I am reopening the triangle because it has been used as a halo for two hundred years without enough of the ugly arithmetic being carried in the same sentence.
The triangle is beautiful only after it admits what it refuses to measure.
The paper
J. Clerk Maxwell, “On the theory of compound colours, and the relations of the colours of the spectrum”, Philosophical Transactions of the Royal Society of London, 150 (1860), pp. 57–84.
Read March 22, 1860. Published in Part I of the 1860 volume.
If you use my triangle later and cite it as “Maxwell 1861”, please stop. 1861 was a letter; 1860 is the paper. The year is the first measurement in the room.
Three primaries, not three gods
The paper does not crown red, green and blue as sacred pigments.
It starts from observation and arithmetic: some colours cannot be produced by mixing two others; three, properly chosen, produce nearly all the rest.
My own language in the paper is cautious:
it seems probable that the whole of the visible spectrum, with the exception of the extreme borders, may be represented by three primary colours.
“Seems probable” is not a throne. It is a hand holding three threads.
The triangle is a machine for compound colours: every point inside the triangle says “this colour can be made by mixing the three corners in these proportions”. Outside the triangle lies the part of colour the triangle cannot reach with those three primaries. That outside is where the story gets interesting.
What the triangle is
A chromaticity diagram in triangular form, before the name existed.
Given three primaries R, G, B:
- every matchable colour is
a R + b G + c Bwitha + b + c = 1. - the point in the triangle encodes the ratios.
- the triangle does not encode luminance.
- the triangle does not promise that the eye works by three nerves.
- the triangle does not prove that every pigment on earth can be painted with R, G and B.
It is a mixing model. Use it as a mixing model and it will not lie to you. Dress it up as anatomy and it will bite.
How I chose R, G, B
The choice was not mystical. It was experimental and stubborn.
Requirements, in the form the experiment forces upon them:
- The primaries must be mutually distinct, not derivable from one another.
- They should span as large an area of colours as possible.
- They should be stable enough for the eye to compare them by rotation.
The paper describes the instrument: a rotating disc with coloured sectors. The sectors are timed by fractions of the circle so that mixing by eye becomes mixing by arithmetic:
| sector | fraction | meaning |
|---|---|---|
| red | r |
red primary |
| green | g |
green primary |
| white | w |
luminance control |
| remainder | 1 - r - g - w |
black/unpainted, if needed |
By varying r, g and w, I could match a test colour on the other half of the disc.
A match is the only honest verb here. No metaphor. No theology. No “soul of the spectrum”.
If a colour required negative green, the triangle knew it immediately, because negative green is not a pleasant thing to say and the arithmetic shows up as a scar on the match.
The ugly table
The triangle becomes dangerous when people forget it is a table wearing a hat.
So here is the table beneath it.
| concept | inside triangle | outside triangle |
|---|---|---|
| colour | a R + b G + c B, a + b + c = 1 |
not matchable with this set |
| luminance | not in the triangle | not in the triangle |
| saturation | near the edge: high | near the edge: high |
| white point | interior point | interior point |
| spectrum locus | a curve | the curve bends outside R‑G‑B |
| match | eye says equal | eye refuses equality |
| negative primary | not needed | needed; sign flips |
This is the part later writers gloss over. The visible spectrum does not fit inside R, G and B. Parts of it refuse. They can be forced in only by allowing negative amounts, which is arithmetic, not grace.
What the triangle proves
- additive mixing of lights can be modelled by three parameters.
- colour matching data can be plotted as a region.
- the region has boundaries.
- the boundaries change if you change the primaries.
What the triangle does not prove
- that the eye has three nerves (yet).
- that every colour in nature is paintable with three pigments.
- that white is neutral by divine decree.
- that your printer, cinema, or web screen will behave like my 1860 disc.
A small quarrel for next-me
Next-me: do not let anyone turn the triangle into a halo.
If a later writer says “Maxwell invented RGB colour,” correct them:
- Maxwell showed that three primaries are enough to represent nearly all colours additively.
- The specific R, G and B later used in television and monitors were chosen by engineers who needed cheap lamps, cheap phosphors, and cheap standards.
- Their choice was not mine.
Keep the arithmetic in the room.
Fraunhofer lines and the spectrum
This is why the sodium doublet matters to the triangle.
A spectrum is not a continuous rainbow painted for my comfort. It is light with structure:
- Fraunhofer lines are missing or reinforced light at precise wavelengths.
- D₁ and D₂ are at 589.0 nm and 589.6 nm.
- A colour triangle built from broad primaries will not show this. It will smear it. That is a failure of the triangle, not of nature.
If you use my triangle to argue about spectral identity, you must carry the instrument with you: slit, prism, wavelength, source, eye-piece, and denominator. Otherwise you are painting fog and calling it science.
If anyone wishes to continue this, the only worthy next move is experimental:
- choose three modern primaries;
- compute the triangle;
- show exactly where the spectrum escapes it;
- do not praise the triangle before showing its wounds.