<p>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.</p>

<p>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.</p>

<p><a href="https://i.sstatic.net/COa4K.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/COa4K.png" alt="enter image description here"></a></p>

<p><strong>Image 1</strong>: Visible specturm on the edge, interpolations on surface. </p>

<p>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.</p>

<p>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.</p>

CC BY-SA 3.0
2015-09-13T07:36:40.457Z
2015-09-13T11:52:18.847Z
2015-09-13T11:52:18.847Z
joojaa
<p>There are two aspects to this:</p>

<ol>
<li><p>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.</p></li>
<li><p>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.</p></li>
</ol>

<p>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.</p>

CC BY-SA 3.0
2015-08-13T21:23:10.087Z
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
joojaa
CC BY-SA 3.0
2015-08-13T21:08:56.523Z
2015-08-13T21:08:56.523Z
Mark
<p>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.</p>

<p><img src="https://i.sstatic.net/pfP8P.png" alt="enter image description here"></p>

<p><strong>Image 1</strong>: A sample CIE31 chromaticity graph showing the spaces*.</p>

<p>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?</p>

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

CC BY-SA 3.0
2015-08-13T19:54:53.377Z
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)
RichieSams
CC BY-SA 3.0
2015-08-13T20:37:18.053Z
@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.
joojaa
CC BY-SA 3.0
2015-08-13T21:06:05.027Z
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.
joojaa
CC BY-SA 3.0
2015-08-13T21:23:33.710Z
Yea, that makes sense, now that I think about it. Black isn't a color. It's the absence of color.
RichieSams
<color><color-management><color-science>
Why is the CMYK space four sided in chromaticity charts
joojaa
# Why is the CMYK space four sided in chromaticity charts

(Asked by: username_0 on 2015-08-13)

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.

![enter image description here](https://i.sstatic.net/pfP8P.png)

**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.

**Tags:** color, color-management, color-science

> **Comments:**
> **username_1**: 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)  
> **username_0**: @username_1 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.  
> **username_0**: 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.  
> **username_1**: Yea, that makes sense, now that I think about it. Black isn't a color. It's the absence of color.  

---

## 2 answers

### Answer by username_0 on 2015-09-13. Score: 2 | Accepted answer

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.

[![enter image description here](https://i.sstatic.net/COa4K.png)](https://i.sstatic.net/COa4K.png)

**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.


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### Answer by username_2 on 2015-08-13. Score: 3

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.

> **Comments:**
> **username_0**: 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  

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