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  Resources - Colour

You will most likely be familiar with the traditional colour wheel.



This doesn't help very much when it comes to mixing pigments from paint tubes. The question often arises: "Why can't I mix the colour of that object in front of me?".

This article will answer the question of which colours you can mix and perhaps more importantly which colours you cannot mix from a given set of pigments.

A more formal statement of what I am showing is:
"Within the universe of all possible colours (all hues, their shades towards black and their tints towards white) devise a pictorial way of showing the subset of colours available when mixing a given three artist pigments."

A Universe of Colours
Here is an alternative colour wheel. Note that the colours get darker towards the centre and the centre itself is black. This is what happens when you mix colours without using white - the colours cancel each other out. (see reference 3 below)


Imagine that the original colour wheel lies on the ground floor of a cylindrical tower. On the next floor, each colour has been mixed with a little white. More white on the floor above that, and so on until the top floor is all white. I haven't shown the top floor - it is just a white circle on a white background.


This shows a slice out of the cylinder. The red slice shows red shading towards black along the base and tinting towards white as it goes up. The blue slice works the same way.


I have now represented all possible colours. Black through greys to white up the centre. Each hue from fully saturated colour (maximum chroma - see definitions below) through tints to white up the outside and also shades through to black in the centre of the base.
This is the full universe of colours. Our mixed pigment colours will lie somewhere within this cylinder.

Three Primaries
For simplicity in this explanation, I am going to restrict the colours I use to these three primaries:
  • alizarin crimson - a red with a purple bias
  • cadmium yellow - a yellow with an orange bias
  • ultramarine blue - a blue with purple bias
Note that white is not being used - I will deal with that later.


Mixing Two Colours
If I start with two colours (in this case cadmium yellow and ultramarine blue) and mix them in different proportions I get a set of colours ranging from yellow through green to blue. Note that I have mixed them along a line. Obviously intermediate colours could also be mixed until there is a continuously changing colour all the way from yellow to blue. Note that the mid green is not a very bright green.


Similarly mixing alizarin crimson and ultramarine blue I get a set of colours ranging from red through purple to blue. These are all very dark in tone and don't show up well in the photo. In practice I will need to dilute the colours with white (more on that later).


To complete the triangle I mix alizarin crimson and cadmium yellow to get a set of colours ranging from red through orange to yellow. I am sorry about the background colour of the palette changing - it is due to changing lighting conditions as I have taken each photo.


The Centre Colours
It is now possible to mix a range of colours within the triangle with black in the middle. These give the tones (darker versions) of each of the outside colours.
I can use tube black, or I can mix black from my primaries. To mix the black, I use some of each colour. Initially it will probably not be black, but it can be adjusted so that it is by adding the opposite (complementary) colour:
  • if the mix is red-ish, add green
  • if the mix is brown-ish (a dark orange), add blue
  • if the mix is yellow-ish, add purple
  • if the mix is green-ish, add red
  • if the mix is blue-ish, add orange
  • if the mix is purple-ish, add yellow
Hint: I need much less yellow (a light tone) than the others.
It may be that with a particular set of primary pigments I do not get black, but a very dark grey. I can still get a neutral grey without any colour bias.

It is now very easy to take some of the black and mix it with each of the outer edge colours to give intermediate shades of colours.


You can see that the mixed pigments match well with the triangle in the colour wheel below. It may be that the straight line between yellow and blue should curve outwards a little to pass through the actual mixed colours. The real point though is that the mixtures do not lie along the rim of the colour wheel but lie somewhere well within the rim of the wheel.


Important Points
Now, some important points arise:
  • The colours I can mix from the set of primaries I have used lie within the triangle.
  • The brightest (most saturated) colours available lie around the rim of the colour wheel. They must come direct from a paint tube.
  • All mixed colours will be duller (less saturated).
  • If I want a bright (fully saturated) green, for example, I cannot get it from the three primaries I have used.
  • All colours are available from my three primaries, just not saturated colours.
  • I cannot necessarily match an observed colour. It may lie outside the triangle of colours I have available.
  • I can match an observed tone, but I may need to add white.
White
My mixed colours lie within the ground floor triangle. As I progressively add white to each colour I am projecting my base triangle up through the cylindrical tower of possible colours. Imagine you now peel the cylinder away to leave a trianglar based tower.
  • Up the red corner there will be a sequence of tints ranging from red through pinks to white.
  • Up the yellow corner there will be a sequence of tints ranging from yellow through to white.
  • Up the blue corner there will be a sequence of tints ranging from blue through to white.
  • Up the centre there will be a sequence of greys ranging from black through to white.
More Colours
If I now add to the pigments I have used I can get a larger range of colours. These are the commonly used 'double primaries' - two reds, two yellows and two blues.
  • alizarin crimson
  • cadmium red
  • cadmium yellow
  • lemon yellow
  • cobalt blue
  • ultramarine blue
Note that the range of colours I can now mix lie within the white polygon. A larger range of colours than before but still not all colours. If I want an even brighter green, for example, I will need to add viridian green or phthalo green. This will take the polygon of available colours more towards the edge of the colour wheel.


Earth Colours
If I use burnt sienna and yellow ochre with ultramarine I get a more restricted range of colours.
  • The range of colours I can now mix still lie within the (new) white triangle.
  • This is a much smaller range of colours than before but can still be useful. In fact it was used a lot by the old masters.
  • Burnt sienna and ultramarine are complements so mixing them gives black without needing a third colour.
  • Neither burnt sienna nor yellow ochre are fully saturated colours, so they do not lie on the perimeter of the colour wheel.


Alternative Colour Wheels
The colour wheels I have used above are the traditional ones used in art books, where the three primary colours are red, yellow and blue, spaced equidistantly around the circle. The secondaries are orange, green and purple.

In all these diagrams I have started with red at the left and progressed clockwise towards yellow. The diagrams are similar but are intended to show the differences.

The first alternative wheel is that used in televisions and computers, where the three primaries are red, green and blue. The three secondaries become yellow, cyan and magenta. It just means shifting the colours around the wheel a bit.


Munsell uses a different distribution of colours, defining five equally spaced primaries, namely red, yellow, green, blue and purple. Note that the complementary colours are not the same as the standard wheel or the computer wheel. Munsell's research was based on the responses of the human eye. Some people argue that they give better results.


Definitions
Hue - the colour itself, e.g. red, orange, yellow, etc and all the un-named colours in between.
Saturation - how intense the colour is. Munsell uses the term chroma. For my purposes chroma and saturation are synonymous.
Tone - the dark to light range whether it is for a colour or black.
Tint - a paler version of a colour, somewhere between full saturation and white.
Shade - a darker version of a colour, somewhere between full saturation and black.

Further Reading
Munsell colour system in Wikipedia.
Michael Wilcox - "Colour Harmony and Contrast for the Artist"
Michael Wilcox - "Blue And Yellow Don't Make Green"

Colour Harmony
It has been said that a restricted palette (few colours) will give a painting colour harmony. As far as I understand it, colour harmony is about complementary colours, analogous colours, split complementary and so on. Even with just the original three primaries, all colours are available, just not saturated versions of them. So to my mind colour harmony rests with the artist and the choice of colours to use in a painting, not the set of pigments he uses to paint with.

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