system
Given the following post, respond as if you're commenting on Reddit:
human
Why is our perception of color cyclical, and is it also cyclical for bichromats and tetrachromats? 

I'm a visual artist, and thus spend a lot of time pondering color perception.

What I'm wondering is... is there a physiological/neurological explanation for why we have a color wheel? Seeing as color is based on the wavelength of light, it seems like our perception of color should be linear, like our perception of sound pitch, yet for some reason we perceive violet as blending smoothly back to red on the other end of the spectrum.

I'm guessing it has something to do with the way the brain has to kind of do some guesswork to determine color in the first place, gauging by the intensity of the activation of cones.

And moreover, do partially colorblind people, with only two sets of cones instead of three, see their limited color spectrum in the same way?  Do tetrachromatic animals, that see mostly the same spectrum we do, plus the infrared or ultraviolet, also perceive color cyclically?  Might they perhaps be able to arrange colors in an even more complicated looping format?  (Say one pigment activates the ultraviolet cones and the blue cones, making the equivalent of fuscia for humans.  What if a pigment activates the red cones and the blue cones, skipping the green?)

I realize there's not exactly a way to test how truly tetrachromatic animals see, but I'm curious how far the theory might be able to predict.

**EDIT:**  Okay, so that wikipedia article on Magenta has helped me articulate my last question a little better.
So apparently magenta is an "extra-spectral" color because it can only be generated by a combination of two wavelengths.

So, say we have a tetrachromat that has cones corresponding roughly to the human's red, green, and blue cones, with a fourth set of cones off in the ultraviolet range.  This, presumably, would mean that their vision has four primary colors, rather than the three primary colors our vision has, right?  What I'm really curious about is, can we tell if they could see two/three extra-spectral colors since there are more possible wavelength gaps?  If something activates their blue and red cones, do they see magenta (or would they just see green)?  If something activates their green and ultraviolet cones, do they see some other extra not-blue, not-violet color that we can't (Octarine!)?  Presumably they see at least one extra-spectral color when something activates their ultraviolet and red cones.   Is this more dependent on their brain structure than on their eye structure?

**EDIT 2:**  I just had the wild idea to look up the wiki article for Violet.
>Spectral-violet looks like purple-violet for the human eye because L-cones have a secondary response in high-frequency blue

L-cones being the red sensing cones.  I haven't found any more info than that, but this article suggests that violet and magenta "blend together" because both colors are caused by activation of the blue cones and red cones.
gpt
It's cyclical because some sections of the wheel don't correspond to a single frequency. What we call "magenta" is a blend of frequencies at the lower and upper ends of the visible range, and the existence of this "non-existent color" bridges the gap, forming a wheel.