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Art Classes with Marc Surrency

Color Overview
Color Science
Artists Color Wheels




Color Science



1.0 A Brief Introduction

The following sections provide a simple primer on the interaction of light and some of the more popular "scientific" color geometric models.  You'll encounter some equations and math.  Don't worry, you don't have to be able to understand them to understand the models.  They are included incase you have an interest in how the color coordinates are calculated and how one color space is mathematically transformed into another.

The geometric models were designed to provide a method for describing and matching colors. What you'll find is that historically there have been two approaches to color matching/description; a) actually matching one color to another and b) measuring the light being reflected by an object and describing it in a coordinates system.  None of the methods provide an absolutely perfect model.

It's my attempt here to make you familiar with the science of light and aware of these models.  In this way, we have a foundation to speak more clearly about the strengths and weaknesses of the artist color wheels and the selections of paints (also known as the palette) in the next segment.

However, if you start to feel overwhelmed by the science or math, then advance to the next page.

2.0  Color Theory

The term color has been previously used several times so lets review a good definition.  One might think that it needs no definition, but a definition will be supplied never the less.  "Color... is the result of the physical modification of light by colorants as observed by the human eye (called a perceptual process) and interpreted in the brain (which introduces psychology)."(Meyer, p1)  This definition contains forms of two terms that are often troubling to scientist (especially those who prefer objective measurements and descriptions), perception and psychology.  Most observers can agree on what the term color means, but if asked to describe the color of an object, will supply different answers.  So how does one accurately describe color?  Does it matter whether the color is a result of an emission or reflection?  Scientist, material engineers, artist, and textile manufactures have been trying to find a solution to the color description dilemma for centuries.  As these groups tried to create systems to measure and standardize colors, they found two important relationships.  The description of color from the emission of  light depended on the source and the observer.  Reflected color depended on the light source, the object absorbing and reflecting light form the source, and the observer.  For the artist, it looks like only systems dealing with reflected light would be important.  This is incorrect, however, because the systems concerning the description of reflected light are dependent on properly describing the light source emission.

emitted light Color

Newton found that white light cold be separated into a rainbow of colors using a prism.



He also found that he could create white light and other colors by mixing these separated colors back together again.  Scientist later found that they could essentially reproduce all of the colors our eyes are able to see by mixing color from three color lights.

(image retrieved from June 18 2006)

If we think of white light as a mixture of three primary colors green, blue and red light we can describe a secondary color of light as resulting from the a combination of the primaries.  This is known as additive color theory and is valid only for mixtures of light.

For example if a red light is mixed with a blue light the resulting color is magenta.  Likewise, if green light is superimposed on a red light, the result is yellow.  Blue light mixed with green light is magenta.

 The Additive Color Wheel

If you're reading this on a color computer screen, you're observing the additive color wheel in action. Television and computer monitor screens use red, green, and blue (RGB) light to create all of their color.

Reflected light Color

Reflected color is a result of the selective absorption of light by objects with the color resulting from the wavelengths of light reflected or transmitted. When we view color from an object the color we see is the color of the light that is reflected.  A red street sign is red because it absorbs green and blue light and reflects red. 

Therefore, the process is subtractive because the reflected light has fewer wavelengths than the incident light.  A white object reflects all of the wavelengths and a black object reflects no light energy. 


We can deduce that the white object contains nothing that will absorb light and that black contains all of the colors (Just the opposite of the additive color wheel above).  The subtractive primaries are colors that remove a single light color from our RGB "white" light.  The subtractive primaries are cyan, magenta, and yellow.




The Subtractive Color Wheel

You might be familiar with these subtractive primary colors as those used by your color inkjet printer. Home color inkjet printers also use black to provide the darker values - remember all three colors mixed together only gives grey not black.  What about the six color printers?  Theoretically you only need the three primary colors, but the world is not perfect and neither are those dyes available to ink companies.

I've seen enough science - let's see some artist's color wheels

The two color wheels are related, but their rules for mixture are not interchangeable.  One example is photography and printing.  Let's say we're going to take a photograph of Oswald's color wheel and reproduce it for a book (we'll discus his color wheel later).   We simply need to record the RGB light being reflected by the object and then create a printed image that reflects RGB light in the same manner.

