A Psychological Color Solid[1]
Dorothy Nickerson, Food Distribution Administration, U. S. Department of Agriculture, Washington, D. C.
AND
Sidney M. Newhall, Bausch & Lomb Optical Company, Rochester, New York
VARIOUS geometrical solids have been designed in an attempt to describe the color space of normal human perception. Such solids, it should be emphasized, are concerned exclusively with the conscious color responses of the organism and have nothing to do with the stimuli except insofar as psychophysical equivalents may prove useful for standardization or conversion purposes.
The most familiar and promising procedure has been to represent the principal dimensions of perceived color by the coordinate axes of a cylindrical system in which lightness is indicated by altitude on the central axis, hue by angle about the axis, and saturation by distance from the axis (1/)-(3).[2]
The ideal psychological solid in cylindrical coordinates would fulfill the following requirements: The dimensional scales would be calibrated in perceptually uniform steps; the units of the several scales would be equated; the surface of the solid would represent all colors of maximum saturation; the volume would be representative of all colors which are perceptibly different; the conditions of stimulation or viewing would be prescribed; and finally, the scales would be standardized in terms of a generally recognized psychophysical system.
In the preparation of a report on the smoothing of the Munsell colors (4), (5), data became available which permit, for the first time, an approximate fulfillment of all of these requirements. By reference to Adams’ plots of “chromatic value” (6) and MacAdam’s theoretical pigment limits (7), it was possible to lay down loci for constant chromas from zero to maximum. Table I presents (to the nearest half step) the maximum Munsell chromas corresponding to nine equispaced value levels and 40 equi-spaced hues. These figures serve to define the surface of the new solid.
Two models have been constructed, one to portray the proportions of a solid when the lightness and saturation dimensions have been equated at a supraliminal level of color difference, and the other when they have been equated at the liminal level. Thus the relatively short model, Fig. 1a, represents color as perceived under more or less usual conditions when no special tax is imposed upon the discriminatory power of the normal observer; the proportions are about right for readily perceived differences of the order of a chroma or value step (8). The taller model,
TABLE I. Chromas[3] at theoretical pigment limits for 40 hues, Munsell values 1/ through 9/.
 | A table should appear at this position in the text. See Help:Table for formatting instructions. |
| Hue | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | |
| 2.5 R | 6.5 | 12.0 | 16.0 | 19.5 | 21.0 | 20.0 | 17.5 | 15.0 | 12.0 | |
| 5 | 6.5 | 11.5 | 16.0 | 19.5 | 21.0 | 20.0 | 20.0 | 17.0 | 14.0 | 11.5 |
| 7.5 | 6.0 | 11.5 | 16.0 | 19.5 | 21.5 | 20.5 | 17.5 | 14.0 | 11.0 | |
| 10 | 6.0 | 11.5 | 17.0 | 20.0 | 18.5 | 16.5 | 14.5 | 14.0 | 10.5 | |
| 2.5 YR | 6.5 | 13.0 | 22.0 | 18.5 | 16.5 | 13.5 | 11.0 | 9.5 | 9.5 | |
| 5 | 7.0 | 16.0 | 21.0 | 18.0 | 15.5 | 12.5 | 10.0 | 7.5 | 4.0 | |
| 7.5 | 8.0 | 22.0 | 19.5 | 16.5 | 15.5 | 12.5 | 10.0 | 7.5 | 5.0 | 3.0 |
| 10 | 10.0 | 21.0 | 18.0 | 15.5 | 13.5 | 11.0 | 8.0 | 6.0 | 3.0 | |
| 2.5 Y | 13.0 | 20.0 | 17.5 | 15.0 | 13.0 | 10.5 | 8.0 | 5.0 | 3.0 | |
| 5 | 20.0 | 19.5 | 17.0 | 14.5 | 12.5 | 10.0 | 7.5 | 5.0 | 3.0 | |
| 7.5 | 20.0 | 19.0 | 16.5 | 14.0 | 12.0 | 9.5 | 7.0 | 5.0 | 3.0 | |
| 10 | 19.5 | 19.0 | 16.5 | 14.0 | 12.0 | 9.5 | 7.0 | 5.0 | 3.5 | |
| 2.5 G | 16.0 | 25.0 | 28.0 | 29.0 | 29.5 | 27.5 | 23.0 | 16.5 | 9.0 | |
| 5 | 13.5 | 22.0 | 27.5 | 28.5 | 29.5 | 28.0 | 23.5 | 17.0 | 8.5 | |
| 7.5 | 10.0 | 16.5 | 19.0 | 20.0 | 19.5 | 19.0 | 16.5 | 12.5 | 7.5 | |
| 10 | 7.5 | 16.0 | 17.5 | 18.5 | 17.5 | 17.0 | 14.5 | 11.5 | 7.0 | |
| 2.5 BG | 11.5 | 19.0 | 22.5 | 24.0 | 23.5 | 24.0 | 21.0 | 15.0 | 8.5 | |
| 5 | 11.0 | 18.0 | 20.5 | 22.0 | 22.0 | 21.0 | 18.0 | 14.0 | 8.0 | |
| 7.5 | 10.0 | 16.5 | 19.0 | 20.0 | 19.5 | 19.0 | 16.5 | 12.5 | 7.5 | |
| 10 | 4.0 | 7.5 | 16.0 | 17.5 | 18.5 | 17.5 | 17.0 | 14.5 | 11.5 | 7.0 |
| 2.5 B | 6.0 | 13.0 | 16.5 | 17.5 | 17.0 | 16.0 | 13.5 | 11.0 | 7.0 | |
| 5 | 5.0 | 10.0 | 15.0 | 16.5 | 16.5 | 15.0 | 13.5 | 10.5 | 8.0 | |
| 7.5 | 4.5 | 9.0 | 13.5 | 17.0 | 17.5 | 16.0 | 13.5 | 11.0 | 8.0 | |
| 10 | 4.0 | 8.0 | 12.0 | 17.0 | 18.0 | 17.0 | 14.0 | 12.0 | 9.0 | |
| 2.5 PB | 4.0 | 8.0 | 11.5 | 16.5 | 19.0 | 18.5 | 16.0 | 13.0 | 10.0 | |
| 5 | 4.0 | 7.5 | 11.5 | 16.0 | 19.5 | 20.5 | 18.5 | 15.5 | 12.0 | |
| 7.5 | 6.5 | 13.0 | 19.5 | 26.0 | 32.0 | 33.5 | 30.0 | 27.5 | 23.5 | 19.0 |
| 10 | 8.0 | 16.0 | 22.5 | 27.0 | 31.5 | 30.0 | 27.5 | 23.5 | 19.0 | |
| 2.5 RP | 8.0 | 15.0 | 21.0 | 26.0 | 28.0 | 26.5 | 23.0 | 20.0 | 17.5 | |
| {{0}5 | 7.5 | 13.5 | 19.0 | 22.5 | 24.0 | 23.5 | 21.0 | 18.0 | 15.5 | |
| 10 | 7.0 | 12.0 | 16.5 | 20.0 | 20.5 | 18.0 | 16.0 | 13.0 |
