Depending on the purpose of what you working with, different color models with different primary colors exist. The primary colors in a system is those colors that make up all other colors that can be made in the visible spectrum of colors.
Below are outlined three color models that all are designed different since also the underlying need and purposes are different:
Even if the whole color gamut can be created in CMY, black is often not produced by this system since the color created does not become true black. The reason for this is that the colored inks always contain minor impurities.
To enhance the color and contrast of black the latter is often added as a separate black cartridge to the printer systems thereby creating the CMYK color model. Most of the color inkjet printers out on the market use the CMYK model instead of the CMY model because of above reasons.
As noted above, there is a difference between the RGB and CMY(K) color model. This is also the reason why you can't produce a photo in RGB mode and expect it to look the same on printed paper. The RGB color model is limited to fewer colors then the CMY(K) color model which means that color shifting can and most likely will occur while going between the two models (i.e. from the screen to the printer).
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