5x7, acrylic on canvas
I'm teaching a color class right now, and one of the things we did last week was to make our own Color Wheel. We discussed color wheels, and made our own, using the traditional primaries of red, yellow and blue.
Ten students chose their reddest red, yellowest yellow, and bluest blue, with the goal of making a twelve hue wheel with the values equal from the three colors. Students could make three-quarters of the wheel perfectly, but one quarter needed the addition of other colors to come out perfectly.
The pigments we use all have a color bias towards either warm or cool. If your yellow was cool, for example, and your red was cool, the resulting color would be too cool/dull for a nice warm, bright orange, since both the cool red and yellow would contain some blue. If your choice was warm yellow and warm red, a nice orange would result. Mixing a nice purple could be the issue if your blue and your red were warm. The yellow bias of the colors would make the purple duller than if you had a cool red and blue.
That's one reason why a three color palette, plus white and maybe black, will give you a wide range of colors but you still will not be able to mix every color that you want. A palette with a warm and cool of each primary offers more versatility.