Some modifications are made to the achromatic color perceptions in Hering's opponent-colors theory. They are the introduction of the reference color Gray and the use of the orthogonal coordinate system. The modified opponent-colors theory has a symmetrical structure for the three opponent-colors axes, whiteness-grayness-blackness, redness-grayness-greenness, and yellowness-grayness-blueness, and it unifies the Hunt and the Stevens and Jameson-Hurvich effects. It is also noted that two kinds of color-appearance spaces exist. One is the color-appearance space derived from color perceptions of object colors (called the CPS color-appearance space). The other is that modeled from their colorimetric values for predicting color perceptions (called the UCS color-appearance space). The CPS color-appearance space is mainly described in this article. Scaling of the CPS color-appearance space and the existence of the reference color perception Gray are discussed in detail.