Listening for a Cosmic Chord
Find a galaxy by ear.
This game makes sound. Not decoration — the sound is the science. Every tone you hear is a real spectral line at its real frequency. Put on headphones if you can.
Hear that? That’s a wave. Light is one too. Now stretch the space it travels through:
Longer wave, deeper note. Astronomers call this redshift, and the universe has been doing it to starlight for 13.8 billion years. Everything else in this game is that one idea, taken seriously.
1 · Everything is running away
Galaxies far away aren’t sitting still. Space itself grows, and the light crossing it grows with it. The farther the galaxy, the more its light has stretched by the time it reaches you.
Here’s the useful part: light from a galaxy isn’t a smooth hum. Atoms and molecules glow at exact frequencies — a barcode, identical in every galaxy in the universe.
Stretch it, and notice what does not change: the pattern. Every line moves by the same factor. That factor is (1 + z), and z is the redshift. Recognise even part of the barcode and you can read off z — and with it the distance, the epoch, the age of the light.
for the curious: why not just use a ruler?
Distance in astronomy is brutal. Almost nothing out there carries a label saying how far away it is, and the tricks that work nearby (parallax, standard candles) run out long before these galaxies. Redshift is different: it is measured from frequencies, which we can measure exquisitely well, and it converts to a distance and an age through cosmology. That is why redshift, not distance, is the currency.
2 · Sixty-six dishes in a desert
You have a barcode to look for. Now meet the machine that has to hear it — because the shape of the machine is the reason every graph in the rest of this game looks the way it does.
ALMA, the Atacama Large Millimeter/submillimeter Array, is sixty-six dishes on the Chajnantor plateau in northern Chile, five kilometres above sea level. The altitude is not for the view. Water vapour in the air drinks up millimetre waves — broadly, and worse the higher in frequency you go — so the stretches ALMA can see through at all are the gaps between water’s absorption lines, and they are only gaps if the air above you is dry. Chajnantor is one of the driest places on the planet. You climb until the sky goes transparent.
What comes back down is not a photograph — and for a redshift search you are barely using ALMA as sixty-six telescopes at all. The sharp images it is famous for come from playing the dishes off against each other; here that is beside the point. You are using them as one enormous bucket, poured into a machine that answers a single question: how much signal arrived, at each frequency?
Frequency is just the other way of counting the wave you stretched in Chapter 0. More waves past you each second is a higher note, so a bigger number of GHz is a higher note — and stretching a wave, which is exactly what redshift does, always pushes it down the scale. Hold on to that one: here, redshift moves lines downward.
Getting it takes a trick. A wave at 100 GHz is far too fast for any electronics to follow, so the receiver plays the incoming signal against a steady reference tone of its own and keeps only the difference — the same arithmetic that makes two nearly-tuned guitar strings throb against each other, and worth remembering, because that throb is the main mechanic of this game. It drops the whole band to a few GHz without disturbing one interval inside it. Then the correlator slices what is left into thousands of channels, each a fraction of a megahertz wide.
That list — how much signal in every one of those channels, right across the slice you recorded — is a spectrum. It is the thing an observation actually produces. Almost every sentence in the rest of this game is about reading one, so it is worth looking at:
Three things to carry forward, because all three words come back. A spectrum is something you have: one measurement, of one patch of sky, over one range of frequency, made once. It has a depth, which is just the height of that noise. And it can be silent — most of any spectrum is nothing at all, and how deep the nothing goes is the whole difference between evidence and an absence of evidence.
ALMA counts those frequencies against a hydrogen maser — a clock perhaps a million times better than this job needs, which is the interesting part, because it means the instrument is never your limit. Chapter 1 said atoms glow at exact frequencies, and they do; but a galaxy’s gas is in orbit, hundreds of kilometres a second, some of it toward you and some away. Every one of those motions shifts its light a little, so what arrives is not a spike but a smear a few hundred km/s wide. How well you can find the middle of it depends on how far it stands above the noise. The galaxy sets your error bar, not the clock.
Which is why redshift here is measured rather than estimated — not because radio beats optical at this, it does not, but because for these galaxies the optical route is shut. They are wrapped in so much dust that almost nothing visible escapes, as you will see next chapter. This is the light there is.
They come in bands. No single receiver covers the millimetre spectrum, so ALMA splits it into ten. This game lives in two of them: Band 3, 84–116 GHz, and Band 4, 125–163 GHz. The gap between them is not an oversight. Oxygen has a line at 118.75 GHz, and oxygen is a fifth of the air on the best night there has ever been — so unlike the water, that gap does not open on a dry night, and no amount of altitude climbs above it.
