## Color wheels, RGB, and CMY

This post has five goals: to describe two color wheels; to describe tints, tones, and shades; to describe the HSB (= HSV) color model; and to relate the HSB color model to tints, tones, and shades.

Correction: having written a first draft, I see that I will need three posts. The purpose of this post is to describe two color wheels.

Here they are. (Two of the greens in the 2nd color wheel look identical on my monitor – but they have different RGB specs. And I am used to putting red on top, but when I assembled them – below – I put red on the right. I had a reason. Next post!)

First, let us recall the color wheel that we probably learned about in grade school. Called the artist’s color wheel, it is the first one that I showed. It starts with three primary colors – red, yellow, and blue. By mixing adjacent primary colors, we create three secondary colors – orange, green, and violet. Finally, by mixing adjacent secondary colors, we get six more colors, called tertiary. The “mixing” in such a case is called “subtractive”. We imagine that we are actually mixing paints, watercolor or oil, but we are physically mixing paints. The two most relevant books for this in my bibliography are Wilcox, and Quiller.

This is one of the two major purposes that I see for this color wheel: to describe the mixing of paints. To my mind, however, that the mixing is subtractive is a side issue. For me, the crucial fact about that color wheel is that green is opposite red. That is related to the second major purpose of this color wheel. I cannot say that I understand it – and I will explain why not, later in this post – but the second purpose of this color wheel is for describing and selecting combinations of color. The most relevant book for this theory in my bibliography is Color Harmony Workbook, but the basic description of color combinations (as monochromatic, analogous, complementary, clash, or split complementary, or primary or secondary or tertiary) can be found in almost any book about painting.

This color wheel is called the artist’s color wheel. I also think of it, personally, as the physiological color wheel because when it is used to select color combinations, it addresses our perception of color combinations.

Then there is the second color wheel I displayed. It starts with either red-green-blue or with cyan-magenta-yellow. In either case, red and cyan are opposites, as are green and magenta, and blue and yellow. So, if we start with cyan-magenta-yellow – as we would if we were discussing printing – we add each of their three opposites precisely opposite them. Or, if we start with red-green-blue, we add each of their opposites, namely cyan-magenta-yellow respectively. (If you haven’t already, note that the order of letters corresponds: RGB ~ CMY.)

In this case, our mental model is that cyan is what is left if red is removed from white light: that is,

cyan = white – red
magenta = white – green
yellow = white – blue.

Implicit in what I just wrote is the idea that cyan plus magenta plus yellow gives us white, or the idea that red plus green plus blue gives us white.

white = cyan + magenta + yellow = red + green + blue.

Even though cyan, magenta, and yellow are the basis for “process color”, more usefully described as “four color printing” – the fourth color being black – the simplest definitions of cyan, magenta, and yellow are: what is left when red, green, and blue respectivey are removed from white light.

(I would be embarrassed to tell you how long and how far I had to search to get someone to say that “process color” was the same as “four color printing”. And just in case you are in the same position I was when I first started looking at all this, “spot color” means “not-process-color”, that is, “Here is the ink I want; please use it.)

That is, although “four color printing” is hardly additive mixing, the easiest definitions of its colors is from an additive model.

Let me be clear: it is an additive model because C + M + Y = white instead of black. Our definition of the artist’s color wheel, by contrast, was subtractive: it implies that red + blue + yellow = black.

I have seen people argue that magenta “is” red, and cyan “is” blue, so CMY “are” the artists primary colors. I would say, no way. The second color wheel (see the RGB additive color space, below) clearly distinquishes blue from cyan. It is also not uncommon for a book to describe one of these color wheels but not the other. Or you may find people associating one of these color wheels with additive, and the other with subtractive color. For that, the issue is whether you are mixing lights or pigments. Do your primaries combine to form white or black?

Now would be a good time to point out that we sometimes need to distinguish between color as a frequency of light and color as a sensation which we perceive.

Again, however, that our initial model is “additive” – white = red + cyan, etc. – is a relatively minor point. The fact is that the mixing of cyan, magenta, and yellow inks (plus black) was the mainstay of the printing industry from the 1930s. Such mixing is not unambiguously subtractive, but it is far from additive – the halftone process, laying down dots of the various colors in various patterns, means that we are getting both active and subtractive mixing. (For a nice introduction to color reproduction, see Rossotti, Hazel. Colour. Why the World Isn’t Grey. Princeton University, 1985 (paperback, with corrections).ISBN 0-691-02386-7.)

For me, the crucial fact about that color wheel is that cyan is opposite red. I do not know of a universal name for this color wheel. Because I first encountered cyan, magenta, and yellow while reading about mixing colors for printing, I first called this the “mixing” color wheel. I think that is a poor choice. A far better name might be the TV color wheel, because our color televisions work by triggering red, green, and blue phosphors on a screen, and are additive mixing. A plausible alternative name might be the printer’s color wheel, because it defines – as the artist’s color wheel does not – cyan and magenta, as well as yellow.

