I posted a swatch yesterday with vermilion and lamp black. Although vermilion and cad. red look very similar, they mix quite differently with black. When mixed with black, cad. red makes dull purples rather than dull mauves as vermilion does.

When mixed with black, vermilion tends toward a dull mauve, which can be quite useful.

I mix these two often. They are not exact complements, but they form a useful set of neutrals. It is particularly helpful that you can get a very dark neutral from them, which I often find to be a good substitute for black.

Update

21 June 2008: For lighter neutrals (grays) I tend to use ultramarine and raw sienna, which makes a more pure neutral. But for darks, burnt sienna and ultramarine is the way to go.

Top row (left to right): Red ochre (Williamsburg), Italian burnt sienna (WB), vermilion genuine (Doak), yellow ochre (WB), Italian raw sienna (WB), raw umber (Old Holland), burnt umber (WB), terre verte (WB), ultramarine blue (Studio Products), German earth (WB).

Bottom row: Florentine lake (Doak), Bohemian green earth (WB), Tuscan red (Studio Products), Pozzuoli earth (WB), Indian yellow (Doak), Fra Angelico blue (Doak), Alger blue (Doak), transparent blue oxide (Doak), milori (Prussian) blue (Doak), indigo (WB).

The ruby is a much stronger tinter than viridian. They mix to a very dark neutral that can substitute for black.

I strongly encourage any painter to do these kinds of experiments with all combinations of the paints they typically keep on their palette.

Although I have more recently been working with an earth palette, I have used cad red + cad green as the basis for flesh tones in a number of figure paintings. Mixed with white, you can create a string of useful caucasian flesh colors. A little extra green makes for good shadows (depending on the light), while a little more red is good for people who have a tan or are naturally more ruddy. But it’s especially good for people with pale complexions, since you can get a good low chroma orange-brown that looks just right for that purpose.

My favorite complementary mixing pair is raw sienna and ultramarine blue. With them, you can mix a lovely range of cool blues, warm browns, and neutral grays. These colors don’t call undue attention to themselves, but they harmonize well with each other and with a wide range of other pigments. It’s a valuable exercise to do a whole painting with just these two colors and white; you’ll be amazed at how much you can do with them. I’ve done lots of paintings in which those two colors predominate, staying in the background and setting the stage to allow other, brighter colors to stand out beautifully. Since both of them vary a bit from manufacturer to manufacturer, it’s worth comparing a few of each with each other. At the moment, in oil, I use Williamsburg Italian raw sienna and Studio Products ultramarine. They mix very well together.

Update

Williamsburg also sells their Italian raw sienna as a pigment; it’s the nicest raw sienna I’ve seen.