4.5 Color bias fails as a concept

The split-primary palette explains itself with the idea of color bias. Every paint is said to lean toward one of its neighbors on the wheel, a blue toward green or toward violet, a red toward orange or toward violet, a yellow toward green or toward orange, and the lean is supposed to decide its mixtures: a blue that leans toward green should make clean greens and dull violets. Section 3.8 tested the palette’s six paints and some of their relatives two at a time, and found the rule right for the six and wrong for several of the others. Here the idea itself is put to the test, on every calibrated blue, red and yellow at once.

For each paint the lean is the hue of its tint, the paint with enough white to bring it to a middle lightness, since a dark masstone hides its hue (Section 4.9). Each paint is then mixed in every proportion with a fixed partner, a yellow for the greens for example, and the chroma of the mixture that lands on a chosen green, orange or violet is recorded; the partners and the target colors are listed in the math box at the end of this lesson. Figure 31 plots the lean against the chroma. If the lean decided the mixtures, the points for each family would climb or fall in a line.

Figure 31: The lean of a paint against its mixtures, for the calibrated blues (a), reds (b) and yellows (c)

Figure 31. The lean of a paint against its mixtures, for the calibrated blues (a), reds (b) and yellows (c). Payne’s gray, which is nearly black, and burnt sienna, an orange between the reds and the yellows, are left out. Across: the hue of each paint’s tint at a lightness of 60 (or of its masstone, for the yellows lighter than that), which is its lean. Up: the chroma of the best mixture it makes with a fixed partner at a fixed hue and lightness, with filled circles for one secondary and open squares for the other. The numbers identify the paints in the keys below.

Only the yellows come close. Apart from the two earth yellows, their greens with phthalo blue fall and their oranges with pyrrole red rise as the lean moves from green toward orange, and Section 3.8 showed why: a yellow’s reflectance is a single edge, and where the edge falls sets both its hue and its greens. The blues follow the lean only roughly, with large differences between blues of nearly the same hue and almost none in their violets. The reds hardly follow it at all, although with five reds that test is thin. Each failure comes from something the lean leaves out, as the tests of Part 3 showed.

A lean is one number, the hue, and a mixture depends on a whole curve. A mixture of two paints of different hues, such as a green from a yellow and a blue, is vivid in proportion to what both reflect in the band of wavelengths that gives the mixture its hue. A blue’s hue is set largely by the balance between its blue reflectance and the tail it has into the red, which pulls it toward violet. Its greens are set by how much green light it reflects, which is a separate matter. Cobalt blue leans toward violet because of that red tail, and the tail has nothing to do with how much green it reflects, which is what decides its greens.

A rule that works for yellows, roughly for blues and not for reds is a correlation, one that holds when a pigment’s reflectance happens to be a single edge. The better guide is to read the curve, or, lacking the curve, read the paint’s lightness and chroma as well as its hue, and expect the middle of the spectrum to dominate any mixture across the circle [15].

The bias test. The lean of each paint is the hue angle of its tint at \({L^{*}} = 60\), or of its masstone for the yellows lighter than that: a blue whose tint leans toward green has a hue nearer \(200^{\circ}\), one that leans toward violet nearer \(280^{\circ}\). Each paint is mixed with a fixed partner in 201 proportions by weight, as in Section 3.8, each mixture is brought to a fixed lightness with white, and the chroma is recorded for the proportion whose hue comes closest to a target hue, if it comes within five degrees. The partners and targets are hansa yellow medium for the blues’ greens (\(155^{\circ}\), \({L^{*}} = 60\)) and the reds’ oranges (\(58^{\circ}\), \({L^{*}} = 65\)); quinacridone magenta for the blues’ violets (\(315^{\circ}\), \({L^{*}} = 45\)); ultramarine for the reds’ violets (\(315^{\circ}\), \({L^{*}} = 45\)); phthalo blue for the yellows’ greens (\(155^{\circ}\), \({L^{*}} = 60\)); and pyrrole red for the yellows’ oranges (\(58^{\circ}\), \({L^{*}} = 65\)). For the blues, the greens are 21 to 25 for four of the five, from ultramarine at a hue of \(282^{\circ}\) to cerulean blue at \(257^{\circ}\), and rise to 42 for phthalo blue at \(250^{\circ}\). Cerulean gives 25 and phthalo blue, eight degrees away, 42: a difference of 17 units. The violets run from 41 for cobalt blue and 40 for ultramarine down to 37 for phthalo blue, a fall of 4 units across the whole range of blues. For the reds, the oranges are 35 for red oxide at \(27^{\circ}\), 64 for pyrrole red at \(14^{\circ}\), 65 for naphthol red medium at \(2^{\circ}\), 46 for quinacridone crimson at \(-3^{\circ}\) and 52 for quinacridone magenta at \(-18^{\circ}\). The violets with ultramarine are 8 for red oxide, 15 for pyrrole red, 24 for naphthol red, 19 for quinacridone crimson and 40 for quinacridone magenta. For the yellows, the greens with phthalo blue fall from 49 for green gold at \(104^{\circ}\) to 21 for diarylide yellow at \(72^{\circ}\), and the oranges with pyrrole red rise from 40 to 76 over the same range, with the two earth yellows as the outliers at 37 and 31. By equation (21) the mixture in each band has a \(K/S\) between the parents’, and a secondary is chromatic in proportion to what both parents reflect in the band that makes the secondary’s hue. Cerulean and phthalo blue make different greens because phthalo reflects far more at \(490\) to \(520\,\mathrm{nm}\) relative to its own total and is a far stronger and more chromatic paint.

Sources

[15] Color Nerd, Split-primary palettes miss this paint mixing insight, Color Wheel Wednesday, episode 29, video, 7 October 2026, https://www.youtube.com/watch?v=R0JkjnerdOw.

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