And they are narrow. Inside a band you pick a setting — a tuning — and one tuning records about 7.5 GHz at once. String a few together and you have a window: the stretch of frequency you actually came away with. This game searches two of them, 89.1–112.0 GHz inside Band 3 and 139.9–162.7 GHz inside Band 4, about 23 GHz apiece. So the nesting runs: the whole millimetre spectrum, then ten bands, then the two windows you chose, then the tunings that build them.
And everything outside a window is not faint, not noisy, not hard to see: it is simply not observed. Wanting more is the entire history of receiver engineering, and it is where this field is going — but not today.
So an observation is a slice of frequency. Draw the slice, and you have drawn the axis:
There it is. The vertical axis is frequency, in GHz, and those numbers are hardware — no amount of clever analysis moves them. The horizontal axis is the thing you do not know. And the curve is one line of the barcode at every redshift it could have: emitted at f0, arriving at f0 / (1 + z), sliding downward as the universe stretches. It is data only where it crosses a window. Everywhere else it is a prediction about a place you never looked.
One last thing, and it is why this game has sound. You cannot hear 155 GHz; nothing can. So the game divides every frequency by 250 million, which drops the whole searched range to roughly 360–650 Hz — a little under an octave, sitting in the middle of a piano. It divides rather than squashes, and that is the part that matters: dividing leaves every ratio between frequencies exactly as it was, so a chord in the sky is still the same chord in your headphones. Your ear is a frequency meter, and it is now pointed at the y axis. Height on this graph is pitch. Everything you are about to do by eye, you can do by ear.
for the curious: how wide is one tuning, really?
About 7.5 GHz — and not in one piece. Differencing against the reference tone leaves two copies of the sky, one from just above that tone and one from just below (the two sidebands), and ALMA records both: four slices of 1.875 GHz, in two pairs, with a gap in the middle. So a 23 GHz window is not three tunings laid end to end so much as three tunings placed with some care.
Why these two windows in particular? Because a pair spaced like this catches two rungs of the ladder at once across the widest span of redshift — which will not sound like much until Chapter 5, and which you get to try to beat in Chapter 9. Every extra tuning costs telescope time, and that fixed budget is the constraint you will be handed there.
It is also the assumption about to expire. ALMA’s Wideband Sensitivity Upgrade will at least double what a single tuning can record, and every extra GHz turns some of the ambiguity in the next few chapters into a plain answer. The last chapter comes back to this.
3 · The galaxy is a chord
The galaxies in this game are monsters: dusty factories building stars a thousand times faster than the Milky Way, so wrapped in dust that visible light barely escapes. But their cold gas glows in the radio — carbon monoxide, of all things — and it glows at a ladder of frequencies:
115 GHz · 231 · 346 · 461 · 576 …
Every rung an (almost) exact multiple of the first. Click them. (The galaxy starts at redshift 1, where the whole ladder sits comfortably in earshot; the off-ladder notes need a lot more stretch before they come down into the clear.)
Multiples of one frequency — a musician calls those overtones. A galaxy’s cold gas is literally a chord. Stretch it with redshift and it stays a chord, just deeper. And a few other atoms sing off-ladder notes in a different voice: ionised carbon, water. Remember that timbre. It saves you later.
for the curious: is the ladder really exact?
Almost. CO’s rotating molecule has energy levels that grow slightly faster than a perfect ladder, so the higher rungs drift a little from exact multiples. The method — and this game — uses the linear approximation, which is more than good enough at the precision a redshift search needs. The rigidity is what matters: whatever the exact spacing, all the lines shift together.
4 · You are a radio telescope
Congratulations. You are now ALMA — or at least the two windows of it you talked a time allocation committee into. The axes are the ones from Chapter 2: frequency up the side, the unknown redshift across, and the purple bars on the left are your windows. The galaxy’s chord is out there somewhere, stretched by an unknown amount.
Chapter 2 drew one line of the barcode sliding down the frequency axis as z grows. A galaxy hands you the whole ladder at once, so you get a whole family of those curves, sliding together: each is where a rung would appear at each possible redshift. The horizontal line is a real detection: 155.772 GHz. It never moves — it’s the data. The moving tones are your model of the galaxy.
How to play: drag the redshift. When a predicted rung approaches the detected line you’ll hear beats — a wobble that slows as you close in and vanishes at the match, exactly the way a guitarist tunes a string. Let go on a match to lock it in. (The cursor pulses at the same rate, so it works with the sound off.)
Keep going and the problem announces itself: the beats stop again. And again. One tone fits thirteen different identifications in this tuning — nine of them rungs of the CO ladder, the rest off-ladder lines. Your single number could mean a galaxy seen 5 billion years after the Big Bang, or 1. We need another note.
