Abstract

This paper deals with processes which operate when pigments are combined. Usually it is assumed that one may learn of these processes only by trial and error and that information acquired in this way cannot be imparted to others. From experience as a painter and decorator the writer has long believed otherwise; that is, that these processes are simple enough so that, given a proper method, useful information about them could be organized and presented in a form understandable to any interested person. With this in mind a simple diagram was devised to show general mixture-relationships among red, yellow, and blue pigments and their combinations. Though this was useful to a degree, its limitations were evident, since it did not deal concretely with most pigments in common use. By trial and error, points indicating a selection of pigments were incorporated into the diagram, with the objective that color-mixture relationships among the pigments should be expressed in terms of linear relationships among the points. The advantages of such an arrangement were at once apparent. Using this as a point of departure and drawing from the experience of people inquiring into similar processes operating when colored lights are combined, a new color system was built, consisting of devices and conventions designed to supplement and facilitate use of information so presented. To what degree the pigment positions had been so arranged as to secure the nearest-possible approach to linear color-mixture relations remained for a time unknown. Meanwhile doubt was expressed that it is possible to arrange them so as to provide useful approximations of the relationships involved. Then a new experimental technique was devised. This led to correction of errors in locating the pigment positions and produced evidence that information about color-mixture relationships among pigments can be summarized very well in diagramatic form. Some features of the color system mentioned are noted. The experiments are described and data presented for review.

© 1959 Optical Society of America

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References

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  1. Called a trefoil because of its similarity to the frame of the Gothic window of that name.
  2. For the genealogy of the diagram the writer is indebted to W. T. Wintringham of the Bell Telephone Laboratories.
  3. This observed relationship does not hold—even roughly—for all pigments. As will appear later, the phthalocyanine green has a color-mixture range comparable to that of the reference red, yellow, and blue pigments of the selection under consideration here.
  4. A ten-step lightness scale was established similar in general appearance to the Munsell value scale, but dissimilar in that its reference black is that of the pigment drop black in mass-tone, and its reference white is that of the white enamel described in Table I. The eight intermediate steps result from intermixtures of this black and this white spaced at visually equal intervals when evaluated against a grey background.
  5. A description appears in Edward Friel, The Friel System, a Language of Color (Trefoil Color Research, Inc., Seattle, 1959).
  6. In terms of a lightness scale which may be constructed separately and especially for different representative selections of colorants.
  7. For a description of the method, see the Appendix.
  8. An adaptation of a technique devised for use in color matching. For a procedure so simple it provides good viewing conditions for chromaticness comparisons of this kind.
  9. Chrome yellow light, chromiim oxide, chrome green light, chrome green medium, phthalocyanine green, chrome green dark, Prussian blue, phthalocyanine blue, ultramarine blue, madder lake, toluidine red, vermilion, chrome orange light, and yellow oxide.
  10. This can be done by any interested person of approximately normal vision at nominal cost. An instructive exercise in pigment manipulation and a short excursion into the realm of color relations are to be had in the process.

Friel, Edward

A description appears in Edward Friel, The Friel System, a Language of Color (Trefoil Color Research, Inc., Seattle, 1959).

Other (10)

Called a trefoil because of its similarity to the frame of the Gothic window of that name.

For the genealogy of the diagram the writer is indebted to W. T. Wintringham of the Bell Telephone Laboratories.

This observed relationship does not hold—even roughly—for all pigments. As will appear later, the phthalocyanine green has a color-mixture range comparable to that of the reference red, yellow, and blue pigments of the selection under consideration here.

A ten-step lightness scale was established similar in general appearance to the Munsell value scale, but dissimilar in that its reference black is that of the pigment drop black in mass-tone, and its reference white is that of the white enamel described in Table I. The eight intermediate steps result from intermixtures of this black and this white spaced at visually equal intervals when evaluated against a grey background.

A description appears in Edward Friel, The Friel System, a Language of Color (Trefoil Color Research, Inc., Seattle, 1959).

In terms of a lightness scale which may be constructed separately and especially for different representative selections of colorants.

For a description of the method, see the Appendix.

An adaptation of a technique devised for use in color matching. For a procedure so simple it provides good viewing conditions for chromaticness comparisons of this kind.

Chrome yellow light, chromiim oxide, chrome green light, chrome green medium, phthalocyanine green, chrome green dark, Prussian blue, phthalocyanine blue, ultramarine blue, madder lake, toluidine red, vermilion, chrome orange light, and yellow oxide.

This can be done by any interested person of approximately normal vision at nominal cost. An instructive exercise in pigment manipulation and a short excursion into the realm of color relations are to be had in the process.

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Figures (18)

F. 1
F. 1

Diagram frame shaped to aid in visualizing pigment positions and in locating them so as to secure linear color-mixture relationships.

