Why is a color spectrum nicely represented as a circular wheel?

November 30, 2006 1:04 PM

In the continuum of visible-light colors that makes a rainbow, we have red, orange, ... blue, indigo, and violet. But aestheticists tend to join the two ends together to make a "color wheel". They use this to predict pairs, trios, or quads of colors that are symmetrically placed in the wheel and therefore look nice or bad together. But, why does the continuum map to a circle at all?

Red down to violet describe the visible colors we humans can see. But, suppose we could see slightly "lower" than red, infrared. Would that fit into our color wheel well? How would that affect the colors we think of as "complimentary" -- which were previously directly across from each other in the wheel, like at 9 o'clock and 3 o'clock, but now with infrared wedged in are now at 9 and 4?

Stated another way, suppose we couldn't see red at all. Would we think that violet and orange merge together naturally? Why or why not?

(My first Ask MeFi question! Be gentle!)

posted by cmiller to science & nature (21 comments total)

We can idealize the colors that make a rainbow as monochromatic colors--light consisting of a single wavelength. It's not a perfect model of an actual rainbow, since the light source which generates a real-world rainbow is not a point source, and different wavelengths are not perfectly separated, but it'll do.

When we do this, it turn out that the two ends of the spectrum don't match up. Take a look at the CIE Chromaticity Diagram. It correlates wavelengths of light, and mixtures thereof, to colors that we actually see. (Note: the colors that appear in the diagram are only approximate, as computer monitors cannot display all colors.)

The colors which appear on the curved boundary are monochromatic--consisting of a single wavelength, and appearing in our idealized rainbow. The numbers on the curved boundary indicate the wavelength of such light in nanometers.

All other colors in the diagram--both those in the interior of the diagram, and those on the lower, straight boundary cannot be made by light of a single wavelength--it takes a mixture of two or more wavelengths to create those.

If you try to connect the two ends of our spectrum of monochromatic colors--those along the curved edge only--they don't match up--you've got red on one end, and at best a bluish-purple at the other end.

When aestheticists make their color wheels, they include the colors on the lower, straight edge in addition to those along the curved edge. Those colors on the lower edge don't appear in our idealized rainbow. Nothing wrong with including those colors in the color wheel, though, and it seems to work well for aesthetics.
posted by DevilsAdvocate at 1:20 PM on November 30, 2006 [1 favorite]

Color theory can get pretty complex pretty quickly, so I'm sure there will be a lot of answers of all sorts here, but here is my take on it (I have some books on color at home and so may elucidate more later): One reason is that color is in large part our perception, and so our brains are wired to percieve colors that way. Another, related fact is that for both subtractive color (like inks) and additive color (like monitors) there are three primary colors that can be combined to produce the intermediate colors; for subtractive color they are the familiar cyan, magenta, and yellow (CMYK, with K being black); for monitors it is red, green, and blue (RGB). In other word, color and the relationships of multiple colors are not determined solely by wavelength but by our perception as well.
posted by TedW at 1:23 PM on November 30, 2006

If we couldn't see the light wavelength that our brain currently interprets as "red", I imagine that our brain's optic cortex would adjust its color identifier to make orange be red instead. Our eyes have evolved to see the mix of our particular visible wavelengths as "white". I think if the range of wavelengths were different, we would still see it as "white", meaning that when split up prismatically, you'd still see the complete color spectrum without any missing pieces. We haven't evolved to see wavelengths outside of our spectrum because seeing those types of light are not important to our survival.

Also, light colors and pigment colors (covered by color wheels) are different beasts. Obviously, if you mix red paint with blue paint (from either end of the color spectrum), you'll get purple, so the color wheel makes sense because there is a continuum. Meanwhile, in mixing light colors, red and blue will get you magenta. Mixing red and green light will get you yellow.
posted by LionIndex at 1:25 PM on November 30, 2006

Cliff Notes version of my comment above, since that ended up being longer than I intended: Some of the purples in the color wheel, especially the more reddish purples, don't appear in a rainbow. Aestheticists don't join the two ends of the spectrum together--they add in other colors to complete the wheel.
posted by DevilsAdvocate at 1:27 PM on November 30, 2006

It seems that the purples on the color wheel are fake colors that don't actually appear in the rainbow at all. They are composites where the 'red' (short) and 'blue' (long) wavelength detectors are firing at the same time - this conjunction cannot happen with a pure frequency.

They look a bit like the purple of the rainbow - but this is more convention than perception. The purple of the rainbow is very subtle - a kind of deep faded blue.

Alternatively - we have three color receptors in our eyes, red, green and blue. the color wheel is a way of representing intensities along the three possible dimensions - there are other ways - you'll find them in the pickers of most windows applications. The red/blue combinations do not represent pure colors but mixtures. They can be created, but not by a prism.
posted by grahamwell at 2:04 PM on November 30, 2006

See also: When the eye perceives light of wavelength of about 0.35 μm the color observed is violet. This is the output of the so-called blue cones unmixed with the output of the green cones. The so-called blue cones should be called the violet cones. They were labeled blue because they are most sensitive to light in the region of the spectrum where the eye observes blue color. But that [perceived] blue color comes from the combined stimulus of the so-called blue cones and the green cones, with some tiny stimulus of the red cones.

