Relationship between color theory and spectrum

Factual Questions
1

Violet can be made by mixing the right proportions of blue and red. But violet is above both of them on the EMR spectrum. So if two colors are mixed, we do not see the color that would be the average of their frequencies–do we? If we did, then red and violet would make green.

With sound, we perceive two tones (sufficiently close together) as a single tone that is the average of the two frequencies, with beats at the difference of the two frequencies. This doesn’t seem to work as an analogy for how we perceive color.

Is there any relationship between colors as frequencies of EMR and how we perceive color mixes?

2

Not true. Blue and red when mixed together in an additive process make magenta. Check out the CIE color space diagram. Note that the colors shown on the diagram are approximate, since the displayable colors on a tri-chromatic system are a subset of perceivable colors.

When you mix two colors together in different proportions, you get an interpolation along a line between the two points in color space.

The human ear has thousands of cilia of varying length to detect different tones, but the eye has only S, M, and L cone cells (often misleadingly called blue, green, and red cone cells) to produce the signals that get sent to the brain.

3

I looked at the color space diagram, although the explanation is a bit dense. I gather that the spectrum of colors is represented by following the envelope of the space. I don’t understand what the x and y axes are. Based on your description, if you pick two colors from anywhere in the space and mix them equally, the result would be on the midpoint of a line between the two, and similarly interpolated for other proportions. I would also infer from that that there are an infinite number of ways to select two colors to combine to produce a color at any given point in the space.

Let’s take the example that I gave and you corrected. If we additively combine violet and red to get magenta (I was thinking subtractive, but I think that a discussion of additive actually works better), can the color magenta be represented as a single frequency, or is it by its nature the presence of two different frequencies, and the fact that we perceive it as a single color is a product of our cognitive hardware? Like I said, if the perception of two frequencies were just their average, then we would see green instead of magenta, which we don’t.

4

The curved edge of the IEC space is the real colour spectrum. Any colour that isn’t on the curve (including those colours on the straight line across the bottom) are not pure spectral colours. Those colours don’t exist in any real way except as an artiface of our brain. Thus magenta, and all colours across the line at the bottom are not spectral. There is no frequency for the magenta on the line, and there is only one possible combination of light wavelengths that can create it. In real life almost everything emits a range of spectra, and so perceived colours are the result of integrating the product of the eye’s response and the intensity across the spectrum.

Otherwise your summary of the the space is pretty much spot on. The only thing to add is that the space doesn’t include the eye’s response to light level - and thus a full description has a third axis representing the same colours, but with diminishing absolute light level. As a rough approximation, the size of the space shrinks as the brighness drops, eventually reaching a degenerate point which prepresents the light level that our sight loses colour perception. It doesn’t shrink evenly, which is a complicating factor in colour perception.

5

As shown in a graph here, there are three types of cone (called H, M, L in the article; called alpha, beta, gamma in most literature; but most simply, if somewhat incorrectly, referred to as red, green, blue). When your eye is presented with green, the green and blue cones are activated (green more so than blue). When presented with magenta, the red and blue cones are activated. Green and magenta are thus perceived as quite different: Except for the effect on cone activation shown in the graph, the frequency of the light is irrelevant.

As shown in that graph, any color which stimulates the green cones will also stimulate red and/or blue cones. The article (named “Imaginary color”) mentions sensor fatigue as a way to experience “Imaginary colors”, e.g. “red redder than red” or “green greener than green.” (There are other ways, more intrusive than simple cone fatigue, to cause such imaginary colors.)

(Going way “off-topic”: Before color sensation gets to cerebral cortex, the output of rods and cones have been processed to get luminance and two chromaticities: red vs green and blue vs yellow. Hence the common use of four primary colors in perception compared with three primaries in either additive or subtractive rendition.)

6

Hardly any of the colors we see in the “real world” (i.e., outside of special laboratory setups) are pure single wavelengths (“monochomatic” light), even when they look like pure unmixed colors or seem indistinguishable from the sensation you get from pure light of a certain single wavelength. Many hues that we experience cannot be found in the spectrum (i.e., cannot be produced by any unmixed wavelength of light), but are only produced by certain mixtures of wavelengths. Indeed, IIRC,* the color that most people judge to be the best, most pure and unmixed looking red, cannot be produced by any single wavelength of light. Any reddish monochromatic wavelength that you choose is going to look either a little bit orangey or a little bit purplish to most people. Subjectively “true” red can only be produced by a mixture of wavelengths.

On the other hand, certain colors that are subjectively indistinguishable to the human eye can be produced in more than one way, by mixing different wavelengths in different proportions. These are known as metameric colors: i.e., two quite different mixtures of wavelengths that produce the same subjective effect, are metamers of one another.

