I really like this page by John Lovett about colour mixing.

We all know that you can’t mix all colours by starting from three primaries. You can’t do this in theory and you can’t do it in practice. You can’t do it with additive colour mixing and you can’t do it with subtractive mixing. In fact, with subtractive mixing, the oft-cited primaries of red, yellow and blue are actually not a very good choice.

Mixing red and blue pigments, for example, won’t give you a great purple. You will lose saturation and you almost certainly won’t get the vivid purple that is suggested by many colour wheels. However, John Lovett’s page explains how, if you do start with red, yellow and blue, you can do a little better by understanding that there is not just one blue and one red, for example. If you want to mix yellow and blue you should use a greenish yellow and a grreenish blue. On the other hand, if you want to mix blue and red you should use a reddish blue and a bluish red. This reduces the loss in saturation.

However, although Lovett’s advice is superb, you still can’t make all of the colours this way (though you can make all the hues of course). And arguably what Lovett is proposing is a six-primary system rather than a three-primary system. Lovett ends up proposing a six-primary system in an attempt to make the out-dated idea of RYB work.