At some point I stopped worrying about additive or subtractive and just focused on there being two slightly different but distinct color wheels. (It’s rather difficult to reconcile cyan opposite red with green opposite red.) Whenever I find myself looking at an arrangement of colors – whether it is a wheel or not – the first thing I look for is: what color is opposite red? There are color layouts which do not use either green or cyan; what I found is what I would, rather harshly and certainly rather hastily, call a copout.

But I really should not be that harsh. There are a whole lot of colors out there, and I haven’t begun to give you a precise definition of “red”, “green”, or “opposite”.

So we have two color wheels. Which of them is right?

Both. They describe different phenomena, and they serve different purposes.

My reservation about the artist’s color wheel are two: it shows violet opposite yellow, and blue opposite orange. In principle, at this stage of my understanding, I’d like to see yellow opposite blue. Let me elaborate, and explain why the artist’s color wheel serves a second purpose, the description of color combinations. We’ll see more of the TV color wheel later.

Artists have known for a long time how to mix the few pigments they had in order to get more colors. In the early 1800s, Thomas Young seems to have suggested the beginnings of the “tristimulus” theory of color: that red, green, and blue light could create all the other colors we see. I think it was Helmholtz who explicitly modeled red, green, and blue receptors in our eyes, in the mid-1800s. (I am not sure of what he did. I know that Young is given the initial credit for the tristimulus theory, but I strongly suspect that Helmholtz did more for Young’s theory than just popularize it.)

Regardless of the exact assignment of credit, the next key figure is Hering, at the end of the 1800s, who advanced the “opponent color” model. While we could, and some do, use more complicated models, a simple starting point for modeling color vision in humans is as follows.

We have three kinds of cones, responsible for color vision, and we call them red, blue, and green. The cones generate three signals denoted R, G, and B. But what is transmitted deeper into the brain – the eyes might well be considered part of the brain – is the following: the sum R + G, the difference R – G, and R + G – B. If we name that sum yellow, so that Y = R+ G, then we can write the three signals transmitted as

Y
R – G
Y – B.

In any case, that R – G signal is the one that makes us perceive green and red as physiological and psychologcal opposites.

That is the source of my reservations: yellow and blue should be opposites exactly as red and green are. But I say again that I have not defined those signals, and I certainly haven’t assigned colors to them. I expect to understand this as I investigate more deeply the transformation from light frequency into color sensation.

I have read (Starmer, Anna. The Color Scheme Bible. Firefly Books, 2005. ISBN 1-55407-032-5) that Hering actually presented a color wheel with 4 psychological primaries. One could say we just declare that red, green, yellow, and blue are primary. Or one could take the union of the sets of artist’s primaries {red, yellow, blue} and the TV primaries {red, green, blue} and end up with a set of 4. (Leonardo da Vinci also favored this set of 4 primaries.) If we form the obvious secondaries, we would get something like:

That’s tempting, but I’m not ready to abandon either the artist’s color wheel or the TV color wheel.

As I said, the artist’s color wheel is most commonly used for two purposes. First, it is used as I introduced it: to describe a double handful of colors as the successive subtractive mixing generated by three primary colors. Second, it is used to describe psychological opposites as part of the theory of color harmony. On the one hand, it describes the subtractive mixing of paint pigments; on the other, it displays red and green as psychological opposites.

I use the TV (printer’s) color wheel for two purposes. First, it gives me definitions of cyan, magenta, and yellow. Let me add that Foley & van Dam et al. describe this model of RGB and CMY as the RGB additive color space (p. 585 of my edition).

black = (0,0,0)
red = (1,0,0)
green = (0,1,0)
blue = (0,0,1)
white = (1,1,1)

and then we have

cyan = (0,1,1) = blue + green = white – red
magenta =(1,0,1) = red + blue = white – green
yellow = (1,1,0) = red + green = white – blue

Second, the printer’s color wheel shows up in some other color spaces, of which I will mention HSB (= HSV), and HSI.

In fact, I think the HSB model is next.

Posted in color. Tags: . 3 Comments »

### 3 Responses to “Color wheels, RGB, and CMY”

1. drj11 Says:

In what sense do the two identical looking greens in the second colour wheel have different RGB specs?

They both display as #00ff00, with or without the iCCP chunk. I used Apple’s DigitalColor Meter to check.

2. rip Says:

No wonder they look they same.

But when I open the original Adobe Illustrator document, the HSB values are 90, 100, 100 and 120, 100, 100; the RGB values are 128, 255, 0 and 0, 255, 0; and even the web safe values differ: 80FF00 and 00FF00.

And even in the Adobe original, i cannot see any difference between those two greens. I guess that what I put is not what I get.

Rip

3. rip Says:

Thanks for mentioning the DigitalColor Meter; I had never noticed it. Anyway, i get just what you said: the two greens are identical according to it.

Rip