Abstract

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 <i>B</i> so evaluated, and such that <i>B</i> is linearly connected to some power <i>p</i>, of the physical measure <i>D</i> (such as distance on any chromaticity diagram) of the differences, the additive constant <i>K<sub>br</sub></i> such that the numbers <i>B</i>+<i>K<sub>br</sub></i> are expressed on a ratio scale may be found from judgments of the ratio of sizes of pairs of differences. To evaluate <i>p</i>, 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 <i>B</i><sub>12</sub> is not much different from <i>B</i><sub>23</sub>. The scale formed by the numbers (<i>B</i>+<i>K<sub>br</sub></i>)<sup>1/<i>p</i></sup> is additive if the <i>D</i> 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 (<i>B</i>+<i>K<sub>br</sub></i>)<sup>1/<i>p</i></sup>scale may be found without evaluating <i>K<sub>br</sub></i> discovery that scales based on the additivity condition: (<i>B</i><sub>12</sub>+<i>K<sub>bd</sub></i>)<sup>1/<i>p</i></sup>+(<i>B</i><sub>13</sub>+<i>K<sub>bd</sub></i>)<sup>1/<i>p</i></sup> = (<i>B</i><sub>13</sub>+<i>K<sub>bd</sub></i>)<sup>1/<i>p</i></sup>, though it implies that <i>K<sub>bd</sub></i> depends strongly on <i>p</i>, are essentially identical regardless of the choice of <i>p</i> between 1 and ⅓. It is sufficient therefore, to derive the additive scale by setting <i>p</i>= 1, and computing <i>K<sub>bd</sub></i> as <i>B</i><sub>13</sub>—<i>B</i><sub>12</sub>—<i>B</i><sub>23</sub>.

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