Ten-Minute Art School Course excerpt from The Creation of Color in Eighteenth-Century Europe by Sarah Lowengard Charts and tables were useful tools for natural philosophers; as classification devices their forms were reinvented and refined throughout the eighteenth century. The three-sided color graph developed by the astronomer and mapmaker Tobias Mayer, for example, drew several themes in mathematics and optics into a descriptive aid for color. Mayer first presented his ideas about a color system at a lecture in Göttingen in 1758. Several German periodicals described the content of the lecture in detail and its information spread quickly, as those articles were republished. Mayer’s triangle became, after Newton’s color circle, perhaps the most recognizable color classification form in the eighteenth-century West. Painters (and amateurs of painting) adopted and adapted Mayer’s conceptualization of a color triangle to regularize their own practices. Natural historians used it to identify objects and to situate relationships between the sciences and the arts. When examined together, Mayer’s triangle and its later variations offer an excellent example of the eighteenth-century effort to create a unified, mathematized description of colors and to extend the value of this description into artisan worlds. As an episode within the centuries-long effort to systematize color as a way to understand and control it, the development of Mayer’s color triangle highlights the constraints produced by materials, the limits of mathematized descriptions, and the relationship of those limitations to representation and understanding of color. Mayer based his triangle on clearly stated precepts that addressed some recognized problems of color display systems. First was the definition of pure and simple colors. In eighteenth-century scientific descriptions, these were often linked to the prismatic spectrum. Seven simple colors, usually the seven Newton identified, were often cited. Pure colors were those made from a single coloring source and not the combination of any others: Orange was a simple color and certain coloring materials provided orange shades, but because the combination of red and yellow pigments could yield orange, it was not a pure color. Following contemporary painters’ practices, Mayer showed that only red, yellow, and blue met his criterion for pure and simple colors. His choices for the best sources for these pure colors, for the liveliest and most beautiful red, blue, and yellow were, respectively, cinnabar, mountain blue (azurite), and gamboge. Mayer’s system also demonstrated the common assumption that, combined in the correct proportions, this small number of basic colors could create all others. This was a more intuitive idea, artisan-based and not always evident in other visual classification systems. Waller’s grid incorporated graded colors in a way that suggested that colors were made from varying combinations of darkness and lightness. Schäffer’s and Werner’s systems relied on the alternative concept of principal colors. Principal colors might be pure in the sense that they were unmixed mechanically, but not all were: For those two systems, principal subsumed the definition of pure. If there are three basic colors, then the triangle becomes an obvious choice to display them succinctly. A different pure color is placed at each angle or corner of the triangle, and the balance may be filled with their mixtures. Appropriately sized, the triangular form could contain all combinations within one system. Mayer’s Color Triangle Mayer also conducted a study to guide the size of the triangle. His tests of visual perception determined that the eye can distinguish only about twelve gradations between any two colors. Accordingly, his triangle has thirteen compartments on each side. At each extreme, the angular color is a perfect or pure color. Each is separated from the two other pure colors by eleven proportional mixtures of them. The two chambers on either side of the angular blue (designated b12 in Mayer’s notation system) would have, respectively, eleven parts blue to one part red and eleven parts blue to one part yellow, and so on. The fifty-two compartments at the interior of the triangle are filled with mixtures of the three colors, each combination calculated according to its position within the triangle. The center block would have equal parts each of red, yellow, and blue (r4y4b4); the compartments surrounding it would have combinations of three, four and five parts of each color, depending on location. Mayer’s complete color system included other triangles made up of the pure pigments mixed with progressively larger quantities of white or black. These triangles had progressively fewer compartments as the colors approached white (lightness) or black (darkness). The first set of pale and dark triangles each had twelve compartments per side rather than the thirteen of the main form. In each, the angular colors were eleven parts pure color to one part black or white. The second set of triangles