There's more. Blue is not a primary color. Violet is.
posted by grahamwell at 2:32 PM on November 30, 2006

I think the short answer is, after reading DevilsAdvocate's response, that the color wheel is basically arbitrary in the physical sense. There's no natural mapping between the portion of the EM spectrum that our eyes can perceive as color, and a wheel. Instead, the wheel is a construct which has more to do with psychological perception. If our eyes were different -- if we had eyes more like some birds (I think it's birds) that could see into the ultraviolet, or down into the infrared (like infants) -- we'd probably have a different wheel.
posted by Kadin2048 at 2:42 PM on November 30, 2006

Color wheels are a human invention. You shoud totally get this book, cmiller. It addresses all these issues as well as some historic perspective on the development of color wheels. It changed the way I think about color.

Blue and Yellow Don't Make Green by Michael Wilcox
posted by Area Control at 2:49 PM on November 30, 2006

I recall reading that the visible colors don't quite span an octave, with the question: if they did, would the octave be to our eyes as it is to our ears: somehow the "same" thing, just an octave higher?
posted by LeisureGuy at 3:12 PM on November 30, 2006 [1 favorite]

I think that's unlikely, LeisureGuy. Pressure waves are detected via hairs in the cochlea of the ear. We're still talking conventional, mechanical vibration at the point we get to those hairs, so while this is purely speculation on my part, it's not unreasonable to think that just as macroscopic strings can vibrate at overtones which are integer multiples of the fundamental frequency for that string, so might the hairs in the cochlea vibrate. A 440Hz tone might activate not just the hair with a fundamental frequency of 440Hz, but also the one with a fundamental frequency of 220Hz, which may be why the 440Hz tone in some sense sounds the "same" as the 220Hz tone.

Electromagnetic radiation--light--is detected via the electronic excitation of chemicals in the retina, and unlike mechanical vibration, the concept of overtones doesn't apply here. If a certain electronic excitation requires energy which corresponds to light with a wavelength of 600nm, only light of that wavelength will do--neither 1200nm light nor 300nm light will cause that excitation to take place.
posted by DevilsAdvocate at 3:26 PM on November 30, 2006

What do the colors just slightly past blue (420) and red (680), that aren't shown on the chromaticity diagram, look like?
posted by smackfu at 3:32 PM on November 30, 2006

Blame Isaac Newton. He used a wheel to describe tone relationships in Opticks and pigment mixers found it a useful tool, although artisitc color theory kind of diverted from optics at that point.
posted by oneirodynia at 3:40 PM on November 30, 2006

we have three color receptors in our eyes, red, green and blue

Except for the mutant human tetrachromats (mostly female) with extra retinal pigments:
Richer color experience in observers with multiple photopigment opsin genes
posted by meehawl at 4:03 PM on November 30, 2006

And oh yeah, Lakoff has a lot to say in Women, Fire, and Dangerous Things about the tension between the neural and retinal substrates for colour perception versus linguistics. A combination of both of these serves to uniquely constrain the perception of colour relations and which colours are generally noted as "fundamental" or primary within different cultures, and how they are spatially related to each other.
posted by meehawl at 4:11 PM on November 30, 2006

That's amazing, meehawl.

Women with four-photopigment genotypes are found to perceive significantly more chromatic appearances in comparison with either male or female trichromat controls.

Who'd a thunk it. Smackfu, you need to find one of these mutant four-photopigment ultrawomen and ask her what those hidden colors look like.

So I guess this really cool chart doesn't apply to everyone. I believe it's showing the traditional RGB-centric view of the world. The dotted line is the percieved color, when the brain combines the other three channels.

If there's another set of receptors, I wonder where it would fall on this chart? Also, I'm signing up for genetic modification trials, because I totally want to see all those extra colors.
posted by Area Control at 5:07 PM on November 30, 2006

I seem to recall reading somewhere--although I can't find anything to back it up in a brief Google search--that tetrachromats have two different types of red cones, which have fairly similar, albeit not exactly the same, frequency profiles. So while tetrachromats can distinguish some colors that look the same to us mundane trichromats, I imagine the world would not look hugely different to them compared to what it does to us. So if you're waiting for genetic modification, it might be worth waiting for some entirely novel (or at least non-human!) pigment which has a markedly different frequency profile than the three you already have.
posted by DevilsAdvocate at 7:08 PM on November 30, 2006

What do the colors just slightly past blue (420) and red (680), that aren't shown on the chromaticity diagram, look like?

The only meaningful answer I can think of to this is "go get a prism and see for yourself." Any description I could think of would only be approximate at best, and even the colors that are shown in the chromaticity diagram are rather poor approximations of the true color.

