From larger—smaller judgments of color differences, compared visually two at a time, the perceived sizes may be evaluated on an interval scale. Given numbers B so evaluated, and such that B is linearly connected to some power p, of the physical measure D (such as distance on any chromaticity diagram) of the differences, the additive constant K_br such that the numbers B+K_br are expressed on a ratio scale may be found from judgments of the ratio of sizes of pairs of differences. To evaluate p, it is sufficient to observe the three differences, 12, 23, and 13 between the pairs of three colors, 1, 2, 3, forming a geodesic series, and chosen so that B₁₂ is not much different from B₂₃. The scale formed by the numbers (B+K_br)^1/p is additive if the D scale is additive. If the largest of the color differences judged exceeds the smallest by a factor not greater than 3, a close approximation to the (B+K_br)^1/pscale may be found without evaluating K_br discovery that scales based on the additivity condition: (B₁₂+K_bd)^1/p+(B₁₃+K_bd)^1/p = (B₁₃+K_bd)^1/p, though it implies that K_bd depends strongly on p, are essentially identical regardless of the choice of p between 1 and ⅓. It is sufficient therefore, to derive the additive scale by setting p= 1, and computing K_bd as B₁₃—B₁₂—B₂₃.

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