Using a limited palette is one of the best ways to gain control over your palette. You will become very familiar with each color you choose and are forced to explore the limits of it’s usefulness to get a full range of value and color in your painting.
Your palette will be purer and your colors clearer if your primary colors contain pigments for only one other color. For example, your warm red will contain red and yellow, and your cool red will contain red and blue. Your warm blue will contain blue and yellow, and your cool blue will contain blue and green. Your warm yellow will contain yellow and red, and your cool yellow will contain yellow and blue.
If you add any secondary colors to this basic palette, you will want to make sure that they are the true compliments of the primaries. If they are they will make a lovely, lively neutral color rather than a dead, flat color. Black should be added to the palette with caution, since it is a subtractive color that takes light and color away. It’s almost never a good choice to darken, and best used purely as the color black.
White can lighten, but it also neutralizes your color. Titanium is a heavy, opaque white used for good coverage, while Zinc white is more transparent. Transparent mixing white is a fairly new color that can be used to thin out and extend your color without neutralizing it.
In today's Everglades painting I’ve used a limited palette of Quinacridone Crimson, Cerulean Blue, and Lemon Medium Azo, Quinacridone Magenta, Ultramarine Blue and Naples Yellow and a Hookers Deep Permanent green to help with the darks, and Titanium White.
You can simplify even further by using only three primaries plus white and still have all the range you need. Try it, and you’ll find that you may produce some of your most colorful paintings.