A new theoretical color order system is proposed on the basis of various studies on color appearance and color vision. It has three orthogonal opponent-colors axes and an improved chromatic strength of each hue. The system has color attributes whiteness w, blackness bk, grayness gr, chroma C, and hue H. A method is given for determining Munsell notations of any colors on any equihue planes in the system. A method is also given for determining grayness regions and grayness values on huechroma planes in the system. It is concluded that colors with the same color attributes [w, gr, bk, C] but with different hues in the theoretical space have approximately the same perceived lightness, the same degree of vividness ("azay-akasa" in Japanese), and also the same color tone. The tone concept, for example used in the Practical Color Coordinate System (PCCS), is clarified perceptually. The proposed system is a basic and latent color-order system to PCCS. In addition, the concept of veiling grayness by a pure color with any hue is introduced. Further, relationships are clarified between generalized chroma c(gen) and grayness. (C) 2004 Wiley Periodicals, Inc.