. A page that loops a recording instead has a seam at the loop point, and the seam is usually audible once you know to listen for it.
Why do the tritone pairs have no correct answer?
Because the two tones occupy the same frequencies. Each is a stack of components an octave apart under one envelope that does not move between them, so the second tone is not higher or lower than the first in any physical sense — it is the same spectrum with its chroma shifted six semitones, and six semitones is the one interval that is equally far in both directions around the twelve. There is nothing in the signal to be right about. What varies is which of the two pitch classes a listener treats as belonging to the lower part of their range, and that is a property of the listener.
A friend hears the same pair going the opposite way. Which of us is hearing it wrong?
Neither, and that disagreement is the actual scientific finding here rather than a curiosity. Deutsch reported that judgments of these pairs form an orderly function of pitch class, that the function has a peak, and that where the peak sits differs from listener to listener while staying stable within one. Two people can therefore hear a C-to-F# pair rising and falling respectively, both correctly. It is one of the few places in perception where you can demonstrate to somebody, with a stimulus you can build in a minute, that their experience of a sound differs from yours in a way neither of you can talk the other out of.
The bottom of the stack is missing on my speakers. Does that change the result?
It changes the second half and barely touches the first. The endless rise survives a narrow output because the illusion only needs several voices audible at once, and the middle of the envelope is where they are loudest anyway — a phone speaker that rolls off below a few hundred hertz still delivers the effect. The tritone pairs are different, because the judgment is known to depend on where the energy sits: shift the envelope and the peak shifts with it. If your output is throwing away the lower octaves, then the spectrum reaching your ears is not the one this page specifies, and your peak belongs to your speakers as much as to you. Headphones with real bass extension are the honest way to run that half.
Does hearing the illusion strongly mean anything about my pitch perception?
No, and it is worth saying that plainly because the surrounding genre invites the opposite reading. Hearing the rise is the ordinary outcome and hearing through it is mostly a matter of having been told how it works — the illusion is built so that the spectrum is constant, and no amount of listening skill turns a constant spectrum into information. Trained musicians are not immune, and the effect keeps working after you have watched the voices wrap on screen, in the same way that knowing an optical illusion is one does not make the lines look equal. What the page can report is the pattern in your tritone answers, and that is not an ability either.
Chroma, height, and why a fixed envelope is the whole trick
Pitch is not one number. A note has a chroma — the name that comes round again every octave — and a height, which is roughly where the energy sits in the spectrum, and ordinarily the two are locked together: play a note an octave up and both increase. Shepard built a stimulus that unlocks them, and the demonstration that made the point was circularity: a sequence of these complexes ascending in semitones arrives back where it started while every step has sounded like a step upward. Chroma is what naming a note means, which is why the perfect pitch test asks for a note name and never for an octave, and why the relative pitch test can work entirely inside one. A Shepard complex has a chroma and no octave at all, which is what makes it useless for those tasks and perfect for this one.
There are exactly two ways to get the synthesis wrong and both are audible within a second. The envelope has to be fixed in frequency: if it travels along with the voices, every voice keeps its loudness as it climbs and what you have written is a glissando, an ordinary rising sound that runs out of range. And it has to reach effective silence at both ends of the span, because that is where a voice is teleported from the top back to the bottom — at 53 decibels down the two ends are at the same inaudible level and nothing marks the jump, while a leaky envelope turns the same schedule into an obvious loop with a bump in it. Most versions on the web dodge both problems by serving a recording that loops, and the loop point is the tell: the stack is only truly seamless while it is being generated, because seamlessness is a property of the schedule rather than of the audio. This page draws the voices as they travel for the same reason the auditory processing test prints the exact duration of every silence it cuts: a stimulus you cannot inspect is one you have to take on trust, and here the construction is more interesting than the effect. It is also worth knowing what the illusion is not evidence of — amusia work of the kind behind the tone deaf test concerns fine pitch discrimination and melodic contour, and this stimulus tests neither.
The measurable half of the page is Deutsch's tritone paradox, which comes out of the same synthesis and is the reason this page has a result at all. Take two of these complexes six semitones apart — the one interval with no shorter way round the circle of twelve — and ask whether the pair rose or fell. The physical answer does not exist, but people answer confidently and consistently, and the answers depend on which pitch classes were involved in an orderly way that differs between listeners. Deutsch also showed the effect moves with the spectral envelope, which is why this page states the envelope it used instead of treating the result as a property of you alone. That combination — an automatic percept that survives knowing how it works, and differs between two people looking at identical input — puts this page next to two others here rather than next to the rest of the section: the Stroop test is the standard demonstration that understanding an interference effect does not disarm it, and the aphantasia test is the other place on this site where two people report different inner experience of the same instruction. If you want the timing side of listening rather than the pitch side, the rhythm test measures what happens when a beat you were following stops.
Why this page reports nothing about the illusion itself
The Shepard scale is a demonstration, not a measurement: there is no correct answer and nothing about the listener to score. No defensible figure exists for what share of people hear it as endlessly rising.
Shepard (1964), Circularity in judgments of relative pitch, Journal of the Acoustical Society of America
The tritone block exists because it is the one thing in this family that does differ between people and can be measured against a visitor's own other answers rather than against a sample nobody collected. Deutsch (1986), A musical paradox, Music Perception. Deutsch (1987), The tritone paradox: effects of spectral variables, Perception & Psychophysics.
One number on this page is a duration and it is a coarse one on purpose. The marker records elapsed audio time from the handle the scheduler returns, and it is reported in octaves of apparent rise to one decimal — at the default speed that is 0.6 seconds per digit, which is far wider than the tens of milliseconds a keypress and an output buffer cost between them. There is no reaction time here to be honest about, because there is no onset to react to: the moment being marked is one the listener chooses, and the only precision it deserves is the precision at which the choice itself is stable.
This is a measurement exercise, not a clinical assessment. It reports what you did on this page against a stated reference and nothing more — it cannot establish a hearing difference, absolute pitch, or amusia. Only a qualified professional, working with more than a browser, can make that judgment.
Nothing on this page is an ability test, so there is nothing here to do badly at. A listener whose rising judgments peak at F and one whose peak at B are both hearing the stimulus correctly, and a listener who cannot hear through the endless rise at all is in the large majority. If a real difficulty with pitch or with speech is what brought you here, the measurement that exists for that is made by an audiologist with calibrated equipment.
Where these tones are made, and where your answers stay
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Your answers, your reaction times and your score are never uploaded, logged or kept — which is also why the test carries on working after you disconnect from the network, and why nothing here can be held back behind an email address.
No audio file is fetched for any of this. Every voice is an oscillator created in this tab and every level is computed here, which is why the number of voices and the width of the envelope can be changed between passes — there is nothing to re-download. Your marks, your up-and-down answers and the seed that ordered the pairs live in the page until you reload it, and the copy button is the only route by which any of it leaves.