With a palette of pure blue, red, yellow, white and black, you can make a whole rainbow of colors, bounded logically by a system called color theory. Isaac Newton created the first color wheel in 1666 in defiance of the then-common and mistaken belief that color was simply a mixture of light and darkness. Newton showed that only light was responsible for color, and his color wheel showed how these colors all correlated, beginning with three primary colors that can't be reduced into other colors: red, blue and yellow. Though now we know that the Cyan-Yellow-Magenta color wheel is most scientifically accurate, the Red-Yellow-Blue model is the color wheel that paint mixing is based on.
As you likely remember from grade school, primary colors can be combined to make secondary colors. Mix equal parts red and blue paint, and you get purple; mix equal parts red and yellow paint, and you get orange; mix equal parts blue and yellow paint, and you get green. If these colors are arranged in order on a wheel (red to orange to yellow to green to blue to purple and back to red), the color opposite each primary is its complementary color – for instance, green is complementary to red. These complementary colors make each other appear brighter because each color provides a maximum contrast.
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These colors are formed by mixing equal parts of a primary color and one of the secondary colors on either side of it. Through this, you can create red-orange (vermilion), yellow-orange (amber), yellow-green (chartreuse), blue-green (teal), blue-purple (violet) and red-purple (magenta). You can also make tertiary colors by mixing secondary colors to create orange-purple (russet), purple-green (slate) and orange-green (citron).
You can combine these new colors, too, to make quaternary colors. Yellow and amber make golden yellow; amber and orange make orange peel; orange and vermilion make persimmon; vermilion and red make scarlet; red and magenta make crimson; magenta and purple make aubergine; purple and violet make amethyst; violet and blue make indigo; blue and teal make turquoise; teal and green make viridian; green and chartreuse make apple green; chartreuse and yellow make lime green. You can also mix russet, slate and citron to make russet-slate (plum), slate-citron (sage) and citron-russet (buff).
These colors, made by mixing quaternary colors, create different shades of grey. They'll never, however, reach black.
In paint mixing, you can use white and black paints to create darker and lighter shades of a certain color, in fact changing the color from near-black to near-white. Also, note that with a pigment color model – such as in painting – all colors added together will create a near black, but it won't be exact.