First, we need to separate the incoming light, a mixture of the primary additive colors, back into their individual components.  We can do this by using camera filters that are the same colors at the primary additive colors.  A red filter will only allow red light to pass.  By placing a red filter in front of our camera we can record all of the red light reflected by the object.  Likewise, we can use a green filter to record the reflected green light and a blue filter to record the reflected blue light. 


The second part is to create an image that reflects back the primary additive colors in the same manner as they were when they were reflected from the object. 

if you want to make something reflect red light you can mix magenta pigment (which absorbs green light) and yellow pigment (which absorbs blue light).   Blue is created by mixing cyan pigment (which absorbs red light) and magenta pigment (which absorbs green). Green is created by adding yellow pigment (which absorbs blue) and cyan pigment (which absorbs red). 

If we take a photograph of the wheel with a red filter, we'll create a record of where the wheel is red.  This will be a photographic negative of the red and is aptly named a "red separation negative". This seems like this negative would provide us where to print red ink, but remember we're printing using the subtractive color wheel, not the the additive color wheel - which is only good for light.  In fact, what we are doing is recording all of the red information to obtain information about it's complement, cyan!

The image in front of the Camera

Red Filter placed over the camera lens
Red Separation Negative

If we create a positive from this negative, we get a record of everything not red - or a record of the mixture of blue and green light (cyan).  For a printing press this would be the cyan printing plate.

positive of the Red Separation Negative (cyan)

In this manner we can use the negative to provide information about the each additive primary's corresponding complement (the subtractive primary).  Remember for printing, we need to know the location of the subtractive primaries, cyan, yellow, and magenta. For example, the negative created from the red filtered light contains all of the information about the red light, but a positive made from this negative contains all of the information about it's complement - cyan.

So here's the theory in action.  We photograph the wheel using red, green, and blue filters separately creating separation negative for each additive primary color.  Each additive primary color (RGB) negative provides the positive for the corresponding subtractive primary (CYM). Positives are made from each negative.  For lithographic printing these positives would be the printing plates.  A black printing plate would be added to increase contrast (all three additive primaries combined only give gray).  The subtractive colors are recombined to give a color image.


Red   Separation

 Negative (Record of all Red light)

Blue     Filter




(Record of all Blue light)

Positive (Record of all Red and Green light)


Red     Filter

Green     Filter

Green Separation


(Record of all Green light)

Positive (Record of all green and blue light)


Positive (Record of all Red and Blue light)


Subtractive Primaries are printed to recreate the original image

Original Image in Front of the Camera


These color wheels are the foundations for color photographic reproduction as well as video and computer screens.  they are extremely important scientifically and explain some of the problems encountered in mixing paints.  However, these color wheels may not be intuitive and sometimes prove cumbersome to use for painting.  But more on this later.


I've seen enough science - let's see some artist's color wheels

2.1  Color Matching

One of the main needs for the ability to describe color is color matching.  This is this is the main reason why artist, textile manufactures, painters and other professions and trades where so interested and driven to standardize color descriptions in the first place.  It remains today as one of the most popular use of the various color description systems.  People still need to match paint manufactured today to paint manufactured a year ago, or printing inks for accurate color reproductions, or dyes for clothing; the list is endless.  The first type of standardization of color was performed by creating a set of reference colors and matching the desired color to a reference color.  The reference color, in turn, was used as a guide in creating the desired color.  The next step in standardization came by arranging the colors in a systematic manner; by hue (blue, green, red, etc.), saturation or chroma (paleness or vividness), and value (lightness, darkness).  Any two of the three components can be represented two-dimensionally, but for all three values to be represented simultaneously, three dimensions are required;  the introduction of the color solids. 


2.1a  Color Solids

 Most color solids are formed by creating a circle out of the visual spectrum by connecting the ends of the spectrum (blue and red) together, which becomes an equator of hues. Sir Issac Newton was the first to create this solid representation which so many artist think of as the color wheel. The third axis is created by a line passing through the polar axis, and represents brightness ranging from black through tones of grey to white (value).  As colors shift radially from the center of the solid toward the edge, they become more saturated (chroma). The most well known and used solids were created by Ostwald and Munsell. 


