D. R. DOHNER AND C. E. FOSS

FIG. 2.

spot accessory sources, with or without gelatinecolor screens.

This apparatus is adaptable to a variety of

DECEMBER, 1942

purposes: the study of object color, colormixtures, absorption, reflection, diffusion, accent,mood, and creative imagination in the organiza-tion of the whole composition. Summer landscapelighting and coloring may be experimented within winter. Changing mood with the sameobject-material in neutral gray clay may beproduced at will, and an entire composition maybe planned experimentally in color before it isattempted in sketch or at the easel. The compo-sition may be produced in different palettes, asit were, each in turn photographed in Koda-chrome and studied at length before any paintingis undertaken. The apparatus has value both asan instrument for individual trial-and-errorplanning of compositions and also for class orgroup demonstration of color properties andcolor phenomena.

J. 0. S. A. VOLUME 32

Color-Mixing Systems

Color vs. Colorant Mixture

DONALD R. DOHNER, Pratt Institute, Brooklyn, Vew York,

AND CARL E. Foss, Color Consultant, New York, New York

(Received August 17, 1942)

AS artists, designers, teachers, and laymen,we are interested in color as a sensation,

but since there can be no standardized psycho-logical system of color organization and notationwithout some sound physical basis, we had bestturn to what the physicist has done for usthrough the aid of scientific investigations andinstruments, particularly in methods of exactcharting of color and color-mixture by graphicmeans.

It is easy to inquire, "What is the best colorsystem," but the answer must depend upon thepurpose for which it is to be used. Color-mixturesystems are represented on diagrams; think ofthem as color maps. You would not ask for abest map of the geographical world, expectingto have everything on it, for you know that

* Head of Industrial Design Department, The ArtSchool, Pratt Institute.

there are all kinds of maps for representing theearth's surface, each made for a specific purpose.

Some of the early color maps are thosedeveloped by philosophers and physicists earlyin the last century. Many of them are like earlyworld maps that are historically interestingbecause one can see how each worker addedsomething here, something there.

Ostwald, in Scott Taylor's translation ofColour Science,' has developed a brief history ofmany of the contributions of past workers; hegoes back to the Greeks and the Romans; toGoethe who collected but never completedmaterial for a history of color; to Newton whofound that sunlight could be broken up into

separate colors; to Le Blond who first usedNewton's seven colors (about 1730) for color

'Wilhelm Ostwald, Colour Science, trans. by J. ScottTaylor, Vol. 1 (Winsor and Newton, Ltd., London, 1931).

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prints and found later that he could obtainthe same result with three; to Gautier hiscompetitor who arrived at an identical solutionabout the same time; to Dufay who, about1737, described how dyeing of yarns and fabricscould be done with three colors; to J. Brennerwho published a Color Table in 1680 in Stock-holm, giving a list of the coloring matters thenknown; to R. Waller who in 1689 made a colorchart with washes of color; to Tobias Mayerwho made charts of all combinations obtainedto 12 steps on a basis of a red-yellow-bluetriangle, with several charts for black and whitecombinations; to J. H. Lambert who made apyramid by pigment mixtures, based on Gam-boge, carmine, and Prussian blue; to Ph. 0.Runge, the painter, who added the idea ofdecreasing to black as well as to white, the basisfor his sphere; to Chevreul, chemist and dyer ofthe famous Gobelin Works, who, although hecontributed nothing new to mixture problems,created much interest and called attention toproblems of simultaneous contrast. Ostwaldpoints out that Lambert, Runge, and Chevreulrecognized the three-dimensional nature of color,that Runge clearly grasped that black and whiteare independent colors (Mayer and Lambert notquite sure), but Chevreul not at all. Up to thistime no workers attempted to produce or suggesta measured system.

In 1810 Goethe published his Farbenlehre.Schopenhauer, a pupil of Goethe's, laid emphasison cerebral activity in color experience. Twogenerations later Hering repeated the physio-logical part of the work, and Ostwald himselfused portions of this theory in his "doctrine ofsemichromes." Helmholtz (1821-94) added theconception of additive and subtractive mixture,and determined complementaries. Young, in1807, contributed the theory that there is a red,green, and violet receiving mechanism in theretina, and Helmholtz developed this theoryfurther. Grassman formulated the laws of colormixture, James Clark Maxwell needed measure-ment, so he used disks, applied Grassman'slaws, and found equations that held, and thatcolors mix on straight lines of junction in acolor-mixture triangle. Hering, 1834-1918, turnedto psychological analysis and inquired into"experience" of colors, not into the spectrum.