had eleven compartments per side; the angular colors were ten parts pure color to two parts black or white. Calculated from perfect colors to full white and full black, the total number of colors in each category, pale and dark, was 364. Added to 91, the number of colors of the main triangle, the total number of perfect and dark and pale colors was 819. That, by Mayer’s definition, was the number of colors in the world, although his color algebra indicated that more colors might exist. Mayer described how these triangles determined and defined colors. His graphs were bi-directional, equally useful to describe a color at hand or to determine the formula to make any color the eye could see. One could compare a color found on an object to the colors in the triangle and, because location on the graph was determined by the proportions of the preparation, know its composition. Alternatively, one could choose a color from the schematic and know immediately the combination of red, yellow, blue, black, and white needed to recreate it. Still, as Georg Christoph Lichtenberg found, to construct Mayer’s triangle was no simple task. Lichtenberg noted, for example, that the most effective way to make the pale colors of the supplemental triangles was a simple dilution of the pure colors, allowing the paper support to transmit the required proportion of white. The complement, concentrating pure colors, was less successful for the creation of the dark triangles however, and the addition of a black tincture made of an equal combination of red yellow and blue pigments was never dark enough. Furthermore, Lichtenberg admitted, it was difficult to obtain all colors from mixtures of only two or three. Even Mayer did not use his angular pigments to mix pinks and violets but instead based them on pure colors available to him. Whether Mayer ever constructed a complete triangle or a set of complete triangles is unclear. Lichtenberg’s effort and discussion of his own version of Mayer’s triangle further demonstrate assumptions about the nature of art and the problems of its use to express scientific ideas. Lichtenberg’s published version of Mayer’s triangle truncated the form to seven chambers per side because of some practical problems. Using Mayer’s methodology of proportional mixtures, for example, resulted in midpoint colors that were dirty-looking, not the clear greens and violets of the imagination. Lichtenberg attributed this to different physical properties of each pigment including differences in their ability to absorb water, the medium. As Waller had used weights, Lichtenberg used specific gravities to compare colors, and he reconfigured his pigment choices so that the initial ratios of yellow to blue was one to six; of blue to red was two to one, and of yellow to red one to three. He also employed different pure pigments from those recommended by Mayer, choosing amber, Prussian blue, and natural cinnabar as the angular pigments. Mayer’s color system was graph-like and number-based. It seemed to achieve the scientific goals common to classification projects: overall simplification, recognition of order, and a clear articulation of the advantages that those two qualities might offer practices via the use of theories. Visually elegant, Lichtenberg’s recalculation of Mayer’s triangle, like Mayer’s triangle itself, was nevertheless a difficult tool to create and to use. One problem related to the angular colors, as Lichtenberg encountered. Although Mayer’s description called for cinnabar as his pure red, the color used in his sample formulas is the more yellow-toned red lead (Mayer’s formula for red lead is r8y4. Although azurite is Mayer’s pure blue pigment (b12), his examples of color mixing and identification relied on Prussian blue (b11r1). Mayer did not explain these discrepancies, and there may be several reasons for them. Cost and availability may have restricted access to the materials that Mayer initially chose. If minium and Prussian blue were less expensive and less difficult to obtain outside of large cities, it would be more practical, as well as more practice-based, to use them. It is also possible that the change from Mayer’s pure colors to other, imperfect or mixed colors resulted from the properties of Mayer’s choices. Neither vermilion nor gamboge is reliably permanent. The practical value of the triangles would be limited if the materials used to construct it were incompatible or otherwise unstable. Finally, although it is unlikely that this was deliberate, Mayer’s use of nonperfect colors in mixtures has the effect of emphasizing his point that nearly any coloring material could be adapted to his techniques of color composition and identification. Mayer’s color classification system illustrates the difficulties of adapting art practices to the sciences. In the imagination or as a hypothesis, the combination was almost effortless. Mixing pigments to achieve specific colors, even when guided by the certainties of mathematics, was considerably more difficult. [taken from the chapter Number, Order, Form]

