A split primary palette is based on the idea that primary colours do not exist, in terms of available pigments. Every colour inevitably leans towards another. As a result, you need two of each. One yellow that leans towards blue, such as cadmium yellow lemon, and one towards red, such as cadmium yellow medium. The same applies to red and blue. With only two pigments in the cold range of their primary counterparts, namely lemon yellow and phthalo blue, this palette emphasizes warmer hues. An ideal choice for someone, like me, who prefers warmer colours, such as in the above landscape, oil on masonite, about 16 by 24".
One of the criticisms of this system is that it does not allow for strong greens. A valid concern, as the lack of a pure yellow and blue could result in a dull green mixture. I compensate by incorporating green pigments, although admittedly preferring to avoid this colour.
At the very least, a split primary palette highlights mixing properties of individual paints; one red alters a colour differently than another. As experience increases, a painter can add and remove pigments in an effort to find a range that best works for them.