Think back to your art lessons at school, chances are that you were taught that every colour can be mixed by the three primary colours Red, Yellow & Blue – and the chances are that when you tried to put that into practice the results were disastrous, the purples you expected turned out brown, and the best green you could manage was a sort of dirty looking olive green.
If this sounds familiar don’t worry, even many professional artists and art lecturers get it wrong too, a case in point was a painting course I attended last year where on the first day the Professor tried to explain basic colour theory – but when he tried to demonstrate how to mix a purple from red and blue it turned out brown – so he dipped his brush in some purple paint and painted over the mud he’d created to fix it! and the strange thing was that it never ocurred to him that the reason he had to do that was that his basic understanding of colour was flawed, and had he been using true primaries then he wouldn’t have needed to fudge it.

The true theoretical primaries, Cyan, Magenta & Yellow
The truth is that the ‘primary’ colours taught at most schools & colleges are wrong, modern colour science has proven that the true pigment primaries are Cyan, Magenta & Yellow – not Red, Blue and Yelow, but stubborn dogma on the part of the art establishment means that many artists refuse to let go of their firmly held beliefs, even the abstract painters seem to adhere to these archaic ideas about colour (which is odd when you consider that they claim to be ‘Modern’ artists and yet totally disregard modern scientific theories about colour!)
Another point of view worth mentioning here is that some people disagree with the idea of 3 primary colours altogether, there are no divisions in real life colour (such as rainbows for example) so all pure pigments are in a sense primary colours, the three colour systems are just an artificial way of trying to organise natural physics into a human framework.
There is actually a lot to be said for this point of view, but if you are going to have a usable colour mixing system then you have to choose a set of ‘Primaries’ that enables the maximum amount of colours to be mixed in the most easily understandable way.

Cyan, Magenta & Yellow mixed together to create the Secondary colours Red, Blue & Green
Now look at the simple colour wheel above, this shows the colours you get when mixing the true modern primaries together, the mixture of Yellow & Cyan gives Green just as you would expect, but mixing Yellow & Magenta creates Red! Red is supposed to be a primary colour (and if you remember what you were taught at school, you can’t mix primary colours from any other colours – thats what makes them primary colours!) also mixing Cyan & Magenta together makes Blue – another supposed primary colour!
So in pigment terms Cyan Magenta & Yellow are (theoretical) ‘primary’ colours and Red, Green & Blue are (theoretical) ‘secondary’ colours, so called because they are made by mixing two primeary colours together to create a ‘secondary’ colour.
One disclaimer I need to make here is that the colours you get in a theoretical situation like a computer program are not the same as the Colours you will get when mixing real pigments, not least of all because even now most pigment manufacturers cannot make perfect Cyan, Magenta & Yellow pigments, (or Red, Green & Blue pigments for that matter) which is why I refer to these colours as ‘theoretical’ primaries & secondaries.

Colour mixing wheel based on Cyan, Magenta & Yellow
Now look at the diagram above, this takes the colour mixing wheel further by splitting it up into 12 sections, so that now for example Yellow and Red are mixed together to form Orange, then Red and Magenta are mixed together to create Rose and so on, the dots around the edge show the proportions of the primary colours needed to mix each colour, so for example Orange would require three parts Yellow to one part Magenta.
using a simple colour wheel like this you could mix almost any colour from just the three primaries with a reasonable amount of success (even with the less than perfect pigments you would use in real life)
One oddity that the above illustration brings up is an interesting question regarding colour terminology, according to tradition only the three colours created by mixing equal amounts of the primaries are called secondaries (in this case Red, Green & Blue) and all other colours are classed as tertiary colours (Tertiary means three or third as in three colours or third colour)
But if you look at the colour mixes none of the colours above have more than 2 primaries in their mix so can any of them be accurately be termed Tertiary colours? Since I’m not interested in perpetuating traditions just for the sake of it I’m inclined to call ALL the colours on the above wheel Secondary colours (apart from the three primaries of course).

A colour wheel created using just three colours of oil paint, unfortunately the photo doesn't do justice to the vibrancy of the colours here.
To prove that this colour theory works the above wheel was created in oils using the three modern primaries – this was done without cheating or enhancing the colours in any way, just straightforward mixing (I have read uninformed comments on other blogs about how Cyan, Magenta & Yellow only works in printing – obviously by people who have never even attempted to actually test their theories out, which is why I felt it important to put my money where my mouth is as they say).
The colours used on this colour circle were: Winsor Yellow (PY74), Winsor Blue green shade (PB15.3) and Quinacridone Magenta (PR122), although these are not perfect ‘theoretical’ primaries (ie not as pure as the colours in a computer model) they do a remarkably good job of creating a range of vibrant clean colours that would be impossible with the traditional Red, Yellow & Blue colour primaries.
Now, the crunch question is: does this mean we should only use Cyan, Magenta & Yellow on our pallettes? absolutely not! just because its possible to mix all colours from just these three doesn’t mean you must do so always (despite what some supporters of the CMY colour scheme would have you believe) there are so many beautiful pigments with unique properties all to themselves that it would be ridiculous not to use them!
Colour theory (particularly mixing circles) are tools to help you understand how all the colours on your pallette relate to each other so you can make better use of them – for example knowing that Ultramarine Blue lies exactly between Cyan & Magenta means knowing that you can create a vivid purple just by adding Quinacridone Magenta to your Ultramarine (or you could just use Dioxazine purple)
Of course what I’ve outlined here is just the simple basics of colour mixing, but hopefully it will help you to get cleaner colours in your paintings, so go experiment and see what wondorous colours you can mix with this knowlege!