F. 2
F. 2

One objective in placing pigment positions on the trefoil diagram is that if a pigment position, such as E, departs from the line connecting, for example, pigment positions A and B in the direction of pigment position F, the chromaticness interval between the optimum mixture m1 of pigments A and B and pigment E is related to the chromaticness interval between pigments E and F as the distance m1E is related to the distance EF.

F. 3
F. 3

A further objective in placing pigment positions is that if a pigment position, such as C departs from the line connecting pigment positions A and B in the direction opposite that of pigment D, the chromaticness interval between the optimum mixture m of pigments A and B and pigment C is related to the chromaticness interval between mixture m and pigment D as the distance mC is related to the distance mD.

F. 4
F. 4

A selection of pigments arranged to show chromaticness relationships between pigments and pigment mixtures as they apply at lightness 9 in a lightness scale of ten steps. Relationships are expressed in terms of the approximate rule that colors produced by mixture appear on straight lines joining the points indicating the pigments mixed.

F. 5
F. 5

Method for plotting data. Points A, B, C, and D represent hypothetical pigments on the trefoil diagram. Chromaticness relationships between an optimum mixture of pigments A and B and pigments C and D are under consideration.

F. 6
F. 6

Point m, indicating an optimum mixture of pigments A and B, is placed on line CD so that the chromaticness interval between mixture m and pigment C is related to the chromaticness interval between mixture m and pigment D as the distance mC is related to the distance mD.

F. 7
F. 7

Point m1, indicating an optimum mixture of pigments A and B, is placed on the extension of line EF so that the chromaticness interval between mixture m1 and pigment E is related to the chromaticness interval between pigments E and F as the distance m1E is related to the distance EF.

F. 8
F. 8

The location of points m, m1 and m2 with reference to line AB indicates the degree to which line AB presents correctly the chromaticness relationships between mixtures of pigments A and B and a number of other pigments.

F. 9
F. 9

The broken line through points A, m, m1, m2, and B shows graphically that the line AB presents useful approximations of the chromaticness relationship of optimum mixture m of pigments A and B to pigments C and D, and of mixture m1 to pigments E and F, but fails to present adequately the chromaticness relationship between mixture m2 and pigments G and H.

F. 10
F. 10

Lines plotted to show chromaticness relationships between some combinations and chromium oxide before correcting the position of chromium oxide. Note that the paths are similarly nonlinear in each case.

F. 11
F. 11

Lines plotted to show chromaticness relationships between mixtures of chromium oxide and chrome green light with to-luidine red and between mixtures of the same two pigments with madder lake before correcting the position of chromium oxide. Note the similarity in nonlinear form.

F. 12
F. 12

Some combinations which produce colors similar to chromium oxide. Chromaticness relationships between these combinations and chromium oxide suggest the compromise position indicated. Note the improved linearity as compared to Figs. 10 and 11.

F. 13
F. 13

Lines plotted to show chromaticness relationships between combinations which include phthalocyanine blue and several pigments of a selection at lightness 9.

F. 14
F. 14

Lines plotted to show chromaticness relationships between combinations which include chrome yellow light and several pigments of a selection at lightness 9.

F. 15
F. 15

Lines plotted to show chromaticness relationships between combinations which include toluidine red and several pigments of a selection at lightness 9.

F. 16
F. 16

Method of specifying a color which results from mixture of two colorants. Point x, indicating the desired color, appears on the line connecting the positions of two colorants A and B. The relative quantities of colorants A and B required to produce the desired color are computed from relationships of distances 〈xA〉 and 〈xB〉 to distance 〈AB〉, modified by the strength scores of colorants A and B.

F. 17
F. 17

Method of specifying a color which consists of a mixture of three colorants. Point x1, indicating the desired color, appears among the positions of three colorants A, B, and C.

F. 18
F. 18

Method of computing the relative quantities of colorants A, B, and C required to produce the desired color x1, described in Fig. 17. Computation is based on relationships of distances 〈pA〉 and 〈pB〉 to distance 〈AB〉 and between distances 〈x1p〉 and 〈x1C〉, modified by the strength scores of colorants A, B, and C.

Tables (3)

Tables Icon

Table I The selection of pigments chosen for consideration. Strength scores state the estimated typical relative tinting strength of the pigments, where lampblack is assigned an arbitrary strength value of 10.a

Tables Icon

Table II Positions of the pigments of the selection described in Table I, expressed in terms of the D and Z scales used in the trefoil system. Pigments of lightness lower than 9 were combined with as much of the reference white of the selection as was reqiired to attain a lightness of 9 for each.

Tables Icon

Table III Data resulting from 101 experiments. The two first-named pigments in each line are the components of a mixture. The third and (where two pigments are involved in the comparison) fourth designate the pigments with which the mixture was compared. The figures state the position of a mixture on the trefoil diagram at lightness 9, from which its chromaticness relationship to the comparison pigments at that lightness may be derived from relative distances on the diagram.

Equations (2)

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V a = x B / A B S a , V b = x A / A B S b .
V a = p B / A B S a , V b = p A / A B S b , V c = x 1 p / x 1 C S c .