Ten-Minute Art School Course

excerpt from The Creation of Color in Eighteenth-Century Europe

by Sarah Lowengard

Charts and tables were useful tools for natural philosophers; as classification devices their forms were reinvented and refined throughout the eighteenth century. The three-sided color graph developed by the astronomer and mapmaker Tobias Mayer, for example, drew several themes in mathematics and optics into a descriptive aid for color. Mayer first presented his ideas about a color system at a lecture in Göttingen in 1758. Several German periodicals described the content of the lecture in detail and its information spread quickly, as those articles were republished. Mayer’s triangle became, after Newton’s color circle, perhaps the most recognizable color classification form in the eighteenth-century West. Painters (and amateurs of painting) adopted and adapted Mayer’s conceptualization of a color triangle to regularize their own practices. Natural historians used it to identify objects and to situate relationships between the sciences and the arts. When examined together, Mayer’s triangle and its later variations offer an excellent example of the eighteenth-century effort to create a unified, mathematized description of colors and to extend the value of this description into artisan worlds. As an episode within the centuries-long effort to systematize color as a way to understand and control it, the development of Mayer’s color triangle highlights the constraints produced by materials, the limits of mathematized descriptions, and the relationship of those limitations to representation and understanding of color.

Mayer based his triangle on clearly stated precepts that addressed some recognized problems of color display systems. First was the definition of pure and simple colors. In eighteenth-century scientific descriptions, these were often linked to the prismatic spectrum. Seven simple colors, usually the seven Newton identified, were often cited. Pure colors were those made from a single coloring source and not the combination of any others: Orange was a simple color and certain coloring materials provided orange shades, but because the combination of red and yellow pigments could yield orange, it was not a pure color. Following contemporary painters’ practices, Mayer showed that only red, yellow, and blue met his criterion for pure and simple colors. His choices for the best sources for these pure colors, for the liveliest and most beautiful red, blue, and yellow were, respectively, cinnabar, mountain blue (azurite), and gamboge.

Mayer’s system also demonstrated the common assumption that, combined in the correct proportions, this small number of basic colors could create all others. This was a more intuitive idea, artisan-based and not always evident in other visual classification systems. Waller’s grid incorporated graded colors in a way that suggested that colors were made from varying combinations of darkness and lightness. Schäffer’s and Werner’s systems relied on the alternative concept of principal colors. Principal colors might be pure in the sense that they were unmixed mechanically, but not all were: For those two systems, principal subsumed the definition of pure.

If there are three basic colors, then the triangle becomes an obvious choice to display them succinctly. A different pure color is placed at each angle or corner of the triangle, and the balance may be filled with their mixtures. Appropriately sized, the triangular form could contain all combinations within one system.

Mayer’s Color Triangle

Mayer also conducted a study to guide the size of the triangle. His tests of visual perception determined that the eye can distinguish only about twelve gradations between any two colors. Accordingly, his triangle has thirteen compartments on each side. At each extreme, the angular color is a perfect or pure color. Each is separated from the two other pure colors by eleven proportional mixtures of them. The two chambers on either side of the angular blue (designated b12 in Mayer’s notation system) would have, respectively, eleven parts blue to one part red and eleven parts blue to one part yellow, and so on. The fifty-two compartments at the interior of the triangle are filled with mixtures of the three colors, each combination calculated according to its position within the triangle. The center block would have equal parts each of red, yellow, and blue (r4y4b4); the compartments surrounding it would have combinations of three, four and five parts of each color, depending on location.

Mayer’s complete color system included other triangles made up of the pure pigments mixed with progressively larger quantities of white or black. These triangles had progressively fewer compartments as the colors approached white (lightness) or black (darkness). The first set of pale and dark triangles each had twelve compartments per side rather than the thirteen of the main form. In each, the angular colors were eleven parts pure color to one part black or white. The second set of triangles had eleven compartments per side; the angular colors were ten parts pure color to two parts black or white. Calculated from perfect colors to full white and full black, the total number of colors in each category, pale and dark, was 364. Added to 91, the number of colors of the main triangle, the total number of perfect and dark and pale colors was 819. That, by Mayer’s definition, was the number of colors in the world, although his color algebra indicated that more colors might exist.

