Tag Archives: subtractive colour mixing

Colour Mixing

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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.

Why yellow and blue don’t make green

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[and why we should stop teaching it in schools]

You will find images like the one above, that show that red, yellow and blue are the primaries and that yellow and blue make green.

Sometimes this is represented as a colour wheel:

So some people say yellow and blue make green. And you will find other answers that say that yellow and blue make black. How can this be?

Well, we need to understand a little science to get to the bottom of this.

The figure below shows what happens when you mix an ideal yellow dye with an ideal blue dye. The blue dye reflects light perfectly in about a third of the spectrum (and absorbs perfectly in the other two thirds). The yellow pigment reflects light perfectly in about two thirds of the spectrum (and absorbs perfectly in the other third).

The problem here is that the blue and yellow pigments (between them) absorb perfectly across the whole spectrum. The people who say that yellow and blue make black are saying so because of this argument.

Note that blue is a particularly bad choice of primary because it absorbs so broadly across the spectrum. [Making the blue even purer would only make the problem worse by the way.] Yellow is a good choice of subtractive primary because it only absorbs in one third of the spectrum.

The problem is, the people who say that blue and yellow make black are wrong of course. Every child knows this. In practice, if we measure the reflectance spectra for blue and yellow pigments they don’t look like those ideal ones I showed above. For a start, they are quite smooth. Here is a reflectance spectrum for a real yellow pigment. (The reflectance factor, by the way, is the proportion – or per cent – of light that the colorant reflects at each wavelength.)

Notice that with a real yellow colorant, it does not reflect perfectly in the middle and long wavelengths and it does not absorb perfectly in the short wavelengths. It reflects and absorbs to some extent all the wavelengths but it absorbs more at the shorter wavelength and absorbs at less the middle and longer wavelengths. The same is true of a real blue colorant; it does not absorb perfectly at the middle and longer wavelengths. The consequence of this is that you don’t get black if you mix blue and yellow. You would get black if the pigments were ideal but they are not. We live in the real world. However, you certainly don’t get a lovely bright green as shown in the colour wheel with red, yellow and blue primaries. You would get a dark desaturated murky dirty greenish colour. The main reason for this is that the blue is absorbing too broadly. Interestingly, if you look at the artist John Lovett’s page he explains that to mix a yellow and blue you should use a yellowish blue (and a bluish yellow). 

Now let’s see what happens when we mix cyan and yellow dyes. We’ll start with the ideal colours.

It’s very nice. We get a lovely green colour. Cyan is a great subtractive primary because unlike blue it absorbs in only one third of the spectrum (the red or long wavelengths). Note that it is precisely because the cyan does not look pure that makes it a great primary – that’s why I get so furious about people saying the primaries are pure colours. The cyan looks bluish-green because it reflects in two thirds of the spectrum and only absorbs in the reddish part. Neither the cyan nor the yellow dye absorb in the middle (green) part of the spectrum and therefore the result of mixing cyan and yellow is a lovely green. Except it is not quite true. Remember, this is for ideal pigments. Real dyes do not look like that. Refer back to the measured reflectance spectrum for the real yellow pigment. In reality cyan and yellow do make green but the green might be a little less saturated than you may wish for because of the unwanted absorptions by the two dyes in the areas of the spectrum where ideally they would not absorb. (It was the great Robert Hunt, who worked for many years at Kodak – for those who knew him – who taught me about unwanted absorptions.)

Have you ever seen this happen. Of course, you have. Whenever you use a printer (which typically uses cyan, magenta and yellow primaries) to get a green, the printer is using cyan and yellow to make the green.

Remember those people who say that you can’t make blue because – yawn – it’s a pure colour that can’t be made by mixture? Well, have you ever printed out blue on a printer? Of course, you have. Let’s look again at our ideal primaries and see if we can explain it.

That’s right. Mixing cyan and magenta makes blue. The cyan absorbs in one third (the red third) and the magenta absorbs in one third (the green third) but neither absorb the short wavelengths.

John Lovett explains that you can do a decent job of mixing red, yellow and blue dyes, but only if you allow yourself to use multiple blues and multiple yellows, for example. If you want to do the best job possible using only three subtractive primaries, then the best you can do is to use cyan, magenta and yellow. 

So finally you can see that the best subtractive primaries are cyan, magenta and yellow because the cyan is red absorbing, the magenta is green absorbing and the yellow is blue absorbing. And what is more, you now understand why this is the case (rather than accepting dogma). You also understand why there is a relationship between the CMY of subtractive mixing and the RGB of additive mixing.

The optimal additive primaries are red, green and blue (I will cover this elsewhere). And for this reason the optimal subtractive primaries are cyan (red absorbing), magenta (green absorbing) and yellow (blue absorbing). 

But don’t be fooled by this lovely subtractive colour mixing diagram. You might not get such lovely blue, green and red colours when you mix real CMY primaries (either on your printer or with inks/paints). Why not? Because of the unwanted absorptions.

