A simple formula for computing fadings or other color differences from Munsell notations has been derived from one simple assumption. Experimental data for the relative visual magnitudes of the Munsell “value” and chroma steps have been incorporated into the formula. It has been tested with several sets of experimental data and found valid even for some large differences. A table of constants facilitates quick application. The formula has been applied to the computation of the color differences of a great many dyes changing in concentration only, for example, from 2 percent to 0.5 percent. This change is known in the textile industry as “on-tone” fading. The user of dyed fabrics dislikes changes of hue more than equally perceptible changes in saturation or lightness, so that acceptability and perceptibility are not identical; hence, the importance of on-tone fading. For the 2-0.5 percent case, hue change as a function of hue of the stronger dyeing gave a well-defined curve. Maximum hue changes occur at 2<i>R</i> and 8<i>YR</i>, with zero change between. The total change is lowest for yellows (explaining why dyers find it most difficult to judge their fastnesses) and highest in the blues. Other published formulas yield the reverse of this fact. The question whether fastness is in large part a matter of perceptibility of changes was examined. The graphs of perceptibility and of average light-fastness ratings, both as a function of hue, show little resemblance, indicating that the fastness ratings are not primarily due to mere concentration change.
I. H. GODLOVE, "Improved Color-Difference Formula, with Applications to the Perceptibility and Acceptability of Fadings," J. Opt. Soc. Am. 41, 760-770 (1951)