I wrote this essay by arguing from aesthetic principles:
Originally Posted by keithwms
But further digging has revealed that the orange-violet-green triplet was used by early tricolor methods. The US patent for Autochrome (here) suggests using this triplet, and I've seen it crop up as a standard filter set elsewhere too. I'm not sure if the triplet was dictated by the availability of suitably pure filters with low absorbtion in the passband, or if it was motivated by existing ideas of which colours were complementary to which on the prevailing colour wheel. Regarding CYM as the natural complement to RGB is a relatively recent phenomenon.
If you look at the CIE diagram and regard it as a coordinate space it is obvious two primaries can only mix to produce the colours on the line joining them in the CIE diagram - if you have three you can access the triangle between them. In principle, any three will do, but 'bad' choices will limit your gamut, and some colours have higher filter factors than others, which has practical implications.
These days a tunable laser or supercontinuum source will allow you to access the entire saturated edge of the CIE plot, and in theory at least produce any colour you like in a projected image. Land's retinex experiments got very close by adding the complementary colour to the primaries, effectively allowing negative values (just as cyan is negative magenta+yellow in RA4 printing). With prints though, you are limited to triangular gamuts.