If you want to to know more you could do worse that get a copy of Measuring Colour, now in it’s 4th edition, and authored by Hunt and Pointer. 

This post gets quite a few hits so I will take this opportunity to direct you to my short series of youtube clips that describe the issues discussed in this post in a visual way. You can see them here. If you want something a bit more technical check out this short lecture on colour primaries or visit my patreon.

Or visit my Patreon page here for more analysis like this

Why the ‘three colour primaries’ rule is wrong

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A great many textbooks state that there are three colour primaries. This is normally followed by the statements:

  1. All colours can be made by mixing together three primaries.
  2. The primaries – which are often cited as being red, yellow and blue – are pure and cannot be created from mixture.

Not only do I profoundly disagree with these last two statements but I disagree with the statement that there are three colour primaries. Here’s why:

It is relatively easy to go into a lab or studio, start with three colours (any three; you pick’em) and find that you cannot make all colours. People who do this will often say, that theoretically you can make all colours from, say, red, yellow and blue but that practically you can’t simply because the primaries are not pure enough. The problem is, the more pure you make the primaries, the fewer colours you can make!! The fact is you cannot make all colours from three primaries no matter how carefully you choose the primaries. You cannot do it practically and you cannot do it theoretically.

We can trace the idea that primaries are ‘pure’ back to ancient Greece. In those times and for centuries afterwards it was even frowned upon to mix colours at all because of the loss of purity.

It turns out that if you want to make a large range of colours using three inks or paints, the primaries you should choose are cyan, magenta and yellow. Don’t just take my word for it. Go and ask HP, Canon or Xerox. These companies have made printers for decades and make a living out of selling devices that allow consumers to make a wide range of colours with just three primary inks. They all use cyan, magenta and yellow as their primaries.

But how can magenta be a primary you might ask? It’s far from pure. That is because the notion of primaries being pure is an outdated idea (outdated for several centuries I might add) and should not be taught in Schools. Cyan, magenta and yellow make good primaries for an ink system precisely because they are not visually pure – they each absorb in a narrow part of the visible spectrum and therefore emit light quite broadly. Blue would make a poor primary in an ink or paint system because it absorbs at too many wavelengths. Mixing together blue and red inks make a very dirty brownish black colour. So the gamut (the technical term for a range of colours produced by some primaries) of colours we can make from red, yellow and blue inks or paints is quite small.

So, we can’t make all colours from three primaries, the best primaries are not those that are pure, and primaries can be made by mixing other colours. It is easy to show that a blue can be made by mixing together cyan and magenta inks and this is shown rather nicely by the artist Scott Naismith in this very nice youtube video.

We tend to use three primaries in many systems because you can make a great many more colours with two primaries than with one and you can make a great many more colours with three primaries than you can with two. But you can’t make all colours with three. You can make more colours (a larger gamut) with four or five primaries – though you still can’t make them all – but we reach the point of diminishing returns. Is it worth the extra expense of having four or five primaries if three do a pretty good job? Usually not. However, sometimes we do think it is worth using more than three primaries. For a start, most printers use CMYK (cyan, magenta, yellow and black) so that is four primaries. Then we have hexachrome printing systems with six primaries. The Quattron TV is manufactured by Sharp and has four primaries (red, green, blue and yellow) whereas most TVs only have three (red, green and blue).

The truth is there is no perfect set of primaries and there is no fixed number. A set of primaries is simply a set of colours in a colour system that can make a useful range of colours (gamut). Very often three hits the commercial soft spot but that’s just about engineering and economics.

For further information list to my podcast about colour

 

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why I don’t like the colour wheel

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There are many reasons why I don’t like colour wheels of the type shown below:

The first reason is because it perpetuates the myth that the subtractive primaries are red, yellow and blue whereas the fact is that red, yellow and blue produces a rather small gamut of colours. It is certainly not the best choice of subtractive primaries though it is taught as dogma in many art and design schools and throughout children’s education. The problem is that whenever two colours are mixed together there is saturation loss; that is, the resultant mixture ends up being more desaturated than the two components were. The saturation loss is greatest when mixing colours on the opposite side of the colour circle where the resultant mixture can be almost grey. However, for certain choices of primaries, the saturation loss is greater than for others. If red, yellow and blue are used as the primaries then of course it is possible to generate any other hue. However, there is significant saturation loss and the above colour wheel gives completely the wrong impression. It suggests that mixing blue and yellow together, for example, results in a really bright vivid green.

The reality of pigment mixing is much more like the triangular colour wheel shown below:

In the above diagram it can be seen that mixing together yellow and blue results in a really muddy dark green. The purple resulting from mixing blue and red is almost black!! Now it is possible to mix together a blue and a yellow to get a better green. For example, mixing a greenish blue with a yellow will give a much more vivid green. Mixing a bluish red with a greenish blue will result in a lovely purple. We have a name for a greenish blue and a blueish red – we call them cyan and magenta. A much better colour gamut is obtained if we start with the primaries, cyan, magenta and yellow.