Schultze in 1866 suggested that rods and conesmight have different functions, the rods todistinguish light-to-dark, the cones to distinguishall color differences including light-to-dark. ButHelmholtz paid no attention to this theory.Later von Kries and Parinaud advised the sametheory, and more recently E. Muller; it is nowgenerally accepted. To this list must be addedthe names of Brewster, Scottish scientist, authorof the red-yellow-blue theory that unfortunatelyhas been so widely used in the American educa-tional system; of Rood, an early American colorscientist, who suggested the use of a double cone,following on the ideas of Lambert and Runge;of Ladd-Franklin who so capably championedher theories of color vision; of Frederick E. Ives,father of modern color printing; of Munsell, whoadded measurement and standardized charts fordemonstration of a color notation; of Troland,whose interests lay in psychophysical problems,of those who developed Technicolor, Koda-chrome, and other processes of modern colorphotography; of Hecht in his physiologicalstudies of vision; and of many a worker in theNational Physical Laboratory of Great Britainand in the National Bureau of Standards of thiscountry who did the careful and tedious workthat necessarily preceded the adoption, in 1931,of data to represent a standard observer forcolorimetry, standard illuminants for color-imetry, standard observing conditions, and astandard coordinate system.

If, today, for color-mixture problems we hadto recommend a single map, we would of courseconsider the one that gives us the maximuminformation with the minimum of disadvantages.Therefore our choice today would be the oneinternationally adopted in 1931 by the Inter-national Commission on Illumination, known inthis country as the I.C.I. system,2 and in verygeneral use among all technical color workers.Perhaps some day we shall have a still bettercolor-mixture map, but now, in 1942, we would

2 Proceedings of the Eighth Session, Commission Inter-nationale de l'Eclairage, Cambridge, England, pp. 19-29(September, 1931); T. Smith and J. Guild, "The C.I.E.calorimetric standards and their use," Trans. Opt. Soc.(Eng.) 33, 73 (1931-32); D. B. Judd, "The 1931 I.C.I.standard observer and coordinate system of calorimetry,"J. Opt. Soc. Am. 23, 359 (1933); A. C. Hardy, Handbook ofColorimetry (Technology Press, Cambridge, Massachusetts1936).

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400 X

FIG. 1. I.C.I. (x, y) diagram. The locus of spectrum colorsis indicated by the horseshoe curve beginning at 700millimicrons at the red end of the spectrum, passing throughthe orange, yellow, green, and blue portions to 400 milli-microns. The non-spectral region which contains the purplesis enclosed by a straight line joining the ends of thespectrum.

select the 1931 I.C.I. mixture diagram as the bestmethod for studying color-mixture.

The I.C.I. mixture diagram is a map, just likeany other map. The type of I.C.I. diagram mostoften used in the past 10 years is the so-called(x, y) diagram, and although color has threecoordinates, by this method only the fractionalparts x and y need to be plotted since x+y+zalways add to a total of 1.0. The color coordinateson the I.C.I. (x, y) diagram may be comparedtherefore to the latitude and longitude ofgeographical maps. If we plot the I.C.I. (x, y)measurements of the pure spectrum colors,wave-length by wave-length, as carefully meas-ured in the laboratories of the physicist, weshall find a boundary which describes the limitof real colors. The visible spectrum arrangesitself in horseshoe fashion, as may be seen byexamination of Fig. 1, with red, 700 millimicronsin wave-length, at one end, passing throughorange, yellow, green, blue, to a very purplish-blue at 400 millimicrons in wave-length. Thosecolors that do not occur in the spectrum, thepurples of the non-spectral region, are enclosedby the straight line connecting the red and thefar blue of the spectrum. Within these boundariesall real colors may be plotted. But just as certaintypes of projections exaggerate certain areas ofthe earth's surface on world maps, so this

diagram exaggerates certain color differences.If you will think of the spectrum for a moment,you will recall that it is not divided into equalhue areas; the yellow and orange bands are verynarrow in relation to the red. If you will lookat the spacing on this diagram for the areasmarked red, yellow, green, blue, and purple, youwvill see that they occupy areas that exaggeratethe greens and minimize the reds. On this mapthe neutral point, although it may shift freelywith change in illuminant, is for ordinaryobserving conditions near to equal parts of xand y and z. This plots it at x= 0.333, y=0.3 3 3.As measured from the neutral point out to apoint at which a straight line intersects the lineenclosing all real colors, it is easy to see thatrelative saturations are not accurately repre-sented in accordance with visual experience,since the line to green is much longer than thatto red. Yet full red has a higher saturation thanfull green.

