A colour wheel represents chroma on a radial axis from the centre, and hue by position around the wheel, but a third dimension representing lightness is necessary if all colours are to be represented. The simplest way to do this is to add this third axis at right angles to the colour wheel, creating a solid such as a sphere or a symmetrical double cone. [A cylinder would also be possible, but would not represent the visual convergence of colours as they approach black and white respectively]. The earliest illustration of a definite colour space of this type is the colour sphere of Otto Runge, published in 1810, and better known to many artists in the recycled version published ed by Johannes Itten (Figure 8.6). The idea of a double cone was used in the colour classification by Ostwald (Figure 8.7).

Figure 8.7 . Colour sphere of Johannes Itten.
Figure 8.8. Symmetrical double cone colour solid by Ostwald.

The problem with both the sphere and the symmetrical cone conceptions of colour space is that, as we have just seen, different hues reach their maximum chroma at different tonal levels.  Putting all of the pure colours on the equator of the solid ensures that the vertical dimension does not represent lightness. Consequently neither the Runge-Itten sphere nor the Ostwald double cone is a true hue-chroma-lightness space. If the vertical dimension of the solid is to represent lightness, then we need in some way to tilt the colour wheel through space, so that yellow occupies a high position opposite light grey and blue occupies a low position opposite dark grey.

This requirement can be satisfied most simply in a skewed double cone, a solution first suggested by Kirschman (1896) (Figure 8.9A). Arthur Pope (1922, 1931) described in detail an essentially similar double cone space, implicit in, though not actually illustrated in, the colour system of Denman Ross (Figure 8.9C). Both of these double cone solids are simple conceptual models in which chroma is normalized, so that they have a simple circular appearance in plan view. Following Ross, the Pope solid uses a hue circle based on the traditional artist's colour wheel, but analogous solids based on hue circles of psychological, additive or pigmentary complementaries could easily be visualized. A simple conceptual model of this sort is extremely valuable for many purposes of practical painting.

Figure 8.9. Representations of hue-chroma-lightness space by (A) Kirschman (1896) (flipped), (B) Munsell (1915), and (C) Pope (1922), and YCbCr spaces, all viewed from similar angles.

The Munsell system uses conceptually similar dimensions, but has a more complex form because it is a physical system showing the absolute variations of actual paint samples. The Munsell solid has an irregular, tree-like appearance, reflecting the fact that the maximum chroma manufactured paints varies markedly for different hues.

Figure 8.10. Two views of the Munsell colour space generated using a programme by John Kopplin (

Screen (RGB) colours have a more complex geometry for a largely different reason. Among full-chroma screen colours, the three secondaries are all lighter than their adjacent primaries: L = 98 for yellow, 60 for magenta and 91 for cyan, compared to 88 for green, 54 for red and 30 for blue. These differences can be accounted for by the fact that in the secondary colours, pixels of both the adjacent primaries are glowing. Magenta and cyan consequently disturb the steady fall in lightness from yellow to violet-blue on both sides of the hue circle (Figure 8.9D, 8.10).

Figure 8.11 . RGB colours arranged in YCbCr colour space, using the program RGB Cube by Philippe Colantoni.
Figure 8.12 . RGB colours arranged in Lab colour space, using the program RGB Cube by
Philippe Colantoni.

The same up and down movement might be expected in surface colours, but is hardly evident in artists paints because our pigments are so remote from ideal magenta and cyan (Figure 8.13).

Figure 8.13. Colours of about 100 coloured pigments from a Winsor and Newton colour chart (pdf version).

Please note that throughout this section I have been referring to all of these systems as colour spaces, because that is how I recommend that painters think of them - as three-dimensional spaces through which the artist manouvres. Arthur Pope in particular has demonstrated in detail how a simple geometric space such as his double cone model can make an excellent mental framework for visualizing and understanding colour relationships. In the context of serious colour science however the term colour space is restricted to quantitative systems that can be mathematically transformed, and that systems that fail to meet this criterion are referred to as colour models.


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Next: Part 9: Brightness and Saturation