Footnote: Some people may look at the triangular colour wheel and think that the reason the colours are dull is that the red, yellow, and blue primaries used are not ‘pure’ enough. Nothing could be farther from the truth. If it was possible to make really vivid and bright red and blue pigments then the resultant colour gamut would be even smaller. Fundamentally, red, yellow and blue just don’t make good subtractive primaries.

subtractive mixing – why not RGB?

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In a previous post I spoke about the difference between additive and subtractive mixing and why the additive primaries are red, green and blue or RGB for short – http://colourware.wordpress.com/2009/07/13/additive-colour-mixing/

The chromaticity diagram – see http://colourware.wordpress.com/2009/09/28/colourchat-audiovisual-guide-to-the-chromaticity-diagram/ – has a very useful property. If you plot the chromaticities of two lights, then the straight line that joins the two points on the chromaticity diagram show you the additive mixtures that can be obtained by mixing together the two lights. If we take three lights, then the additive mixtures that can be obtained are defined by the triangle that is formed if the chromaticities are the vertices of the triangle. Ok – that’s a bit of a mouthful so let’s have a practical example. The triangle in the diagram below shows the gamut that can be achieved when we have three additive primaries that are positioned at the corners of the triangle.

rgb_gamut

 From this diagram it should become obvious why the additive primaries are RGB. Say, we chose, two reds and a cyan as the three additive primaries – well, the triangle would be tiny. In other words, the gamut would not be very big. The biggest triangle in the chromaticity is one whose vertices are formed by a red, a green and a blue. WhichRGB will give the biggest triangle? I don’t know – it’s been something that has been puzzling me for the last few days and I’ll come back to this in a later post. But certainly any RGB triangle is pretty large as long as the red, green and blue primaries chosen are reasonably saturated.

So what happens if we choose RGB as the subtractive primaries? Subtractive colour mixing describes how inks and paints mix together to form colours. The first thing to point out is that subtractive colour mixing is not additive and linear – you remember I said that when you mix two lights together the colour mixtures all fall on the straight line that joins the  two points in the chromaticity diagram that represent the two lights? Well, this is only true for additive colour mixing. So to work out the gamut for subtractive systems is not an easy thing to do. However, if you do select the three subtractive primaries as RGB you’ll get a gamut that looks something like this:

rgb_subgamut

Notice that the gamut is concave. Mixing red and green lights produces a nice yellow. You can test this by going into your colour-picker in software such as Photoshop or Powerpoint and setting the RGB values to be 255:255:0. You’ll get a nice yellow. But mixing red and green paints – it will give you a similar hue to yellow but you’ll get something quite desaurated; most likely you’ll get a brown. So using RGB as the subtractive primaries would not be a very good thing at all.

It turns out that additive and subtractive colour mixing are very related. The best subtractive primaries are the ones that control the amount of red, green and blue light reflected. A yellow dye applied to textiles, for example, mainly absorbs short wavelengths in the blue section of the spectrum, allowing the other wavelengths to be reflected by the textile. The “other wavelengths” that are reflected give yellow. But the important point is that the yellow dye absorbs blue. Similarly, a magenta dye absorbs green and a cyan dye absorbs red. This leads to the idea of the optimal subtractive primaries being those that are cyan, magenta and yellow or CMY. This leads to a gamut somewhat like this:

cmy_gamut

The biggest gamut for subtractive mixing is obtained by using CMY as the primaries. But weren’t you taught at school that the subtractive primaries are red, blue and yellow? Almost certainly you were – and this is because it is accepted dogma at most art colleges and in many art and design textbooks. But it is quite easy to show that the optimal primaries – those giving the largest gamut – are CMY not RBY. If you were building a colour-reproduction system using only three colours such as a printer you would come to the conclusion – as companies such as HP, Xerox, and Epson have done – that you get the largest colour range with CMY. So why has it become commonplace for artists to refer to red, yellow and blue as the primaries? Could it be a colour naming and language issue – that they really mean cyan when they say blue and it’s just a naming error. Possible, but not likely in my opinion.  I think it is more likely that most artists are not overly concerned that RYB gives a smaller gamut than CMY because they rarely restrict themselves to three primaries. An artist would typically use 6 or more primaries. For example, they might use two blues (one that is reddish and one that is greenish), two reds (one that is yellowish and one that is bluish) and two yellows (one that is greenish and one that is reddish) in order to easily be able to mix a wide range of colours. The (mis-)identification of RYB as the subtractive primaries has much to do with colour wheels. I like to keep each of these blog posts reasonably concise – if I start writing about the problems of colour wheels now I will be writing for another 2 hours. And it’s nearly midnight now so colour wheels will need to wait for another day!