2.1b  Ostwald’s Solid

Ostwald's solid is arranged as double cone and is based on 24 hues arranged around the circumference.  Each hue is combined in fixed proportions with each of 8 equally spaced neutral values ranging from black to white.  Ostwald’s solid, therefore, is based on pigment ratios creating the saturation steps.(Billmeyer, pp.26-28; Rossotti, pp.144-150)


                                    Ostwald’s' Solid and X-section



2.1c  Munsell’s Solid

Munsell's solid is arranged so that increasing saturation is created by a series of visually equal steps and contains nine neutral colors.  The number of steps to maximum saturated depends on the value and hue, which results in an unsymmetrical solid often called a color tree.(Billmeyer, pp.30-35,52; Rossoti, pp.144-148)


                                    Munsell's solid, pole view and x section





Both Ostwald and Munsell's systems rely on the observer matching a color to a reference color, which is still a subjective measurement.  Although the color is matched to a reference color, which has been defined by its chroma, value and hue, the observer and light source, still have not been defined.  Since the reference and the color are being lit by the same source and observer, isn't  the source and observer parts of the equation canceled out?  The answer is yes and no.  Since the observer and the source are the same for the matched color sample and reference sample, the difference can be ignored, but they still must be defined.  Metamerism is a perfect example why the source and observer are always critical to color matching and definition.

2.2 Tristimulus Colorimetry

2.2a  Maxwell’s System

A system that addresses the observer and source, as well as, value, chroma, and hue, in defining a color is based on Tristimulus Colorimetry.  In 1855, Maxwell found that most colors either emitted or reflected could be matched by mixing three primary colored light sources.  The matching took place in a darkened room, where he projected equally-balanced white light to the object he was trying to match.  Three lights (red, green, and blue) with rheostats, were to control their intensity, were arranged so that their beams would be superimposed onto a neutral screen.  Colors where matched by adjusting the intensities or amounts of light projected onto the screen.  He found that he could match most of the colors in hue, but not saturation.  His system for describing color as a combination of three light sources was the foundations for the system widely used today. (Rossotti, pp.153-157)

Maxwell Color Triangle



Mathematically the coordinates are determined as follows:  the color reflected by an object (C) or (λ) is composed of a mixture of varying intensities of red (R), blue (B) and green (G) light. (R),(G), and (B) are the intensity or amount of primary colors.  The distribution coefficients for those primary colors are derived by expressing the light intensity as a fraction of the total luminescence.

 C(λ) = R(R)+G(G)+B(B),

where R,G,B, are the amounts of colors present and (R)+(B)+(C) = 1.


C(λ) = R(R)+G(G)+B(B)  and  C(λ) = R(R)+G(G)+B(B)


1.0(λ) = R(R)/C+G(G)/C+B(B)/C and C= R+G+B


1.0(λ) =)+G(G)/( R+G+B)+B(B)/( R+G+B)


1.0(λ) = r(R)+g(G)+b(B)


r= R/(R+G+B), g=G/(R+G+B), and  b=B/(R+G+B)



I've seen enough science - let's see some artist's color wheels

2.2b  CIE Colorimetry

In 1931, the Commission International de l’Eclairage (CIE) adopted the use of tristimulus colorimetry.  They recreated Maxwell’s work with defined light source E, defined tristimulus sources (R=700nm, G=546.1nm, B=435.8nm) and created a standard observer.  They matched the colors of the spectrum by varying the intensities of the tristimulus colors and recorded the results, creating a chromaticity diagram.  They observed the same problems that Maxwell encountered.  While they could match all colors in hue, they were not able to match some in saturation.  The blue-greens could only be matched by maximizing  the saturation of the blue and green lights, then desaturating the object color by adding red light to the neutral light illuminating it, until it matched the blue-green tristimulus lights in hue and saturation.

Now our equation for Chromaticity Coordinates becomes

C(C) = R(R)+G(G)+B(B)  for violet and orange to red hues and C(C) +R(R) = G(G) +B(B) or C(C) = -R(R)+G(G)+R(R) for blue-green hues.  This also introduces negative values for some of the coordinates.  The shaded area of the chromaticity diagram in the following figure, corresponds to hues and saturation’s possible by mixing three primary light sources.  The unshaded area of the “horseshoe” corresponds to those hues and saturation’s requiring the desaturation of blue-green by the addition of red.(Walls, p. 342)




The tristimulus values (rλ ,gλ ,bλ ), also known as the distribution coefficients for the tristimulus sources can also be represented in by their spectral curves.