5 · Two notes are (almost) a song
Your other window catches something: 93.463 GHz. Two steady tones now. And a candidate redshift has to lock both — the whole chord shifts together, remember?
Feel the difference. Nearly everywhere, one tone locks and the other beats angrily against the model. Almost every impostor dies.
Almost. There are two survivors: z = 2.70, where the lines are CO(3-2) and CO(5-4) — and z = 6.40, where the very same two frequencies are CO(6-5) and CO(10-9). Both fit perfectly. Huh.
6 · The impostor
Here is the dirty secret of ladders: they are too regular. If two detections are rungs 2 and 3 at one redshift, then somewhere deeper there is a redshift where the same two frequencies are rungs 4 and 6. Double every rung number, stretch space to compensate, and the music is identical.
A different galaxy this time, with lines at 107.229 and 160.844 GHz. Three redshifts fit both lines. Hear each one — then answer, using one of the two buttons at the bottom of the panel. That choice is the chapter: you are being asked whether the evidence lets you name a redshift, and one of those two answers is honest here.
Solution C is worth your attention first, because it is the one the data can actually throw out: z = 5.45 explains both detections (rungs 6 and 9) but it also insists on CO(5-4) at 89.36 GHz and CO(8-7) at 142.97 GHz — both sitting inside your windows, both silent. A redshift that predicts lines you did not see is dead. Now notice that you cannot say anything like that about A or B.
There is none, because there is none to hear. Both are exact. The universe is not going to tell you which. An astronomer who publishes one of these as certain is guessing — and this exact trap is why redshift papers have erratum sections.
(You may have spotted a third marker, at z = 5.45. It fits these two lines as well — rungs 6 and 9, the same ladder times three. Hold that thought: it is the one impostor here that can be killed, and the next chapter shows you how.)
for the curious: when does the twin exist?
Whenever the two transition numbers share a common factor. Rungs 2 and 3 share nothing, so a 2+3 pair is safe; rungs 4 and 6 share a factor of 2, and that factor is exactly the multiplication that builds the impostor. The paper writes the resulting redshift offset as Δz/(1+z) = (b−a)/a — which is just "how far apart the rungs are, in units of the ladder spacing". Wide spacing, distant twin, easy to tell apart. Narrow spacing, close twin, trouble.
So how do you break a perfect tie? You cheat. Three ways.
7 · Listen for the silence
Cheat #1 — the dog that didn’t bark
Back to the galaxy from chapter 4, sitting at its impostor redshift of 6.40. That redshift doesn’t only explain your two detections. It predicts more lines: CO(7-6) at 109.04 GHz and CO(9-8) at 140.195 GHz — both inside your windows, both loud, if the galaxy were really there.
They show up as hollow, fluttering ghost notes — the red dashed rings on the graph. You have to point the telescope at one to find out that nothing is there: click a ring, or use the 🔭 button under the slider, which does the same thing and names the line it is checking. The panel tells you what is still to do.
Nothing. A galaxy at z = 6.40 would be singing there. It isn’t. Silence is data, and the impostor dies of it — z = 2.70 stands alone.
Cheat #2 — a rough guess is still a guess
Before pointing a single antenna, we photograph these galaxies in other light. The colours of their dust give a fuzzy redshift: z ≈ 3, give or take a lot. Useless for precision, perfect for tie-breaking.
Here’s a different galaxy: one loud line at 144.089 GHz, and a photometric redshift near 3. The green glow is that prior — you can hear it as a warm hiss that swells as you drag through it.
Three things to do here, and the panel keeps score:
- Drag to a candidate that predicts a second line — z = 2.20 and z = 1.40 both do — and press the 🔭 button. Nothing is there; that candidate dies.
- Do it once more at another candidate.
- Then drag to z = 3.00, the one identification that predicts nothing you failed to see, and release to lock it.
(A candidate can also be struck off by the photometry alone, if it lies more than five sigma outside the glow: click its circle on the graph. At this prior that only reaches the very deep ones, which is itself the lesson — a photometric redshift is a weak weapon, so use it only where it is decisive.)
Cheat #3 — the off-ladder note
Remember the atoms with a different voice? They are not on the CO ladder, so the multiply-everything trick fails on them: there is no "double every rung number" that also works for ionised carbon. One off-ladder note locking together with one CO note kills every ladder impostor at once. It is the cleanest kill in the business — when you are lucky enough to get one.
for the curious: when can you not trust the silence?
