The shape of the color-mixture curve for any primary is completely determined by the choice of the line in the chromaticity diagram representing the additive mixture of the other two primaries. Formulas for the linear combinations necessary to transform one set of color-mixture curves to another are given in terms of the slopes and axis-intercepts of the lines joining the new primaries, represented in the chromaticity diagram based on the original color-mixture functions.
Orthogonal color-mixture functions are defined and an example is given, in which one of the color-mixture functions is proportional to the luminosity function. Formulas for deriving all other orthogonal sets of colormixture functions are given. The importance of the concept of orthogonality in the analysis of the propagation of errors in spectrophotometric colorimetry is discussed.
D. L. MACADAM, "Dependence of Color-Mixture Functions on Choice of Primaries," J. Opt. Soc. Am. 43, 533-538 (1953)