Mayer described how these triangles determined and defined colors. His graphs were bi-directional, equally useful to describe a color at hand or to determine the formula to make any color the eye could see. One could compare a color found on an object to the colors in the triangle and, because location on the graph was determined by the proportions of the preparation, know its composition. Alternatively, one could choose a color from the schematic and know immediately the combination of red, yellow, blue, black, and white needed to recreate it.

Still, as Georg Christoph Lichtenberg found, to construct Mayer’s triangle was no simple task. Lichtenberg noted, for example, that the most effective way to make the pale colors of the supplemental triangles was a simple dilution of the pure colors, allowing the paper support to transmit the required proportion of white. The complement, concentrating pure colors, was less successful for the creation of the dark triangles however, and the addition of a black tincture made of an equal combination of red yellow and blue pigments was never dark enough. Furthermore, Lichtenberg admitted, it was difficult to obtain all colors from mixtures of only two or three. Even Mayer did not use his angular pigments to mix pinks and violets but instead based them on pure colors available to him.

Whether Mayer ever constructed a complete triangle or a set of complete triangles is unclear. Lichtenberg’s effort and discussion of his own version of Mayer’s triangle further demonstrate assumptions about the nature of art and the problems of its use to express scientific ideas. Lichtenberg’s published version of Mayer’s triangle truncated the form to seven chambers per side because of some practical problems. Using Mayer’s methodology of proportional mixtures, for example, resulted in midpoint colors that were dirty-looking, not the clear greens and violets of the imagination. Lichtenberg attributed this to different physical properties of each pigment including differences in their ability to absorb water, the medium. As Waller had used weights, Lichtenberg used specific gravities to compare colors, and he reconfigured his pigment choices so that the initial ratios of yellow to blue was one to six; of blue to red was two to one, and of yellow to red one to three. He also employed different pure pigments from those recommended by Mayer, choosing amber, Prussian blue, and natural cinnabar as the angular pigments.

Mayer’s color system was graph-like and number-based. It seemed to achieve the scientific goals common to classification projects: overall simplification, recognition of order, and a clear articulation of the advantages that those two qualities might offer practices via the use of theories. Visually elegant, Lichtenberg’s recalculation of Mayer’s triangle, like Mayer’s triangle itself, was nevertheless a difficult tool to create and to use. One problem related to the angular colors, as Lichtenberg encountered. Although Mayer’s description called for cinnabar as his pure red, the color used in his sample formulas is the more yellow-toned red lead (Mayer’s formula for red lead is r8y4. Although azurite is Mayer’s pure blue pigment (b12), his examples of color mixing and identification relied on Prussian blue (b11r1). Mayer did not explain these discrepancies, and there may be several reasons for them. Cost and availability may have restricted access to the materials that Mayer initially chose. If minium and Prussian blue were less expensive and less difficult to obtain outside of large cities, it would be more practical, as well as more practice-based, to use them. It is also possible that the change from Mayer’s pure colors to other, imperfect or mixed colors resulted from the properties of Mayer’s choices. Neither vermilion nor gamboge is reliably permanent. The practical value of the triangles would be limited if the materials used to construct it were incompatible or otherwise unstable. Finally, although it is unlikely that this was deliberate, Mayer’s use of nonperfect colors in mixtures has the effect of emphasizing his point that nearly any coloring material could be adapted to his techniques of color composition and identification.

Mayer’s color classification system illustrates the difficulties of adapting art practices to the sciences. In the imagination or as a hypothesis, the combination was almost effortless. Mixing pigments to achieve specific colors, even when guided by the certainties of mathematics, was considerably more difficult.

[taken from the chapter Number, Order, Form]

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