Tuesday, December 24, 2019

What is the most accurate color wheel?

I received a question the other day. This happens to me all the time. Just a thought here... Maybe I would get fewer questions if I pretended to be ignorant rather than all this pretending to be an expert? I will have to talk with an image consultant about that.

Here is the latest example of things that people want to know.

I have a question for you. I understand that there are different color wheels for different subjects. ... I haven't noticed before...there seems to be two "main" color wheels, but which one is the most accurate?

With the wheels that have 12 colors there seems to be two that come up - one with a red-orange and no magenta, or one with a magenta and no red-orange.

Which one is more accurate? Or are they both accurate but for different reasons?



I have a lot to say on this topic -- enough that I will break it up into two blog posts. In this blog post, I will look at various color wheels, with a eye toward the underlying theory. In the subsequent blog post, I will look at the more general question of the utility of color wheels in general.

Red, blue, and yellow primaries

Here is a color wheel that does not have magenta. This beautiful little color wheel with 72 spokes dates back to a book by Michel Eugene Chevreul in 1839. He was a chemist involved in the dyeing of carpet. His work on color perception came out of trying to understand why dyeing did not always turn out as one expected. This color wheel was his first step in understanding color.

This is kinda pretty, but the left-hand side of this color wheel is a bit dark for my taste. It could be that the colors faded -- after all, this book was made in 1839 afterall. Or it could be that the creation of the color plates suffered from the fact that a good magenta pigment wasn't invented until 1858.

The image below (on the left) is a black and white version of Chevreul's color wheel, with color words for each of the 12 basic colors. Each of these 12 colors are subdivided into 6 steps to make a total of 72 colors in the wheel. At the right, I show my colorized interpretation.

I drew a little triangle inside my rendition to make a point. The colors red, blue, and yellow are all explicitly called out, and are conspicuously 120 degrees apart. The Chevreul color circle is based on the artists' primaries, red, blue, and yellow.

This color wheel satisfies Ashley's first criteria: "one with a red-orange and no magenta". RO is red-orange, and VR (violet-red) appears maybe somewhere around where magenta might be. Perhaps if the color name magenta existed at this time, it may have been incorporated into the color wheel, but I haven't had the opportunity to query M. Chevreul on the topic.

Red, green, blue primaries

My computer monitor doesn't use the artist's primaries. For some silly reason, it uses red, green, and blue. (Note to self: I need to contact those people who design computer monitors and televisions and screens for cell phones and tablets. They need to learn about the artist's primaries, because clearly that would be a much better way for them to encode color.)

I did a little playing in PowerPoint (my graphics design program of choice) and came up with my own  twelve step program... err, twelve step color wheel. I hope that everyone reading this takes a moment to step back and say "ohhhhhhh...." in appreciation of my epic artistic skills.

The Seymourian twelve-step RGB color wheel

For those interested in the details, the red, green, and blue anchor points are (255, 0, 0), (0, 255, 0), and (0, 0, 255). The halfway points between them are yellow (255, 255, 0), cyan (0, 255, 255), and magenta (255, 0, 255). I filled in the points between using HSL coordinates. The hue of HSL goes through steps of 21.3333 from 0 to 235.

This color wheel fits Ashley's second criteria: "one with a magenta and no red-orange". The magenta is at the very bottom, and there is red, and there is orange, but no steps in between.

Cyan, magenta, and yellow primaries

I have a little bonus for those involved in my twelve step program: a color wheel that is specially designed for anyone involved in printing. Here we see that the basic colors are cyan, magenta, and yellow. Please note carefully that the cyan-magenta-yellow color wheel bears no resemblance at all to the red-green-blue color wheel. None whatsoever. Completely different.

The Seymourian twelve-step RGB color wheel

That last line was just a tiny bit of sarcasm. I said that as a way to highlight the fact that these really are the same color wheel. Both are based on RGB color theory, which is a simplification of scientific color theory. This is a fascinating and illuminating topic, and one which is worth a whole blog post to itself.

Oh... I should mention one thing here. Cyan, magenta, and yellow don't do so well at getting all colors. Early printers found it was a good idea to add black. Oh yeah, one more thing... When you print magenta over cyan, you don't really get blue. It's usually more of a purple. And when you print yellow over magenta, it's not a good red. It's a little too orange.

As a result... lately there has been a lot of kerfuffle about expanded gamut printing, where you print with CMYK, but then add in orange, green, and violet inks to extend the range of colors that you can get. Or sometimes you use red instead of orange, or blue instead of violet.

