If your idea is to match human perception of some small variation, note that most human perception (any sense except smell) will be logarithmic - so not only taking the square root of the arithmetic mean of the sum of the squares (rms,

https://en.wikipedia.org/wiki/Root_mean_square), but taking some kind of logarithm of that, might be worth trying.(b) added 3o points from G (157 & 97)

Yes, my objective is to try to approximate how a human (with good vision) would rank order the shades of a color.

After I implemented an RMS metric, I noticed that it is smaller that the Sum Squares in every case, but they are in the same order. So I took the ratio. The RMS metric is exactly 57.735% of the Sum Squares metric. That makes sense since the RMS is the square root of the sum of the squares of the three differences divided by 3, whereas the Sum Squares is that same thing, but without dividing by 3. So the ration is 1/sqrt(3) = .57735....

If this is for an AI learning program to match human visual perception in general - a bot that sees as humans see -

Naw, I'm not nearly smart enough to do that.

you will need to include specific information about the position on the frequency spectrum.

Isn't that what the RGB values are? A color with RGB values of 000 127 255 would have 0% red, 50% green, and 100% blue.

Small differences toward the red end will not register the same as small differences in the middle or toward blue

I took the (000 127 255) color and (a) added 30 points to R (30), (b) added 3o points to G (157), (c) subtracted 3o points from G (97), and (d) subtracted 30 points from B (225). Of the 4 results, I could just barely see the difference in the R & G values (near the end of the spectrum), but both changes in G were easily visible. So, as you say, it appears that changes in the middle are perceived as greater than those at the ends for the same absolute change.

I think that this means that any logarithms will need to be two-tailed.

(the R, B, and G will need separate transformation before total sum or rms calculation).

Yes, because they will be at different points on the spectrum (closer to one end or the other and closer or farther from the middle).

None of that is "the accepted way" of doing anything, afaik.

For my purposes,