Lightness and Brightness and Other Confusions

tions for mapping colours of light, visible to the average human, in a way that
allows their reliable scientific definition and comparison. Another starting
point for the work was Hermann Grassmann’s (1809–1877) three laws of
additive colour mixture. 81 This simple psychophysical law laid the ground for
the colour matching experiments involving three ‘primary lights’. As Fred
Billmayer and Max Saltzman say in their book Principles of Color Technology,
there is nothing magical about these monochromatic lights. The CIE
could have chosen any other set of colours, provided that they are sufficiently
wide apart in the spectrum. (Billmayer & Saltzman 1981, p 40; Kuehni 1983, p
73). 82 In fact there is no set of three primary colours with which it is possible
to mix all possible colours visible to the human eye. So, in order to derive a
system for describing all colours as perceived by humans that was based on
three primaries, negative values were assigned to some of the colours in the
equation. This led to the designation of the three ‘imaginary primaries’ X, Y
and Z. They became imaginary, because in the geometry of the CIE Yxy colour
space, for mathematical reasons, they had to be placed outside the gamut of
human colour vision.
The history of the CIE-colour spaces (there are several) is one of transformations,
technical compromises and abstractions. Therefore the so-called RGBprimaries,
which are very much a child of this enterprise, should be treated
with the same coolness as any other technological colour application. There
may be a set of three primary lights that excite the colour sensitive cones
maximally, but four or five would do it even better. The CIE 1931 Yxy colour
space should therefore not be regarded as a model of how the human colour
vision system functions. Neither should it be used as source for drawing conclusions
about how many and what are the primary colours – or at least not
outside the logic of the CIE system.
Grassmann’s First Law: Any colour can be matched by a linear combination of three
other colours, provided that none of those three could be matched by a combination of
the other two. Second Law: A mixture of any two colours can be matched by linearly
adding together the mixtures of any three other colours that individually match the two
source colours. Third Law: Colour matching persists at all luminances. This law fails at
very low light levels, where scotopic vision (rod-receptors) takes over from photopic
vision (cone receptors).
In this sense the primaries underlying the CIE 1931 Yxy space are somewhat like
ordnance survey points in triangulation: one could start anywhere and still end up with
an accurate measurement of the terrain.
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