# Why is the CMYK space four sided in chromaticity charts

In chromaticity charts the CMYK color space is usually four-sided. I've lately had to read quite a few charts and it suddenly dawned to me that I don't really understand why. It has just not been something I've needed to think about until now.

Image 1: A sample CIE31 chromaticity graph showing the spaces*.

One of my working hypotheses is that it is actually a triangle. This triangle just clips for some reason. But there might be other reasons such as non-ideality of the color primaries, or bad plane. So why is it squarish?

* This image is not so clearly a polygon, like it's usually depicted as, but it's the best one I had at hand.

• Perhaps because CMYK has 4 components? RGB is a triangle, where each corner represents one of the components. So, it would makes sense that CMYK would be a 4 sided shape, since there are 4 components (Cyan, Magenta, Yellow, Black) Aug 13, 2015 at 19:54
• @RichieSams yes, thats what i used to tgink. but black is absense of luminance the luminance is on a axis thats perpendicular on your screen. So black should be away from your viewing direction. Aug 13, 2015 at 20:37
• Ok, i think i know why... i need to check this from the media department. But ill leave this question for a while so others have time to answer the question. Its definitely not the K component. Aug 13, 2015 at 21:06
• Yea, that makes sense, now that I think about it. Black isn't a color. It's the absence of color. Aug 13, 2015 at 21:23

There are two aspects to this:

1. The traditional chromaticity graph is actually a two-dimensional slice of a three-dimensional volume. The slice usually used is one that matches up (more or less) to the fully-saturated primaries of an RGB-based colorspace; the full RGB colorspace is a tetrahedron.

2. CMYK is a four-primary colorspace, with primaries that are not linearly independent. This makes the full volume a complex shape. Further, at least one (black) and possibly all four of the primaries don't lie on the plane of the 2D chromaticity graph.

The CMYK space is four-sided because it's a 2D slice of a complex 3D shape that (probably) doesn't lie on any of the surfaces of that shape.

• Actually i think its clipped that way for the same reason that the cromaticity graphs outer edge abruptly changes direction. The space model is not entirely trivial but yes your right the space shape is complex. And its volume cant be drawn because my fogra measurements in the icc profile dont work all the way.+1 Aug 13, 2015 at 21:23

It turns out that the chromaticity chart is harder to read than I anticipated. The CMYK slice is actually triangular of sorts its just that the chromaticity chart is not really linear.

The chromaticity chart is made with the assumption that light is a spectra. The curved arc is the pure spectral color of the rainbow. Everything in between is interpolated edge values.

Image 1: Visible specturm on the edge, interpolations on surface.

Now magentas are a bit peculiar. They only exist in our brains interpretation, thus they can not be measured. Magentas are sort of virtual colors that make the color circle full. This means that when you move from absence of blue towards absence of green your line kinks since the graph has no well defined direction for magenta's. This makes a 4th corner where none should be located.

Magentas are thus a bit of virtual colors that only exist in our brain. Not in physics, they are 2 spectra interleaved. There are off course many such metamers.