The CIE chose to get rid of the negative coordinate system by a mathematical transform and the adoption of new reference stimuli (X,Y,Z) that lie outside of the spectral locus with a new set of spectral distribution coefficients (xλ ,yλ, zλ ).  The purpose of the new reference stimuli , which exist without luminosity and are often referred to as imaginary, was to define references which when mixed together could create all of the hues and saturation.(Rossotti, pp.154-157)


The New Reference Stimuli (X, Y, Z)

Overlaid on the RGB Chromaticity Diagram



The Standard Observer Distribution Coefficients

(the tristimulus power distributions)


The new chromaticity coordinates which express hue and saturation in positive numbers are obtained by taking the ratios of X, Y, and Z present in the object.(Walls, p.348)


x= X/(X+Y+Z)             y= Y/(X+Y+Z) z= Z/(X+Y+Z)


Since x+y+z=1,  only two of the chromaticity coordinates are needed to completely describe the chroma and saturation; the CIE chose x and y.

Now a chromaticity diagram describing all possible colors in positive numbers is possible.  The result was the Horseshoe shaped CIE Chromaticity Diagram.


The CIE Chromaticity Diagram (1931)

The horseshoe curve represents all real visible spectral colors and is called the spectrum locus.  The straight line connecting the ends of the spectrum locus (between 420nm and 700nm) creates the purple hues not seen in the spectrum.

E represents equal balanced white light and is created from equal parts of all three colors and exists at coordinates (0.33,0.33).  The curve connecting A,B, and C is the locus of the black body sources.  A, B, and C are the standard light sources; A is a tungsten filament light operating at 2858K, B is A through a liquid filter to simulate noon light,  and C is A through a liquid filter to simulate overcast  daylight.  One clarification should be made for the CIE diagram,  Source refers to real physical light sources whose power distribution can be experimentally determined; Illuminant is a light defined by a power distribution, which may or may not be able to be created by a source.  Actual daylight is an example of an illuminant which can not be created by a source.

 (note: In the following text, the bars above x-bar, y-bar, and z-bar may not be properly aligned with the text. My apologies)

Now that we have the chromaticity diagram, we can define an objects color by CIE chromaticity coordinates and find its location on the diagram.  There are two ways we can accomplish this.  One way is to measure the matching color with three light sources. The first step is defining which standard illuminant to use to illuminate the object whose spectral reflection distribution is (R).  Once the illuminant (P) has been decided on, the object is illuminated, and its spectral reflection (PxR) is matched using RGB tristimulus color values.  The resulting match equals the  measurement (P) x (R) x (rλ ,gλ ,bλ ), These are then transformed to spectral distribution coefficients (xλ ,yλ, zλ ) and produce measurements corresponding to (P) x (R) (xλ ,yλ, zλ ).  Since, (P) x (R)  x  (xλ ,yλ, zλ) = X,Y,Z,  and x = X/(X+Y+Z), y =Y/(X+Y+Z), we are obtain the tristimulus coordinates x and y and plot the point on the graph.  The second way to determine the Chromaticity coordinates is by recording the spectral response of the reflected light from the object and superimposing it onto the standard observer spectra then finding then performing integration on the results.  A spectral Representation of this appears as follows:

 (note: In the follwoing text the bars above x-bar, y-bar, and z-bar may not be properly alligned with the text. My appologies)

(adapted from Billmeyer, p.46)


Once these spectra are obtained X, Y, and Z are obtained by the equations:

X=k   PRx-bardλ, Y=k   PRy-bardλ, and Z=k   Prz-bardλ, then x and y are then calculated by X, Y and Z.

