Color scales that are effective in both color and grayscale

We consider the problem of finding a color scale which performs well when converted to a grayscale. We assume that each color is converted to a shade of gray with the same intensity as the color. We also assume that the color scales have a linear variation of intensity and hue, and find scales which maximize the average chroma (or “colorfulness”) of the colors. We find two classes of solutions, which traverse the color wheel in opposite directions. The two classes of scales start with hues near cyan and red. The average chroma of the scales are 65-77% those of the pure colors.