If you convert the red-orange scheme to grayscale you'll see that both the ugly and nice schemes have the same value contrast. If you convert the green-blue scheme to grayscale you'll see that the ugly combination has more value contrast.
The author uses the Müller Formula to explain it, but I'm not convinced about the "follow the natural brightness" argument – does that explanation still make sense if you reorder the colors in the scheme?
I learned this stuff in color theory without this formula. It's simply this: combinations of colors with similar hues don't look good together.
Obviously the left scheme doesn't look great in that graphic because all the colors have the same value. But you can see that it looks better than a scheme with colors of similar hue.
You have the shittiest “convert to grayscale” I’ve ever seen: it doesn’t come close to preserving the value of the colors. Convert the image to Lab, and look at the L channel, and you will see that the “ugly” combinations have very little value contrast, while the “nice” ones have a great deal more.
Notice that in the bottom row, where we take the value from ugly and nice combinations and reverse them, the combinations with the “nice” choices of hue are now looking ugly as sin, while those with the “ugly” choices of hue no longer look so bad.
Also, in your second image, the green stripe on the left is quite a bit brighter than red or blue stripes, which is the dominant reason that the combination on the left looks “better”, while the three stripes on the right side are of quite similar value.
I didn’t really have the half hour to spend on this (paper due tomorrow; blargh), so hopefully someone finds it edifying.
(Edit: None of this is to say that there isn’t some real truth to the link’s author’s claims about commonly preferred color combinations based on hue. It’s just that the graphics he uses to demonstrate it [and also the one you made] are horribly misleading, and mostly reflect a completely unrelated effect)
----
Another edit to add: the hang-up may be that the “value” of the HSV model has almost nothing to do with the term “value” as used by artists or color scientists. So that may be the source of your confusion. HSL and HSV were designed for the 1970s and are nearly useless in an age of fast computers.
Your second edit nails it. I thought the brightness in HSB was equivalent to value, which is what I built my second graphic around. If you use my shitty grayscale converter (Desaturate in Photoshop) they all come out to the same gray, so I thought I had it right.
Using Black & White gets me results much closer to what you've made.
Thanks for criticizing my graphics and putting up improved ones. (The second one isn't working, but I understand your point about the green – again, Desaturate convinced me they were all the same value.)
It's really hard to isolate and demonstrate one property of color at a time.
Yep. It's true. Which is why it's annoying when posts like the article linked from the top of this thread attribute effects to one of those “properties” which are clearly mostly caused by another.
Anyway, I wasn't trying to be overly aggressive in calling your grayscale conversion “shitty”. Hope it didn't come across the wrong way. :)
More useful link: http://handprint.com/HP/WCL/color11.html