Colour samples and colour rendering of light sources

In the CIE method for specifying colour rendering properties of light sources, a rating is evaluated according to the average colour shift for eight colour samples. It is shown here that if a group of m colour samples contains n complementary pairs then the rating can, under certain conditions, be based on a weighted sum of colour shifts for only m - n samples, instead of the average for all m. The CIE group includes three approximately complementary pairs. If these are close enough in complementarity, then according to the above, it should be possible to base the rating on the shifts for only five instead of all eight samples. The outcome of computations for 58 light sources shows that for all practical purposes this is a valid assumption.