Primary Colours

Question

(a)

red

yellow

blue

(b)

magenta

yellow

cyan

(c)

red

green

blue

(d)

extreme red

psychedelic aquamarine

extreme purple

Answer

Later on you learned that those are “subtractive” primaries, good when colours are produced by subtracting light, as in printing, or when mixing colours from a paintbox. You further learned that a better set of subtractive primaries is

(b)

magenta

yellow

cyan

.

You also learned that there are “additive” primaries, good when colours are produced by adding light, as in TVs and computer monitors,

(c)

red

green

blue

.

The magenta-yellow-cyan and red-green-blue primaries are good in the sense that their combinations yield a wide range of colours from only three primaries. However, as seen on the chromaticity diagram on the  Where's purple? page, three primaries can produce only colours within their gamut, leaving many colours, such as disco purple, beyond the pale.

Suppose that you could, by some magic, tickle each of the three types of cone in your eye individually, or in any proportion, at will. Clearly you could produce any possible colour — along with some impossible colours — by tickling your cones in the appropriate combination. As discussed immediately below, the colours that correspond to tickling each cone separately are the cone primaries, or fundamental primaries,

(d)

extreme red

psychedelic aquamarine

extreme purple

.

It should be emphasized that the colours you actually perceive are coloured by processing in the brain, and do not depend simply on how much each cone type is tickled. The complicated wiring that converts what you see on your retina to what you get in your brain is traced for example in the lucid text by D. Falk, D. Brill & D. Stork (1986) “Seeing the Light”.

The Fundamental Primaries

Just as any colour can be characterized by its CIE \(X\), \(Y\), \(Z\) coordinates, so also can any colour be characterized by its \(L\), \(M\), \(S\) coordinates. The \(L\) coordinate of a spectral distribution \(P_\lambda\) of light power is an integral of the power over the sensitivity \(L_\lambda\) graphed at right, \(L \equiv \int L_\lambda P_\lambda d \lambda\). The \(M\) and \(S\) coordinates are defined similarly.

Stockman et al. normalize the cone sensitivities to one at their peaks, as graphed. With this normalization, an equal energy white spectrum, \(P_\lambda =\) constant, of unit luminance corresponds to \begin{equation} \label{eq1} L_\textrm{eq} = 1.051 \ , \quad M_\textrm{eq} = 0.873 \ , \quad S_\textrm{eq} = 0.508 \ . \end{equation} The three numbers in equation (\(\ref{eq1})\) are in proportion to the areas under the corresponding sensitivity curves. Unit luminance means \(\int V_\lambda P_\lambda d \lambda = 1\), where \(V_\lambda\) is the photopic luminosity function. The luminosity function used here is the 2-degree \(V^\ast(\lambda)\) from A. Stockman & L. T. Sharpe (2000 Vision Research, 40, 1711) available at the CVRL database.

The \(LMS\) sensitivities could be normalized in other ways. For example, the 1931 CIE \(XYZ\) functions are normalized so that equal energy white of unit luminance corresponds to \(X_\textrm{eq} = Y_\textrm{eq} = Z_\textrm{eq} = 1\). One might consider normalizing the \(LMS\) primaries similarly, so that equal energy white of unit luminance would correspond to \(L_\textrm{eq} = M_\textrm{eq} = S_\textrm{eq} = 1\). However, the resulting equal energy white point in the \(lm\) chromaticity diagram (see immediately below), at \(l_\textrm{eq} = m_\textrm{eq} = 1/3\), would be too close to the monochromatic boundary to offer a balanced palette of colours. Stockman et al.'s normalization locates the equal energy white point somewhat more judiciously in the \(lm\) chromaticity diagram.

The white point in this chromaticity diagram has been taken at equal energy white, equation (1), with \(lm\) chromaticity coordinates \begin{equation} \label{eq3} l_\textrm{eq} = 0.432 \ , \quad m_\textrm{eq} = 0.359 \ . \end{equation}

The three fundamental primaries lie at three corners of the chromaticity diagram. These are the colours I call extreme red, psychedelic aquamarine, and extreme purple, at \((l,m ) = (1,0 )\), \((0,1)\), and \((0,0)\) respectively. Maybe extreme purple should be called extreme violet. But violet whispers pale, while purple shouts vibrant, clearly a sounder choice.

What do the fundamental primary colours look like? All of them lie outside the range of colours that can be produced by ordinary light, so you have to stretch your imagination. Extreme red and extreme purple lie close to crimson red and disco purple, the colours of monochromatic light at the longest \(\lambda \geq 700 \textrm{ nm}\) and shortest \(\lambda \leq 425 \textrm{ nm}\) wavelengths. So perhaps those are not too much of a stretch.

The colour of the green fundamental, at (\(l\), \(m\)) = (0, 1), is quite another trip. I call it psychedelic aquamarine because it lies well outside the range of physically realizable colours, at least for people with normal three colour vision. The nearest monochromatic colour, obtained by adding white to psychedelic aquamarine, is around 497 nm, about the colour of the water around the reefs of Heron Island in the Great Barrier Reef of Australia, which I had the privelege of visiting in 1995. You should mentally subtract white to imagine psychedelic aquamarine in its vivid primal hue.

In the brainless theory of colour, people who are red colour-blind (protanopic) should see psychedelic aquamarine at the longest wavelengths. In reality, however, the colours people actually perceive depend not only on the relative stimulation of the different cone types, but also on processing by the brain. Next time you meet a protanope, ask him (1% of males are red colour-blind, but only 0.02% of females) what he sees when he sees red.