Now that we have the hue and saturation, what about the value?  The CIE Chromatictiy Diagram has the value or luminosity on a third vertical axis and is defined by the variable Y. Y is defined as equaling 100 when a white object reflecting 100% white light at all wavelengths for non fluorescent material.  Therefore, Y provides information on the value regardless of the hue or saturation.  Black appears anywhere where Y=0.(Billmeyer, p.52)


CIE Chromaticity Diagram with Luminosity (Y) as Isobars




Three-Dimensional CIE Chromaticity Diagram




The chromaticity diagram is arranged so that many relationships between colors can be easily measured or calculated.  For example, is we have an object whose color is (W1), we can calculate the chomaticity coordinates and plot is on the chromaticity diagram.  We can find the dominant wave length of the color by drawing a straight line from the illuminant (C), through the color (C) to the spectral locus.  The point where this line intersects the spectral locus is the dominant wave length(λ).   All points (colors) along the line Cλ will have the same hue as W1 but will have different saturation’s.  The percent purity or saturation of the color can be calculated by the ratio of the length of C(W1) /Cλ.  For example in the following diagram C(W1)= 8, and Cλ= 10, thus, the saturation is 80%. 

Therefore, color W1 can be created by mixing 8 units of λ with 2 units of white light C.


Calculations made from the Chromaticity Diagram




The Complement wavelength λc to the dominant wavelength, λ, is found by drawing a straight line from W1 through the illuminant, C, to the spectrum locus.  The complementary color (W1’) to color W1 is found on the line C(λc), the same number of units away from the illuminant as W1

Color can also be created by mixing two spectral colors. W2 can be created by mixing  λa with λb with the ratios determined in the same manner as C and λ.

If  the dominant color is not on the spectral locus, such as D in figure below, a similar approach is used.(Rossotti, p 156-162)  Color W3 lies between the illuminant and the nonspectral straight edge of the color tongue.  A line is drawn from the illuminant C through W3 to the edge, D.  The dominant color, D, consist of a mixture of the two spectral end points, A and B.  In this case D lies 7 units from A and 3 units from B.  Therefore the dominant color D can be created by mixing 7 units of red with 3 units of blue.  The luminosity is obtained in the same manner as the other examples


Colors Which Do Not Exist on the Spectral Locus


Over the years several attempts have been made to make the colors of the chromaticity diagram more evenly spaced.  The first CIE adoption was a linear transformation an is known as the 1960 CIE Chromaticity Diagram.  The second adoption and the currently recommended diagram is a nonlinear transform, known as the 1976  Metric CIE Chromaticity Diagram.  All of the relationships of the 1931 CIE Chromaticity Diagram still hold for the 1976 Diagram.  The 1931 Tristimulus values (X,Y,Z) are related to the 1960 chromaticity coordinates (u,ν) and the 1976 chromaticity coordinates (u',ν') by :


u' = u = 4X/ (X+15Y+3Z) = 4x/(-2x+12y+3) 


ν'= 1.5n = Y/(X+15Y+3Z) = 9y/(-2x+12y+3)

(Wells, pp.55-59)


The 1960 CIE Chromatictiy Diagram



The 1976 CIE Chromaticity Diagram





A couple of final comments on the CIE Chromaticity Diagram.  The colors illustrated on the CIE Chromaticity Diagram cannot be used to match colors to locations on the diagrams, they are there only to give a sense of what colors are located in particular areas.  Another misconception is that the browns are not represented.  Browns are actually desaturated yellow-oranges and are represented on the diagram.(Rossotti, p.165)


I've seen enough science - let's see some artist's color wheels

Opponent Color Systems

Opponent color systems are based on the opponent color theory for human vision.  It’s generally accepted that humans do not see red and green at the same time nor yellow and blue.  Therefore single values can be used to describe the red or green and yellow or blue of an object. (Hunter)  The first system, developed by Richard Hunter and E. Q. Adams became known as the Hunter L,a,b, color scale and was later reworked and adopted by the CIE (CIELAB and CIELUV).  The CIELAB and CIELUV are uniform color spaces calculated from the tristimulus values (XYZ).  The CIELAB scale is primarily used with pigmented objects, while CIELUV, is primarily used with color lights.  The CIELAB, has three axis, a*,b*, and L*.  The a* coordinate determines the greenness (-a*) or redness (+a*), the b* coordinate determines the yellowness (+b*) or blueness (-b*) of the object, while the L* coordinate determines the lightness value.(X Rite, 1994; HunterLab, 1996)




© 2006 Marc J. Surrency. Physical or electronic reproduction in whole or part is unlawful without written permission of the artist.



© 2006 Marc J. Surrency.  Artist scans, images, and web design are protected by copyright. Physical or electronic reproduction in whole or part is unlawful without written permission of the artist.