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Update: thanks for all the great explanations!
The reason the visible colors form a horseshoe rather than a triangle is due to how the cones’ sensitivity ranges overlap [1]. They cannot be excited independently by the primaries of a display.
[0] https://upload.wikimedia.org/wikipedia/commons/1/1e/CIE1931x...
[1] https://upload.wikimedia.org/wikipedia/commons/thumb/0/04/Co...
I'd like to add that no light source can lie outside the horseshoe of the CIE xyz diagram: pure wavelengths are points on the curved line, everything that mixes them moves towards the inside of the space. So you're stuck with triangles that fit within it.
https://www.jackgaller.com/colorspace
If we had primary color wavelengths that could stimulate each cone independently, then it would work just like you say, and we'd only need 3 of them. But because the cone spectra overlap, we don't have "orthogonal basis vectors" to work with. Our primary colors each excite a mix of cone responses.
But no problem right? As long as each primary color has a different response, we at least have linearly independent vectors, and any student of linear algebra knows you can mix those together to act as an orthogonal basis and get any desired excitation of the cones. Right?
And that would be true, except that linear algebra assumes you can freely add or subtract vector amplitudes, but with LEDs we can only generate light, we can't send a beam of "negative green". So we're constrained to the subset of colors where the basis vectors all have positive amplitudes. And that's the smaller color space that results.
*edit: found the link I was after on this: https://moultano.wordpress.com/2026/06/19/where-to-find-the-...
RGBY televisions do exist, but their goal is to boost brightness in the yellow region, not color gamut.
Cone cell activation is complicated. Displays with three well chosen primaries are economical and effective, but they aren't intended to produce every perceivable color. And our chromaticity diagrams, that pointy splotch that's often used to compare display gamuts, is based on a "standard observer" that is a simplified model for human perception.
An ideal pixel would be able to emit any kind of electromagnetic radiation of any intensity, kind of fun to think about but unrealistic and impractical.
What additional primaries mathematically do is expand a gamut from a triangle to a convex polygon. While ten or a hundred primaries would be bonkers, I bet we could fit a quadrilateral or a pentagon to the perceivable gamut in ways that'd see some gains.
Anyway, things like the green (or blue -can't remember) receptor have a strong curve in the green spectrum, but also a "bump," over in red (I think).
We're an organic mess.
Looking at RGB curves for LEDs, they are three perfect little mountains. No "bumps," anywhere.
I guess that the goal is to try to mimic the "messy" human visual perception.
Also, expect these monitors to be non-cheap. Companies like Eizo are having a difficult time, justifying their prices, these days.
The green-sensitive cones overlap with the red-sensitive cones, and to a smaller extent also with the blue-sensitive.
Full saturation red and blue are possible by emitting light on the edges of the visible spectrum.
Full saturation green, however, also activates the red and blue cones.
To cover the whole gamut is impossible, but you can approximate it with ~three green tones: a 490nm deep cyan that hits blue and green but not red, ~510nm that hits red and blue equally, and ~540nm the peak of the green cone.
The RGB setup we have strikes a balance between cost and visual quality. If the cost of adding primaries goes down you can add more to increase the quality. One issue is that the signals often assume RGB (channels), so the hardware manufacturer would have to adapt the RGB signal to their multi-primary hardware.
"TV Displays Explained at the Fundamental Level" https://www.youtube.com/watch?v=WhFwPAfwdLo
¹https://gbaptista.github.io/luminous/doc/en-US/
Or -using same # of subpixels per cm^2- would perceived display quality be similar due to better color representation?
However, there are tasks that benefit from better color reproduction. There are also screens where the pixel size is well below the human discernable limit.