But this is not a diagram to foretell visualappearance, it is a color-mixture map, developedto plot and foretell color mixtures; and on thismap all color mixtures lie in straight lines.

This diagram is also useful for other purposes:we can record many kinds of color data, nota-tions, specifications, and gamuts of color. Forinstance, if we want to standardize the Munsellsystem,3 t or the Ostwald,4 we measure theindividual color samples and plot the resulting(x, y) data on this type of diagram. This hasalready been done for the complete Munsellsystem and for some of the Ostwald samples.Data of this sort indicate the contour or limitof the equal chroma samples of the Munsellsystem when those samples all have equalMunsell value. We have to make the limit of"equal iMiunsell value" or "equal lightness,"because this I.C.I. diagram does not allow us todistinguish between colors of different light-nesses. This takes us back to our geographicalmap: elevations are not usually apparent from aroad map. Similarly, two colors, one light and

t See footnote references and bibliography in reference 4.3 James J. Glenn and James T. Killian, "Trichromatic

(I.C.I.) analysis of the Munsell Book of Color," J. Opt. Soc.Am. 30, 609 (1940).

4 Milton E. Bond and Dorothv Nickerson, "Color-ordersystems, Munsell and Ostwald," J. Opt. Soc. Am. 32, 709(1942).

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one dark, that may have identical (x, y) values,will differ; they will have neither the samelightness nor the same saturation. They willhave the same "purity," for the points at whichthey are plotted are equally displaced from theneutral point toward the spectrum locus on thediagram. But the light color may look twice asstrong in saturation as the dark color. This isan important difference, and is the reason forkeeping our color language consistent. When wethink in terms of color mixture and the I.C.I.diagram we may speak of dominant wave-length,luminance (luminous apparent reflectance), andpurity.** These are psychophysical terms becausecolor mixture is a psychophysical matter. Whenwe speak of color as we see it, in terms of colororganization as opposed to color mixture, we mayspeak in terms of hue, lightness (value), andsaturation (chroma).** These are psychologicalterms, for seeing color is a psychological matter.There is a relation between the two sets ofterms but it is not so simple as the uninformedoften assume.

Ordinarily we think of colors as belonging tosurfaces, but there are times when we cannottell whether a color comes to us from a reflectingsurface or through a filter placed over anaperture light source. For example, if you placea piece of red paper behind a slightly recessedhole in the black front surface of a box withinternal illumination, you may find observersquite unable to tell whether the red comes froma surface or through a filter or even from a redlight inside the box.

A point on the I.C.I. diagram would representthe chromaticity of the red. This (x, y) specifi-cation of the light that reached our eyes; it is aspecification of the quality of that light. Aspecification for quantity of light is also necessaryand this is expressed in terms dependent uponthe mode of appearance of the color. The(x, y) diagram adequately specifies only thechromaticity of a sample.

** Terms from OSA Colorimetry Committee Report, nowin preparation. This report will contain definitions, also atable, showing the relation between the terms used to de-scribe the color stimulus (physical), color (psychophysical),and the color sensation (psychological). Color mixture is apsychophysical matter; color organization is a psycho-logical matter. There is no attempt in this paper to touchupon spectrophotometric methods for studying the colorstimulus (physical).

The purpose of the foregoing example is toshow that color is the property of light thatreaches our eyes. We can make a filter take on asurface appearance; or, we can take a surfacecolor and make it modify light like a filter.5 It isobvious therefore that no distinction betweensurface colors and aperture colors is necessaryas far as chromaticity is concerned. It is betterto think of both surface and filter as modifiersof the original light, even though they modifyit by entirely different methods. It does notmatter how we create the modifiers; they aresimply a means for changing the light to get theeffect we want.

This approach to the subject has been madein order to indicate that there is only one kindof color, and consequently there can be only onekind of color mixture. A specification of thequality of light is the specification of its color,and such a view makes the problem of colormixture easy to understand.

The I.C.I. system and diagrams developed fromit are developed to foretell color mixture, andon such diagrams all color mixtures lie in straightlines. If we plot points to represent red andgreen on this diagram, Fig. 2, and draw a straightline between them, that line will represent allpossible mixtures of those two colors. Yellow lies

xFIG. 2. I.C.I. (x, y) diagram. Color mixtures always lie on

straight lines on this diagram. The line of mixture for redand green passes through yellow. The line of mixture ofyellow and purple-blue passes through the neutral point,indicated on this diagram by the point representing I.C.I.Illuminant C.

