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Johannes Itten's color sphere is described here. The description includes an English translation. Here is one of his drawings:

Color sphere of Johannes Itten

For reference, here is a vertical cross section of Albert H. Munsell's color sphere:

Color sphere of Albert H. Munsell

And here is a vertical cross section of Phillip Otto Runge's color sphere:

Color sphere of Phillip Otto Runge

Itten did not draw the inside of the sphere in mathematical detail. I am interested in what an interior vertical cross section might look like. How do you think Itten's sphere might have been structure internally? There are some odd sketches at the top-left, top-right and bottom-right of his drawing, but the precise mathematics is ambiguous.

Thanks!

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    It's not very useful to ask what we think, because Itten has published a book (in English =Art of Color) about his thoughts about color. You had a former case about Munsell. You found some Munsell's original documents which revealed his results. Munsell was a painter like Itten, but Munsell was also a systematic scientist who measured things. Ittem seems to have handled color intuitively and trying to find mystical relations. If you find his book, let us know.
    – user82991
    Aug 16, 2018 at 0:01
  • Thanks for the tip!!! "Art of Color" is available on Amazon. However, a PDF of "Itten: The Elements of Color" can be found easily, and it contains the info I needed, with very clear drawings.
    – posfan12
    Aug 16, 2018 at 3:00
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    Gongratulations again!. I haven't read that PDF before. A big part of the content is how Itten tried to create some order to subjective things. He had numerous geometrical and numerical relations in graphical presentations (sphere, circle) of colors. He writes that the found relations explain also subjective impressions and how seious artists have made their color decisions. It's of course possible. Consider "mystical relations" in my previous comment as an output of an average punter who hasn't got what's needed to build between one's ears some order to colors and their combinations.
    – user82991
    Aug 16, 2018 at 8:57
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    (continued) There's some things that surely at least some technocrates cannot accept, for ex. his photo test. An object was in neutral light. A green light beam was directed to the object. The shadow seemed to be red. It was seen also in a photo, which proved the red shadow to be real. His real was different than physical, measurable real.
    – user82991
    Aug 16, 2018 at 9:17
  • @user287001 human white balance has a tendency to do things like that.
    – joojaa
    Aug 22, 2018 at 3:54

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The reason why these guys that you ask about, dont describe the interiors all that well is that color does not actually work that way that they describe. Munsell did eventually realize this which is why the later iteration of munsell spaces aren't nice spheres.

But Itten is basically describing is a derivate of a double conic HCL colorspace. While contemporary people tend to draw the space with linear sides. This is just because they are mapping some sort of visual linearness. If you'd draw real lightness the result would be more drop shaped than that.

enter image description here

Image 1: Contemporary drawing, wikimedia commons.

Now even very bright whites can be colorful so thinking the shells as colorfulness out of center is what would happen. So for example you often see cyan in the sky just because they are very very bright deep blues just becasue human senses will flood over. Off course this neglects the fact that cyan can also be cyan, but also dark bule.*

All this spaces even exception of the really hard to understand and interpret CIE spaces, that dont really tell anything meaningful of the colors. Don't actually reflect well how light and human sensing really work. But are artistically easier to work with and so they do have some merits.

* if you go into 3d graphics, then you will be confronted by this fact when you try to make reflections match reality

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  • I know all this, thanks. I am only interested in the geometry of the historical document.
    – posfan12
    Aug 15, 2018 at 21:46
  • You do understand that then you must just rely on what Itten describes and live with what you think he does not describe @posfan12 asking us wont make you any happier since your scoping is unknown to us.
    – joojaa
    Aug 16, 2018 at 5:36
  • I never asked for an opinion or analysis of the subject, thanks.
    – posfan12
    Aug 21, 2018 at 22:14
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Thanks to @user287001, I found documents showing the inside of the sphere as looking similar to this:

enter image description here

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