For one thing, the chromaticity diagram is for a standardized reference observer, and different individuals will perceive colors in different ways. The fact that tetrachromats have two different red-sensing pigments suggests to us that some trichromats have one of those red-sensing pigments, and some have the other, and these two groups will not perceive color in exactly the same way. Just as one example of how different people may perceive color in different ways. So if the chromaticity diagram only goes from 420 to 680nm, that's all that's visible to our standardized reference observer. For people who perceive color like our standardized reference observer (I don't know if there are in fact people like that or not, but if there aren't, it's a bit useless to draw a chromaticity diagram that way), light outside of that range doesn't "look like" anything, since it's not visible to them.

It's also worth keeping in mind that computer monitors only display a fraction of possible colors, and thus the colors that you see in the chromaticity diagram here are not the colors that should appear on a "true" chromaticity diagram. Think of it this way: imagine you have a true chromaticity diagram (perhaps, even, keyed to your personal color perception, rather than that of a standardized observer) where the actual colors generated by monochromatic light appears on the curved edge. Now, take three points inside the diagram--one each roughly in the green, red, and blue areas of the diagram--corresponding to the colors of the phosphors on your computer monitor. These points might be near the diagram's boundary (or they might not be that near it), but they definitely won't be on it, as your phosphors don't put out monochromatic light. Now, draw a triangle with those three points at the corners. Your computer monitor can only display colors within that triangle. Any colors outside of the triangle can't be displayed on your monitor. Now, try to draw a representation of that chromaticity diagram using only the colors that can be displayed on your monitor--you can easily imagine that in some places the representation of a chromaticity diagram displayed on your monitor will not be all that close to the true color which should be displayed.
posted by DevilsAdvocate at 7:38 PM on November 30, 2006

If you're even remotely interested in this stuff you can spend a lot of time reading about it on handprint.com.

It's a really good site.
posted by aubilenon at 9:02 PM on November 30, 2006 [1 favorite]

Also, I'm signing up for genetic modification trials, because I totally want to see all those extra colors.

I think, basically, you would just notice when colors are "off" what they should be, a red may be a blue-red, or orange-red. (This may be why your wife is so picky about the living room walls.) On an unrelated note, I have always wondered if it is possible to have a green-red without being brown. Apples, for example.

I don't know much about light, but I mix colors for painting, and I gotta say the color wheel works. Yellow too green, add red. As other commenters have noted, we have filled in the violet to make a good circle. It works.
posted by bobobox at 9:08 PM on November 30, 2006

I found this on Digg a while ago -- it's called "The Origins of Color." I just thought you might enjoy reading it; fairly complex and thorough.
posted by Lockeownzj00 at 3:35 AM on December 1, 2006

That handprint site linked by aubilenon is the best resource linked here.

Our eyes have 4 lightsensing cells, 3 cones which are commonly described as Red, Blue and Green, but more appropriately described as Long, Medium and Short Wavelength sensitive, and rods which function at much lower low light levels (ie single photons). (There are actually more light sensitive cells in the retina but they are "non image forming" and serve other functions)

Each cones is sensitive to a broad range of frequencies.

To understand color it's worth looking at the rod system. At night we loose the ability to see color because we have only one functioning photoreceptor at low light levels. Color, or wavelength discrimination comes from the ability to compare the inputs of multiple photoreceptors. Two colors which seem different in the day time can appear the same at night. These are called metamers because they equally stimulate rods, even though they are of different frequencies. This can be because they are roughly equidistant from the rod's peak absorbance but in opposite direction, or, because one is further from the peak but more intense so the net effect is the same.


So our perception of color comes from the combination and comparison of the stimulation of three different cones, each maximally sensitive to different wavelengths. The output of the cones gets combined in what are called opponent pathways, one is Red-Green, and the other Blue-yellow. The Red-Green pathway compares the output of the Red and Green cones and the Blue-yellow pathway compares the output of the blue cone with the sum of the red and green cones. This is why you will never see a color that is reddish-green or blueish-yellow at least in the additive sense that red+blue=violet and yellow+blue+green.

The question is why does extremely short wavelength light appear to contain a reddish component. I don't believe that anyone knows the answer to that yet. But the hypothesis is that somewhere along the path from cone to cortex the input from a blue cone and red cone combine which turns our perceptionof an extremely short wavelength light into a combination of short wavelength light (blue) and extremely long wavelength light (red). So our sense of color becomes a continuum that loops back on itself as opposed to our sense of pitch (which is also frequency or wavelength).

Interestingly people who have had their lenses removed are somewhat able to percieve ultraviolet light. This is because the lens ordinarily blocks UV light and blue cones are sensitive to UV light but very little ever penetrates to the retina. Apparently they see it as lilac.

Many mammals, fish, birds, insects, and reptiles (basically everyone except us) are able to see UV light as well. It's a good that we can't for two reason. One is that there is more chromatic aberration at shorter wavelengths. Basically blue light bends more than red light. This makes focusing more difficult. Also, more importantly, UV light damages DNA which is a very, very, bad thing.
posted by euphorb at 1:58 PM on December 1, 2006