6 David Katz, The World of Colour, trans. by R. B. Mac-Leod and C. W. Fox (Kegan Paul, Trench, Teubner andCompany, London, 1935).

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on that line. Let us try out mixtures of red andgreen to see if they result in yellow. Try it withlights, as with green and red spotlights. Theresult is yellow. Next, let us plot points torepresent blue and yellow on the same diagram.On a line connecting those points all colorsresulting from their mixture will be represented.The line goes through, or nearly through, theneutral point of the diagram. If we try out themixture with lights, as with filtered spotlights,the result will be neutral, or some color repre-sented on the line drawn on the diagram de-pending upon the proportion of each light usedin the mixture.

Other forms of color mixture can be describedin a similar manner. For example, if we haveMaxwell disks, the color of the mixture of twodisks is determined in the same manner. It isonly necessary to draw a straight line connectingtwo points on the chart which represent thedisk colors, and the mixture colors-no matterwhat their proportion-will be represented by apoint on this line. The use of more than twocolors in the disk mixture is merely an extensionof this fundamental principle. In a multicoloreddesign whose elemental color areas are small soas to be beyond resolution at certain distances,the apparent color may be predicted by themethod described above, or by means of rotatingsectored disks.

If we were required to choose three lightswhich, when mixed together, would give amaximum gamut, the choice would be made bymeans of this mixture diagram. As may be seenfrom the shape of the boundary colors, the threecolors which would best satisfy this requirementwould be red, blue, and green, since pointsrepresenting these colors define a triangle whichencloses the gamut of color obtainable by mix-tures. If we do not confine our discussion to thecombination of positive amounts of light, wefind that any three colors will do (providing onlythat no two will match the third), for if we arepermitted to use negative amounts of these (asimple process in the laboratory) we then canmatch all colors. Any three lights, no two ofwhich will match the third, can be calledprimaries in a color-mixture system. The reasontdat red, blue, and green are in common use isthat they include the greatest gamut in positive

mixtures. This is extremely convenient formany reasons.

The most important commercial applicationof these primaries is in color photography. Aphotograph of the subject is made through eachof three filters, red, green, and blue, and positivesmade from these separation negatives are placedin three projection lanterns together with theirrespective taking filters. The projected imageswhen superimposed on the screen provide a colorreproduction of the original subject. The variousdensities of the separation positives control theamount of the red, green, and blue primarieswhich mix to reproduce the original colors of thesubject. While this is not the method in commonuse today, it, nevertheless, demonstrates theprinciple underlying color photography.

These, then, are the fundamentals of colormixture. But you ask, and you may well ask,since you work with colorants: How about paintmixtures-pigment, dye, and ink mixtures? Theanswer is: Colorants merely control light. Thisis important: COLORANTS MERELY CON-TROL LIGIIT.

Any mixture of colorants is merely a meansto produce a desired color. All colorant mixturesor gamuts are unique, and are controlled byfactors which have no relation to color mixture.For example, in modern color photographicprocesses requiring a single projection device orwhere colored photographs are obtained asprints, the red, green, and blue primaries arecontrolled by blue absorbing, green absorbing,and red absorbing colorants. These colorantsare chosen on the basis of how well they controlthe primaries and how complete a color gamutis within their range. The three colorants thatare used look like magenta, yellow, and blue-green. They may be in the form of dyes whenthey are used in photographic emulsions, or theymay be in pigment form when used in an artist'spalette, or in printing inks as used for thecolored illustrations in magazines.

Just as three colorants control the lightprimaries in color photography, so all colorantscontrol light in a general sense. Wheneverpaints, pigments, dyes, or inks are used, theyact as modifiers of the light under which theyare viewed. They should not be judged on thebasis of their apparent color, but only on a

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y \ 300 0 0 9;r

00reernc \Prsa bu Titanium White \ene e2 Prussian ieBlue FIG. 3. I.C.I. (X y) diagram. Colorant mixtures indicated

by the gamuts for cadmium yellow and titanium white (seereference 2), Prussian blue and titanium white (see refer-ence 2), Prussian blue and cadmium yellow (see reference3). Each pair of colorants is a case by itself; sometimes suchmixtures are near to straight lines, sometimes they are farfrom straight lines. Colorant mixtures can be predictedonly on a basis of experience.

basis of what each contributes to the desiredresult.