The artists' primaries

Allow me for the moment to revisit the concept of artists' primaries on which the Chevreul color wheel is based. I was taught in kindergarten that:

1) Red, blue, and yellow are the primary colors.
2) You can make all the colors by mixing appropriate amounts of these three primaries.
3) Red plus blue is purple. Red plus yellow is orange. Blue plus yellow is green.

The first is more of a definition than anything that you can test. But the second and third are testable. The second is hard to test, but I tested the third one during lab period in kindergarten. An actual image of the results of my experiments has not survived, but a rough approximation is shown below.

Artists conception of the artists' color wheel

I recall presenting my disappointing results to Mrs. Reidhouse, who was the main lecturer in my kindergarten class. I also vividly recall trying to explain to her that the lack of saturation in the pairwise mixtures was predictable using the Kubelka-Munk equation. But I don't recall her offering a cogent counter argument in support of the artists' primaries theory of color. I do recall being told that it was nap time, though.  

I was trying to articulate to her a basic postulate of paint mixing: Mixing pigments will usually lead to a loss in richness (chroma) of color. In other words, you can't get a rich, vivid green by mixing yellow and blue. You can't get a rich purple by mixing red and blue.

If you find yourself disagreeing with this, then I suggest you visit an art supply store. If Rule 2 were correct, then you would generally see beginner paint sets with five different paints: red, blue, yellow, white, and black paints. Maybe you would see sets with more colors premixed, but if you look at the ingredients, you would only see those five basic pigments. There would be no need for any others.

This set contains 12 of the most popular colors in 2 oz (59 ml) tubes, including Burnt Umber, Burnt Sienna, Raw Sienna, Yellow Oxide, Naphthol Crimson, Cadmium Orange, Phthalo Green, Yellow Medium Azo, Cadmium Red Light, Ultramarine Blue, Titanium White, and Mars Black.

Still not convinced? Then take a trip to the hardware store and ask to see their paint mixing equipment. Count the canisters... do they mix all the colors of paint with five pigments, or are the dispensing devices "Available as either 12, 14, or 16 canister turntables"?

Here's another suggestion for those not yet convinced. I put together a little a do-it-yourself guide to printing with the artists' primaries instead of CMY. Visit my blog post, print out the supplied images, and see what kind of results you would get if HP supplied you with red, blue, and yellow ink cartridges.

In order to get a full range of colors, you need to start with a variety of pure pigments that cover the full range of colors. The theory of the artists' primaries is just plain wrong. 

Red, yellow, green, blue, and purple primaries

Albert Munsell was a smart guy when it came to color. As proof, there was once an upstart wannabe color guru who was so bold as to refer to Munsell as the Father of Color Science. Munsell devised a color wheel that he actually manufactured with paints. (Before I go on, I need to say that his color wheel, was just part of the Munsell color space.)

Munsell started with five primatries. There were an additional five secondaries squished between those five primaries, and each of those ten hues had ten levels in between. Munsell's color wheel thus had a total of 100 different hues.

My rendition of the Munsell color wheel

I want to share a bit about how he created his physical actualization of the color wheel. I share because this is interesting and not well known. Part of this is reverse engineering and presumption on my part. If I have errors in this, I would be happy to recant.

Munsell started with five primaries: red, yellow, green, blue, and purple. With the exception of purple, he had pigments for each of these that he felt truly exemplified the colors. He had to mix two pigments together to get purple, but I mean, how could he avoid purple?

Next he used a creature known as a Maxwell disk to find complements to each of his first five primaries. This spinning disk would have a portion colored with one of his primaries, like red, and another portion colored with a potential shade for the compliment. The complement of red he called "BG" or "peacock blue". He would adjust the pigments mixed for the second pigment until he attained a gray color when the disk was spun.

The ten basic colors in the Munsell color space are listed below. The primaries are in bold type, which coincidentally all have single letter Munsell hue names. Note that Munsell made these with 8 different pigments.

Munsell hue
Color name
Venetian red
Orange cadmium
Raw sienna
Grass green
Emerald green and raw sienna
Emerald green
Peacock blue
Viridian and cobalt
Purple madder and cobalt
Purple madder

(From Albert Munsell, A Color Notation, 1919. Pigments are from paragraph 104, pps. 66 – 67; common color names are from paragraph 58, page 35. I received an email from Robin Myers which recounted the formulations for the ten basic colors that were used in the 1st, 2nd, 4th, 5th, 6th, and 7th editions. The only change over that time was that in the first two editions, 5BG was made with viridian as the only pigment, and later editions mixed this with cobalt. I appreciate having the help of experts like Robin to make sure that my blog posts are precise!)