Furthermore, some colors that we routinely experience cannot be made merely by mixing wavelengths of light in any way whatsoever. So called “contrast colors” are only experience when a surface with one pattern of spectral reflectivity is adjacent to a surface with a certain range of other spectral reflectivity. Brown is a good example. You cannot make brown light by mixing together any wavelengths of light in any proportions. Furthermore, you cannot fill your entire visual field with brown. The nearest you will be able to get is some sort of orangey or yellowish color. However, if you place something of the appropriate orangey or yellowish spectral reflectance adjacent certain other colors (generally lighter ones), it will appear brown. Of course, in real life our visual field is almost never filled with only one spectral mixture, so in practice, brown can, and does, appear quite frequently. (I stumped more than one of my high school physics teachers, trying to teach us about the spectrum, by asking them where brown comes from. I did not find out the real answer until several decades later.)

All in all, the eye is not a spectral analyzer, and the colors that we see and can distinguish between are only related in a very indirect and complex way to the actual spectral reflectances of objects. Presumably, the color distinctions we can make are those that were adaptively useful to our ancestors (it is very useful for many monkeys, for instance, to be able to distinguish between ripe and unripe fruit, and between unripe fruit and leaves), plus others that we got for free along with the mechanisms that were selected for making the useful distinctions.


*My uncertainty here is over whether this applies to red, as opposed to one or other of the other so-called "primary" colors. I think it is red, but it might possibly be subjectively pure green or blue (or perhaps even all of them, or two out of the three) that corresponds to no monochromatic wavelength. If anyone knows about this, and can provide a cite, I would be grateful.



[quote="CookingWithGas, post:1, topic:543231"]

 
With sound, we perceive two tones (sufficiently close together) as a single tone that is the average of the two frequencies
[/QUOTE]


This does not sound right to me, but I am not certain. Does anyone know better, or have a cite?
7

It should be emphasized that there’s no inherent physical significance to color theory. When one says that yellow paint and blue paint mix together to form green paint, or that red light and green light mix to form yellow, that’s not a statement about physics. All of that is just an artifact of the way our eyes happen to work. An alien might well be baffled that we can’t tell the difference between yellow and a mixture of red and blue, and think that images on our computer screens or TVs look completely unlike the things they’re supposed to represent.

8

It’s true, but they have to be pretty close in frequency. This is easy to demonstrate on a 12 string guitar. The bottom four pairs of strings are a heavy low string paired with a much thinner string tuned one octave up. The top two pairs of strings are two identical strings though. If you tune them exactly to the same frequency the pair just sounds like one string. If you tune them just slightly off from each other then you get a richer sound, but it sounds like only one note. Tune them too far apart though and it starts to sound bad, and if you keep tuning them farther apart you can soon hear the two different frequencies.

The reason for this is that your ear hears in the frequency domain. Inside your ear (after you get through the eardrum and all of those funny little bones) the final stage of hearing is a bunch of specialized nerve cells called hair cells. These kinda work like itty bitty bandpass filters. They each respond to a small range of frequencies, not an individual frequency. If you get two tones close enough in frequency some of the hair cells are going to respond to both tones.

Your hearing works pretty close to in the frequency domain because your ears have a whole lot of different hair cells that respond to very narrow frequency ranges all the way up through the audio frequency range.

Your eyes are significantly different because they only have three broad frequency ranges that they respond to, so they aren’t converting the incoming signals into frequencies.

Very true.

In World War II, they always tried to have one colorblind person among the group examining recon photos. To someone with all of the normal color receptors in their eyes, yellow and blue paint make green. To someone who is missing one of the color receptors in their eyes, the frequency combination you get by adding yellow and blue paint together doesn’t necessarily equal green, and that green camouflage that perfectly fooled the normal folks is easily spotted by the colorblind person.

If the frequencies added together to make a green frequency then the colorblind person’s perception wouldn’t have been different from the others.

9

It might not even take an alien. A bird or an insect might be that way.

10

I found out this one in high school, too, but in chemistry class. We were looking at “emission” samples thru a spectroscope, and I saw a “brown” line. “BROWN?” I said. “Where the hell in the spectrum is BROWN?” My chem teacher then explained that brown is essentially “dim orange”. The planet Mars is the same color as chocolate (maybe that’s where they got the name “Mars Bar”), only lighter than it’s background. If you are seeing brown, it’s because you are seeing orange, but it’s dimmer than what you are comparing it to. I guess Chemistry teachers are smarter than Physics teachers (at least at the high school I went to). :smiley:

11

Actually I think mine were too.

From my physics teachers I got the following answers about brown:

“That’s a good question. Ask me again next week.”
And when I did ask again next week:
“That’s a stupid question. Shut up!”
Then, the next year, with a different teacher:
“Well . . . It’s not in the spectrum . . . . [Change of subject]”

I had some great Chemistry teachers though (but the question of the nature of colors never came up with them).

