# How the Munsell Display Calculator Works

The Munsell Display Calculator is a tool for studying and comparing the perceptual uniformity of color spaces. It is based on the Munsell Renotation System (Color Science: Concepts and Methods, Quantitative Data and Formulae, Wyszecki and Stiles, pp. 507-509). The data set used was obtained from W&S, pp. 840-852, where it is tabulated as xyY, relative to CIE Standard Illuminant C. The Munsell Renotation System is based on three reference parameters: Hue, Value and Chroma, which are perceptually evenly spaced. Thus, all colors having the same notation for Hue (e.g. 5.0 YR) will appear to the eye to be the same hue, regardless of their Value and Chroma. This should be contrasted with the hue angle associated with the CIE Lab and Luv color systems, where this property is not always true (e.g. the "Blue Turns Purple" problem).

With the calculator, you may display the colors in any of three color spaces: xyY, Lab or Luv.

Since the number of colors in the set is so large (2734), the calculator has controls to restrict the display to certain subsets of Hue, Value and Chroma. For each of these three attributes, you may select an individual item, or all items (the All setting is always found at the extreme right end of the sliders). By experimenting a bit, you will quickly learn how this works, and the usefulness of these controls. With them, you may, for example, display all colors of a certain Value, or all colors of a certain Hue, or all colors of a certain Value and Chroma. The best way to learn is by trying it for yourself.

Finally, the actual drawing of the colors may be controlled to better display the relationships among the colors. Rings will connect those colors sharing a common Chroma, which makes it easier to see the shape (which ideally should be circular). Radials will connect those colors sharing a common Hue, which allows you to see how straight the lines are.

## Attributes of a Perceptually Uniform Color Space

For a given Value, all rings of constant Chroma should be circular in shape, and the increment in radius between neighboring rings should be constant. Also for a given Value, all radials of constant Hue should be straight lines, and the angle between neighboring radials should be constant (9 degrees, since the Munsell Renotation System data has 40 Hues: 360 / 40 = 9).

Furthermore, as you compare colors of different Value, the rings should align, as should the radials.

See the Uniform Perceptual Lab page for an implementation of a color space with these perceptual properties.

## The "Blue Turns Purple" Problem

Many people have experienced the disappointment of printing an image, only to find that the rich blues seen on their monitor have turned purple on the print. The reason this occurs is explained here.

The problem starts with the observation that a typical full blue on a monitor simply cannot be reproduced on a printer. Since an accurate reproduction is physically impossible, a substitute color must be used in its place. It would be nice if this substitute color was the same apparent hue, although perhaps less saturated. A printer profile will typically choose the substitute color by selecting a color of similar hue angle, as measured in the CIE Lab color system. Unfortunately, the Lab color system is not perfect in its ability to match its hue angle with perceptual hue. This is easier to understand by looking at a picture:

Let's say our monitor displays the saturated blue color indicated as "Before" in the picture. Since this color is outside the color gamut of the printer, a typical profile will choose a substitute color along the same hue angle (i.e. moving towards the origin as shown by the red line) until a color is found that is within the color gamut of the printer (labeled "After"). We can see that doing this causes the visual Hue (of the Munsell system) to change from a blue (7.5 PB) to a purple (5.0 P).

A similar "Red Turns Orange" problem occurs for the same reason. This is left as an exercise for the reader, but you can see it if you select Value = 5, and observe the curved radials in the red region (10.0 R).