I don't know if anyone knows, I can only guess as written: Two audio sources are panned left and right. How wide is the stereo image?
They implement two audio sources from the same instrument, each a bit different, and pan them to each's own channel. That is fact.
1 ) Afterwards, my guess is that they probably use a plugin / algorithm to change the mid/side correlation by messing with the phase at a certain amount (as you do with mid/side config).
You declare that amount with the game UI. The click of the mouse sends your answer from 0 to 1 and checks if its in the boundaries of the actual answer.
2 ) They could also do something different and simpler, and actually pan 2 almost similar mono sources by an amount and the same idea goes with you choosing the answer, and the game checks if its in the boundaries.

I am not very knowledgable in the topic, you could send them a support ticket if you really want to know (If they'll even tell you, but you can try). Cheers.

yeah, I already know what could have been done. I might just add:
- there is no difference in volume, and
- the basis is one track, not two different tracks played two times, adding random subtle differences, as ChatGPT suggested.

also, I don't think there is a delay added to just one of the channels, I tried that and than feel different, you can feel a direction there, nor there is a different reverb or distortion, as far as I can tell — but this is just my guess

My guess is they don't do anything to make it wide. It's very likely an already wide sound that they are making mono by some arbitrary percentage.

Logic comes with a stock tool called Directional Mixer that will do this so I've never had to use a 3rd party tool but apparently Boz has a free plugin called Width Knob that will do the same thing.

Creating width artificially is, in my experience, always noticeable. Width is the difference between left and right. If two things are algorithmically different', our brains are pretty tuned to notice that.

Narrowing a sound, however, is very transparent. The sound simply seems like it's coming from a more specific direction rather than being unnatural.

Hope this helps!

hmm, somehow I am not convinced …

you are just deffering the question. how then is the already wide sound made in the first place? recording with a stereo mic does not make it (that) wide, you would have to have the mics very wide appart or something, and placing mics wider than a head-width already breaks the spatial illusion—trust me I've, done a thesis on binaural perception

I know how to make sound appear to come from a certain direction: it's a combination of a bunch of bin-aural cues, like delay, volume, applying filters to emulate the earlobe attenuation to name a few, but I have no clue whatsoever how to make it wide, that's why I'm asking.

Like Jay Kay said, any difference can make it wide. It can be volume (which is just Pan, so not relevent in StereoHead), it can be EQ (which is volume, but just on some frequency bands), or it can be de-sync, which is more probable here.
For me, the wideness is made by delaying the left and right channels slightly, for a few ms.
You can check Haas effect online for more info about the process.

Stereo width can be created in many ways. It's basically (usually) subtle difference in timings between the left and right channel. But different EQ bands for the left and right channel, dynamic resonance suppression, distortion, reverb, phasing applied on the individual channels can also widen the sound. As well as playing the same notes with a slightly different guitar for example. Or a slightly different sound but not too different.

How it's done exactly for the Stereohead game is a question only Soundgym can answer really because there's a lot of different ways to do this. Even something as iZotope imager can basically create this. Though i think the answer is closer to what @Jay Kay described in his comment.

Can you be more specific in your question? Because the question you asked has been answered - are you asking more generally what causes width rather than what causes it specifically in Stereohead?

Width is literally the difference between the left and the right channel - that's it.

If you have a guitar track and you duplicate it and pan them both hard left and right, you have NO width. You have the exact same information in the sides as in the middle - so you've effectively turned up the volume and done nothing to the width. This is why tricks like the haas effect are used - haas is just delaying the duplicated guitar by a super tiny amount of time and this creates width - because the guitar on one side is no longer identical to the guitar on the other.

You can actually hear this exact thing in the delay game at certain levels. If the delay is below maybe 15ms, it doesn't sound delayed at all - it sounds wider or thicker.

BretzL + Aike have explained this as well, idk if my explanation helps or is just more of the same but if you ask what you really wanna know (e.g. how can I add width to mono instruments or why does my mix sound centered when I've panned everything wide) then you'll likely get better info. This is just the objective truth of what width is.

OK, I am planing to do a series of experiments and delve deeper into whatever theory I will find and will get back here to report my finding when done, in the mean-time: yes, even thou my question was about StereoHead specifically, what I am actually interested in is how, when you already have just one mono track, can you make it wide—so duplicate recording and alike do not count. Just a reminder thou: for example panning to one side, or making one side louder/quieter technically makes the two channels different as well, but, I hope we will all agree, that that does not make the sound wide.

and one additional thing: by wide I mean the specific property of spatial perception of wideness that you can subjectively measure on a scale, just like in Stereohead. so it is NOT just ANY difference in the channels whatsoever.

Thank you for the question! Got me doing a few tests in Ableton. I duplicated a mono track, panned one the left, one to the right. At that point, it sounds mono. Then I started delaying one track, one ms at the time. It got wider and wider until about 18ms, then the time difference between left and right starts to be audible, it stops being width. Changing the volume of one track didn't do anything in terms of width. Adding an EQ on one track did add some width, but it felt hard to control the width that way.

Search for the Haas Effect (for the theory). You can do the same with a Stereo Delay. Try Left 0 ms/Right between 5 and 40ms.

This seems like the smoking gun: ***panning to one side, or making one side louder/quieter technically makes the two channels different as well, but, I hope we will all agree, that that does not make the sound wide***. This is not true. Literally ANY difference between the left and right will create width.
If you increase the volume of the left channel but not the right channel, the stereo image will be objectively wider. It won't really sound wider, it'll mostly just sound stranger. But since you said this: ***I mean the specific property of spatial perception of wideness that you can subjectively measure on a scale*** - I'm confident in continuing with the technical definition instead of the musical one.
The measurable, technical reality of width is that it is - full stop, no exceptions, 100% always - anything in the left that is not in the right or anything in the right that is not in the left. That is width. Period.

Changing the levels of the left or right channel only changes the location of the sound in the stereo field but does not make it wider.
To make a sound wider that is stereo you can use mid-side processing and boost the sides / attenuate the mids.
To make a mono sound wider, you can use a delay / Haas effect as described. You can also experiment with applying EQ to different bands on the left and right channel (e.g. boost 1khz and cut 2khz on left channel and boost 2khz and cut 1khz on right channel to create an illusion of width). More complex stereo wideners e.g. the mentioned Izotope use a combination of this frequency shuffling / comb filtering, delays and micro-pitch shifting to widen the signal without causing too much phase cancellation issues / preserving mono compatibility – unless you crank it too much, I guess.

There is a video in learning that really helped me understand this. I am going to try to remember which one. Basically I approach the game as if it is Wall of Sound recording or if it is like a jazz mix where the sideman takes the lead. In Wall of Sound everything is centered and pushed to the audience member. But mixing Jazz you may start with Trumpet center and hot. But as the clarinet takes on the focus, make it hot and center but maybe warming up the bass, so both sound closer to the audience and centered. Obiviously the trumpet might still be playing before tapping out for focus to go to the next player. So make the trumpet sound to left (or right) but further away. I do remember there is another video in learning about 1950s recording-- where 1 suspended mic records the whole rockabilly band. The mix is live and controlled by the musicians moving closer to the mic for featured sound. Not something that a DAW is created to replicate. But you can hear the movement from left/right/center.