No exact forecast, no plotting of the result ofcolorant mixtures (often called "subtractive"mixtures) can be foretold from the color of thecomponents alone. They cannot be predictedin the exact manner of color (or "additive")mixtures. There are many specific peculiarities-selective absorption, refractive index, particlesize, etc.-and most of teatrouble in under-standing this subject of colorant mixture hasoccurred because broad, general assumptionshave been made, and have been assumed to beas rigorous as are the rules of color mixture.Until new and untried colorants are found notto fall into happenstance categories, the artistand art teacher often fail to realize the differencebetween the nature of color mixture and colorantmixture.

The easiest and most satisfactory way to studythe mixture of colorants is to make the mixtures.(Certain physical data, the absorption andscattering coefficients of colorants, are of extremevalue in predicting a gamut, but their considera-tion is a technical study in itself.)

If, for instance, we are working with pigments,and select those that give complete hiding films,a good mixture example would be that of

cadmium yellow and titanium white. Aftermaking chips in a sufficient number of steps torepresent various proportions of these pigments,we would have actual evidence of the colorgamut possible with these two materials. If wethen evaluated, or measured, the chromaticityof the chips and located them on the I.C.I.mixture diagram, as in Fig. 3, we would see injust what way the colorant mixtures varied inchromaticity, and how close or far the gamut ofthe colorant mixture departs from the straightline that can be predicted for color mixture.Another representation is shown in Fig. 4 forthis same gamut. This time we have departedfrom the (x, y) mixture diagram in order to seehow the color of the mixture decreases in purityas the mixture increases in luminous reflectance.

In the case of colorant mixtures of Prussianblue and titanium white on the (x, y) diagram,Fig. 3, the mixtures with the first small amountof white show an increase in purity of color, andnot only do they increase in purity, but theyswing slightly toward a more purplish blue, untila maximum purity is reached, then the mixturesturn back toward the green-blue as the mixturesapproach a maximum of white-pigment content.Another representation of this color gamut isshown in Fig. 4 in order to illustrate how anincrease in purity accompanies an increase inluminous reflectance up to a certain proportionof the two colorants, then there is a decrease inpurity as the reflectance is further increased.

Prussian blue should not be called an opaquepigment in the sense that cadmium yellow ortitanium dioxide white are called opaque, butit does a good job of hiding the support onwhich it is applied, because of its considerableabsorption of light. If the film is applied over awhite reflecting surface, and successively reducedin thickness, another color gamut is producedwhich may look similar to the one producedbefore, but is not exactly the same. In fact,we can take two different Prussian blues, whichmight have the same mass-tone, and from themproduce entirely different color gamuts onextension with the same opaque white or byfilm thickness variations.

The mixture of Prussian blue with cadmiumyellow offers further interesting results which,

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because of the wide variations in color attributes,are difficult to visualize except with a three-dimensional model. Reduced to two dimensionsthe chromaticity is shown effectively on theI.C.I. diagram, Fig. 3.

Once the picture is clear in our minds of theway in which color gamuts are apt to departfrom the straight line relations of color mixture,it will be evident why attempts at simplificationlead only to confusion. All mixtures of colorantsshould be considered special cases since that iswhat they actually are. Any similarity to theaccurate and simple rules of color mixture ispurely accidental.

Until we know pigments through experiencewith their mixtures, or through knowledge oftheir spectral absorption and scattering coeffi-cients, we do not know what will happen northe rate at which it will happen.

Perhaps it is as well that colorant mixtures docall for experimentation, for too many peoplewant only a formula or recipe to produce anyrequired result. In the teaching of color anddesign there has been too much of a tendency

to rely upon formulas, many instructorsreferring to so-called "laws," in an attempt toarrive at some sure-fire way of creating eternalbeauty. Many of these theories have long sincebeen outmoded in the light of scientific investi-gation; many are as yet scarcely formulated;most of them deal with the subject in theabstract and have absolutely no bearing orinfluence upon the arts as they are lived andpracticed. Formulas may well serve as thelife-giving foundation and structure of science,but they are the assassins of an imaginative,creative, and vital art. They should be sorecognized by the artist and the art educator,and used as an intelligent means to orient-notto substitute for-the creative impulse. Anunderstanding of color mixture and of colorantmixture, with the consequent ability to plot andplan at arriving directly at the goal should be tothe artist what the ability to make and readmaps is to the explorer. If the explorer knowshis goal, and has all these modern aids, theyhelp him to reach his goal with a minimum ofwasted effort.

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