12

That is all well and good, but I do not see how it supports CookingWithGas’s claim that “we perceive two tones (sufficiently close together) as a single tone that is the average of the two frequencies” (emphasis added). You have simply explained how it is that we can make fine, but not arbitrarily fine, tone discriminations.

Incidentally, what you say about the hair cells does not, as it stands, explain why two very slightly differently tuned guitar strings give a richer sound than ones tuned exactly the same; but, in any case, a richer sound is not the same thing as the average of the two tones.

I would like to see a cite for this story. I suspect it is either an urban legend, or badly garbled. To be color-blind is to be unable to distinguish certain colors that look quite different to the normally sighted. It does not give you the power to see color distinctions that normals cannot see. That is why we call it color blindness, rather than color super-vision! The color-blind might not see the camouflage as green (depending on what form of color blindness they suffer from), but they won’t see the leaves or grass as green either. They will still look the same as each other (probably brown, or, rather, the indistinguishable brown-green color that they see when they look at both brown and green things).

To put it in more technical terms, color blindness does not give people the ability to distinguish metameric colors. I think I have heard that color-blind people can sometimes match shades better than people with normal color vision, because they are not so distracted by differences in hue, but I do see how that would be useful in the sort of situation you describe.

13

I’m also a very skeptical. First of all, the camera film is based on only three color receptors, too, so it’s not like there’s a whole wealth of frequency spectrum detail in the pictures anyway. And secondly, even if there was some detail to find, color filters plus regular analysts are easier and more reliable than finding and training color-blind analysts.

14

My father is moderately colorblind, and served in the Korean War/police action/whatever. He doesn’t like to talk about it much, but he will say that he was one of the people who looked at recon photos, and the reason for it is because of his color blindness.

15

I have a friend who’s red-green colorblind. I’ve asked him about this, and compared impressions of the colors of things, and from what I got from what he says, it’s best described as:

I can mix yellow and blue paint to where it looks to be the same color as the grass or tree leaves I am comparing it to. He doesn’t see the yellow the same way I do. When the mix looks right to me, the mix is very wrong to him. Mix it so he sees them as the same color, and it looks very wrong to me. Camo only works if the eyes you’re camoflaging from see the colors of the paints you are using the same way you do.

The story you are asking for a cite for may or may not be true, and I’m not even going to try to google that one to try to find out, but it is highly believable, given what my friend tells me about things with mixed colors. Yes, “colorblind” people see things very differently than you and I do, and it’s hard even getting on the same page, when discussing the word “color”.

16

http://webcache.googleusercontent.com/search?q=cache:lPxayiDvpOIJ:positron.ps.uci.edu/~dkirkby/music/html/lectures/Lecture9.pps&cd=15&hl=en&ct=clnk&gl=us

http://www.phy.mtu.edu/~suits/beats.html

17

There are plenty of cites for this sort of thing. Here’s one:

National Defense: Color-Blind Observers
Time
Monday, Aug 5, 1940

The Wikipedia article on colorblindness mentions it too. You can look in their reference section to see where they got their cite from.

18

“Richer” may not be the best way to describe it. Human cognition responds better to change than sameness. A pure sine wave tone can actually get pretty annoying. Even a pure tone from a skilled singer can be less than beautiful after a couple of seconds, which is why singers and instrumentalists play with vibrato (not because they can’t produce a steady pitch).*

The beats introduced by two close tones are a pulsating change in volume , which can be pleasing to the ear if the rate is not too fast (2-3 Hz is probably optimal). Once the tones get a little farther apart and the beats are around 8 Hz or so, it gets annoying and perceived as dissonant.

*A lot of people don’t care for bagpipes, and I think it is because of the drone notes.

19

What Wikipedia actually says on the topic is this:

an interpretation that seems to be born out by this article, and this one.

So yes, some colorblind people may be less likely to be fooled by certain forms of camouflage than normally sighted people are, but this is not because they are able to make color discriminations that normally sighted people cannot. Rather it is because normally sighted people can be distracted by hue differences, that are actually irrelevant to the task, from the texture and shape cues that can actually reveal the location of the camouflaged object. The colorblind do not see these color differences, so they are not distracted by them.

20

My officemate is colorblind, more severely than anyone else I have met. Near as I can tell, he can not detect red whatsoever, and green lights look yellow to him. For example, he has a really hard time finding a red laser pointer on a white background; it is all but invisible to him. I showed him an American Geophysical Union EOS article on presenting data for the colorblind. They gave examples of what someone might see if they were colorblind, and sure enough, he couldn’t figure out why they plotted the same data twice.

It is fascinating plotting data with him. He can distinguish red from purple much better than I, mostly because purple is his favorite shade of red, and he only sees the red because of whatever other color is mixed with it.

I haven’t had him try and spot camouflage, though.