Red, yellow, green, and blue primaries

A quick review...

The Chevreul color wheel and its derivatives is based on the dubious assumption that red, blue, and yellow paints can be mixed to make all colors. The RGB color wheel is based on the primaries RGB that work well for computer monitors and televisions and cell phones and tablets, and have always worked well in coordinating my underwear. The CMY color wheel is based on the colors of inks that seem to work well, but you almost always want to at least add black. Then you have the color wheel based on Munsell's color space, which in turn was based on a set of paint pigments that Albert Munsell decided upon back in the early 1900's.

These color wheels are all based on the color capabilities of physical stuff. Which is a bit odd, since "color" is largely a function of the spectral response of the cones in the eye, and the brain's processing of the signals from the cone.  It would seem that a color wheel would best be based on what goes on inside the human head, doncha think?

Ewald Hering proposed the idea of color opponents in 1892. His theory was that we sense an object as being reddish or greenish, but never both. There is a continuum of red to green where every color falls. Similarly, there is a continuum from blue to yellow. All color are perceived as somewhere on this continuum. Finally, there is a third such continuum between white and black. This general idea has been borne out with what we have learned about how the cones in the eye and the neurons leading to the brain work together to create color perception.

This idea was incorporated into the color wheel of the Natural Color System (NCS) shown below. This system was developed by Anders Hard and first described in 1966. The rendition below shows 40 steps. The NCS color system is perhaps not as well known as the Munsell color system, but both companies are in existence today, both selling books of colors.

This idea of color opponents (red vs green, blue vs yellow, and white vs black) can also be seen in the design of CIELAB, shown below.

Image from XRite website

I won't say much about CIELAB in this blog post, partly because I am getting tired of typing and suspect that most everyone is getting tired of reading. But, I think I can get away with not talking about the CIELAB color wheel, since I don't recall ever seeing a color wheel that was explicitly built on CIELAB. I say this not to diminish anything about CIELAB.

So, what's the answer?

Which one is more accurate?

The color wheel based on the artists' primaries is not bad, but it is based on a flawed proposition about the primaries.

The RGB color wheel works well for colors on a computer screen. The CMY color wheel works marginally well for printed colors. The two together are compatible, which makes them a very good conceptual model.

The color wheels based on the Munsell and the NCS color systems both have a great deal of research built into them, and accurate physical renditions of each can be purchased. They are both a bit of money, but they exist. And  I would call either of these accurate.

I will leave this discussion for the time being. But beware, I will have more to say..


  1. To me, "Accuracy" will be for ever debatable. I suspect a broader concept as "Applicability" is more "useful". It's like using different pair of glasses to examine a given problem, one pair of glass may not be suited for all situations. But I understand the idea that there ought to be one "color wheel" that is bound to be "more accurate" than others. In a way, all "perspectives" on this "age-old" problem are good and have their advantages/disadvantages. I like Munsell because of its natural ties with CIE Lab, and because, in color reproduction work, the idea of complimentary colors canceling each other out is so fundamental to using a rich set of tools like Photoshop, to remove color casts on an image. But I would not insist of mixing paints using CIE Lab wheels, pigments are unlike "light sources". In a way, "Different strokes for different folks". I commend you for your efforts, Mr Seymour, for having contributed to the rich field of "Color wheels" :-)

  2. Thanks for your comments about the difference between "Accuracy" and "Applicability". This idea will find its way into the next blog in this series.

  3. According to Harald Kueppers (engineer of pintmaking) printing takes eight basic colours.


  4. As I see it, RGB or CMY color wheel allow you to predict the results of color mixing (a trichromatic wheel if you want), while an opponent color wheel like NCS allow you to predict the relationships that exist between colors, from the point of view of their perception, how we experience them (so a opponent color wheel).
    An artist color wheel, of course, does not allow anything except confusing schoolchildren...

  5. Since we can get CMY by mixing RYB, we can get all resultant colors too. Don't you think so?

    1. I disagree with the premise ("we can get CMY by mixing RYB"). Anytime you mix two pigments, you are likely to lose saturation. The cyan that you get by mixing Y and B will not be as bright as a mono-pigment cyan. Same goes for magenta.