Entering the twilight zone of pure speculation: humans experience color temperature as a banded gradient. It is fairly easy to demonstrate that the bands of the rainbow have no object reality, and yet we see seven or so fairly distinct bands. If color information is coded as neural firing rates, the bands could be heterodynes.
If we had more color receptors, we might experience more "primary" colors. Do you happen to know how how many rainbow colors are seen by colorblind people? I am a bit embarrassed asking this, because my son is red-green colorblind.
From what I understand, color perception involves the ratio between the stimulation of the photoreceptors, not the direct intensity of light reception of an individual receptor.
I could not tell you about what a rainbow would look like to a red-green colorblind individual. One experiment you could try to do is load a high color quality photo of a rainbow into some good image editing software and manipulate the redcs and greens so they are the same color. I used to have links to websites that simulate what a colorblind person sees.