When the line you expected would have been too faint to see anyway. The argument "this redshift predicts a line, I see nothing, therefore no" only works if your observation was deep enough that the line would have been obvious. That is why this game’s exclusions use the bright CO rungs and the strong atomic lines, and why the faint ones — [CI], water — are drawn and heard but never used as evidence unless the survey is deep. Silence from a shallow observation means nothing at all.
8 · Three real galaxies
Enough training. Three observations, the full toolkit, no hand-holding. Drag, listen, click ghosts, strike off what the photometry forbids — then answer.
Galaxy A
Galaxy B
Galaxy C
That third answer — "we don’t know yet, give me more time" — is the most important thing this game has to teach. Real astronomers say it for a living, and the ones who don’t end up writing errata.
9 · Design the search
Final promotion. You’re not the observer any more — you’re the one writing the telescope proposal. Thousands of dusty galaxies are waiting, and you choose the frequency windows everyone else will listen through.
Below: your two windows (drag them), the real redshift distribution of a real survey, and a live score — the paper’s own metric, computed on every galaxy in the sample every time you move. Robust means the redshift is pinned down. Ambiguous means you got lines but more than one answer fits. Silent means the galaxy said nothing at all: a night of telescope time for nothing.
You start with both windows crammed into the 3 mm band, which is exactly the tempting mistake: cheap, contiguous, and it leaves half the population ambiguous. Chase the score. Notice what happens when you cluster the windows together, and what happens when you split them across the two bands. Then ask the paper for its answer.
for the curious: what the score actually counts
It is the figure of merit the paper optimises: every galaxy in the survey is classified by what your windows would catch, and a galaxy whose redshift you could pin down counts 1, one that gives you lines but more than one possible answer counts ½, and a silent one counts 0. The classification is the same code that judged your answers in the earlier chapters.
One simplification: a real ALMA tuning is a handful of narrow spectral windows in two sidebands, not one clean block. This sandbox slides one contiguous block per band, the same total bandwidth the paper used, so a block that scores a point or two above the paper's tuning does exist here. The shape of the answer — one window per band — is what survives.
The real version of this puzzle was solved in the paper this game is built on, and the answer — you need both the 3 mm and the 2 mm band — now steers real time on the largest array on Earth.
10 · This was real
Every number you just played with is real. The galaxies are real: Herschel and South Pole Telescope surveys of dusty star-forming galaxies. The windows are ALMA’s. The method is Bakx & Dannerbauer (2022), MNRAS 515, 678 — nicknamed "High-z Sudoku". The code scoring your sandbox is the paper’s own redshift-search-graphs, ported to JavaScript and checked line by line against the original.
If you want to keep playing, there is one more thing: the redshift search bench is this graph with the guard rails off. Four real galaxies from the paper are waiting there with their answers not written down, and you can also build your own — any lines, any windows, the redshift under your finger and the beats in your ears. You do not need data of your own to use it.
And if you do have data: the sandbox above accepts real tunings and scores
them with the real metric, and the bench prints the RSGplot() call
for whatever you build in it. Astronomers, steal either for your next
proposal.
With thanks
This game was built with the support of INFRAVIS, the Swedish National Infrastructure for Data Visualization. Turning a diagnostic figure from a paper into something a stranger can play is a visualization problem before it is a coding one, and INFRAVIS is the reason it was treated as one.
That support is also why the sound is not decoration. A method that exists as one dense graph is a method some people simply cannot read; rendering the same physics as pitch, beats and silence gives it a second door. Every audio cue in this game is written out in text as well, and the whole thing is designed to be playable with the sound off — or with the graph ignored entirely.
And the windows are about to get wider
Everything you just played with assumes today’s receivers: a slice of frequency at a time, and a puzzle because of it. That assumption is the part that is changing.
- ALMA Band 2 opens the 67–116 GHz window, the lowest rungs of the CO ladder for the redshifts these galaxies actually live at — its redshift-search power is worked out in Bakx et al. (2026). Put that band into the sandbox’s logic and the ambiguous fraction is a different number.
- The Wideband Sensitivity Upgrade (WSU) widens what a single tuning can record. Every extra GHz of instantaneous bandwidth turns "one line, thirteen answers" into "two lines, one answer" for more of the sky — the impostors in this game die of bandwidth.
- ALMA2040 is the long view: the development roadmap that decides which of these puzzles our successors still have to solve by hand.
Which is the honest ending for a game about a graphical trick: the trick exists because our windows are narrow. Widen them and the sudoku gets easier — and the galaxies we cannot reach today start answering.
Made with sound on purpose. The universe is a chord; someone had to play it. — Built as an outreach project; no trackers, no accounts, no dependencies. Code under MIT, words under CC BY 4.0 — take either.