Firstly, there is no such thing as true, correct primary colours. They all are arbitrary choices, and they all have faults. It’s only a question of how good is it. Red, yellow, blue is a valid additive and subtractive primary colour scheme. It’s just not very good.
Humans have three types of cone cells in our eyes. Cone cells are what pick up coloured light and let us see with colour vision. This means if you are picking a set of primary colours, the best choice is three. One or two will be very limited to a human, and four or more will give a wider gamut (range of possible colours a human cam see), but is overkill with diminishing returns. A TV for dogs would probably only need two, and a TV for birds would probably need four. Different animals have a different amount of cone cell types.
So what do the three cones cells in the human eye pickup? Well, we call them the Long, Medium, and Short cones. Referring the the wavelength. Long is good for reds. Short good for blues. And mid is good for greens. But it’s not quite that simple, they respond to a range of wavelengths. And M and L overlap a LOT. [Here is a graph](https://en.m.wikipedia.org/wiki/Cone_cell#/media/File%3ACone-fundamentals-with-srgb-spectrum.svg).
Now, taking a look at that graph, it’s pretty clear why yellow is a poor choice for a primary colour. It’s closer to the L than the M. That means if we used yellow and red as primary colours, they both would cause the L cells to respond more than any other cone type. Definitely not ideal.
Is red, green, blue the perfect choice? No. In fact, if you did four primary colours with yellow included, you’d get a wider gamut.
You can represent this in a [graph called a colour space.](http://www.deprintedbox.com/blog/wp-content/uploads/2014/03/color-space-diagram.jpg). Don’t worry really about how you get this graph or what X and Y means, but this show all the colours a human can see. Don’t take the colours too literally, your phone or monitor can’t display all the ones you can actually see. The outside curve of the graph is the rainbow colours, the numbers are the wavelength. You can see the standard sRGB primary colours form a triangle in this space. Anything inside, a RGB display can show you. Anything outside, it cant. This triangle isn’t the whole space, sRGB is not perfect. There are green hues a TV or phone can’t show you.
Also shown is a hexachroma, or six primary colours space. Also shows a better Adobe RGB triangle, using more pure tones of RGB closer to the rainbow, to get a larger triangle. That’s also why QLED, or quantum dot LED, TVs are all the rage. The quantum dots are just fancy ways to make the pixels a more pure tone of each colour, getting a wider triangle.
Also shows CMYK, or cyan, magenta, yellow, black, what printers use. A subtractive colours space. Red, yellow, blue, the subtractive (paint, pigment) primary colour scheme many are taught in grade school is also a very poor choice. CMY is way better, but most kindergarteners don’t know what magenta is, so use red. And blue for cyan.
Now imagine you replaced green with yellow on the sRGB triangle. See how much the triangle would shrink in area? That’s why we don’t use red, yellow, blue. It would suck.
You can make any primary colour scheme you want. Just pick colours on this graph and draw a polygon with them. The more pure the colours are, and the more you pick, the larger you can make the area, and the better it is. The perfect primary colour scheme would to have thousand of primary colours all around the rainbow. Would perfectly capture human vision, but your TV would be a $2 million and need a server farm to store a single movie. It wouldn’t be worth it.
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