For instance if I had these two 'color schemes':
http://beta.dailycolorscheme.com/archive/2006/09/20
http://beta.dailycolorscheme.com/archive/2006/09/19
Do you have any pointers or ideas for this problem, HN? Thank you!
So, start with the color sphere: a unit sphere, and each point in the volume represents a color. Around the equater is arranged the hues, roygbiv. Moving north or south changes value, by adding white or black, respectively. Moving inwards toward the north-south axis reduces saturation; the exact center of the sphere is a perfectly neutral 50% gray.
Traditionally a set of colors is supposed to be 'harmonious' together if, when one constructs a polyhedron inside the color sphere, with each vertex being one of the chosen colors, the polytope formed has it's center of balance at the center of the sphere.
That is a 'designer' set of colors --- emotionally flat but visually pleasing. Emotional content is added by moving the centroid off center, charging the whole color set with a color 'cast'.
This definition, of course, fails when monochromatic schemes are chosen, but monochromatic schemes are almost always highly emotional unless a suitable accent color is chosen (usually a complementary, so as to move the COB to the center of the sphere).
For more information, read Itten, Keely, Albers, &c.
Then there's the issue of print versus the web. In print, you can call a color neutral because it reflects light which is the same color as the illuminant. I'm skeptical about "neutral gray" on a website, viewed in a variety of different environments with a variety of different backlights. Fill your screen with pure white, look at it on a sunny day and then again late at night. You'll find it's shifted from a yellowish white to a bluish white.
I'm also skeptical about a mathematical formula for "emotionally flat colors". It seems I could choose a bright red, yellow, and blue and get them to center on neutral gray, and use that for my american hot dog stand. Then I could take a few shades of black and white, centered on neutral gray again, and use them to paint the corporate office. Neither seems emotionally flat to me.
Re: how do we know? Well, mostly this system is based on the work of a number of thinkers, starting with Goethe and running through Munsell, Itten, Kandinsky, and a bunch of others, who spent a great deal of time putting colored squares next to each other. They discovered physiological effects of color, like simultaneous contrast. They attempted to learn about psychological effects of color. They admitted that, while some color combinations are attractive only to individuals, there were other sets that seem to have universal appeal. One of the things that those universal combinations had in common was that they centered themselves on the color wheel.
We know, more or less, by science. It is a largely empirical question (put some colors together, see if people like it). You can repeat the experiments yourself, if you like --- you asked 'how can we know'? Either take their word, or try it yourself.
And finally, in reply to the my use of the word 'emotional' --- if I were to say that colors whose center of balance is far from the center axis of the sphere are more surprising, and less comfortable, is that acceptable? I don't mean to say that red and green don't evoke different emotions than yellow and purple --- but they are both comfortable, obvious, familiar combinations; while, say, magenta and brown is less comfortable and takes more work to accept.
Or just make a site that claims to, and then you have somewhere you can post your color schemes every time you need to test one.
http://en.wikipedia.org/wiki/Color_theory
Another challenge is what is it you want to achieve? Do you want people to say "ah, nice", or do you want them to "react" (click something for instance). Those two may be mutually exclusive in some instances, as generations of neon signage, "sales" banners and similar are living proof of.
It's been quite a few years for me since I took color theory in college for my art degree. I think that you can automate color compliments with 2, 3, 4, or x colors by using "vectors" to compute the opposite hues... cutting the HSV model in halves for two colors, thirds for three, etc.
To get to the aesthetics, you'll have to use voting or surveys, and the reason is somewhat straightforward. Here are a few resons (not all):
The appeal of colors change over time with fashion and trends. In the US, mint green and canary yellow in the 1930s, white and cherry red in the 1940s, the list goes on for consumer goods and their colors. Think of vintage goods and their colors. Pantone produces color forecasts and tweaks their colors over time to reflect tastes.
Cultural differences. Color symbolism plays a large role - after all part of a designer's skill is selecting the right color for the specific context of an assignment. White for mourning in Asia != white for a wedding. One thought is that the region or location may be significant in the aesthetic judgment. If I remember correctly, the ArthurAnderson logo was orange because it was a color that could be used globally without negative meaning.
One last note, which comes from my training in a modernist driven school, is the form and the function of a design in black and while should be rock solid and work before adding color and the complexity... I think this was taught so that the novice students we were would learn the basics of typography, form, and balance before getting into colors.
As to the aesthetics: You can use the voting model like colorlovers (I hope that older votes are when tracking current color trends), use A/B testing if you are a web designer, or fall back to a company like Pantone to help you find current trends. Someone like google might be able to tie click paths to color schemes ... in other words data mine to establish what is a trend.
I'd suggest you put your candidates up on http://www.colourlovers.com/ and have them vote.
Every situation is different. A color palette like on kuler or colorlovers doesn't represent the real environment those colors will be found in. It doesn't include amounts, gradations and lighting, all things our brains evolved to process. For example we need to compensate for changes in lighting on a forest with fruits, because we'll be there at different times of day.
You could develop an objective aesthetic rating for a domain like picking fruits, based on what time of day should you pick a fruit to get the best taste, nutritional content.
Giving arbitrary ratings to color palettes has already been done on kuler and by color theorists, but when the reasons behind the ratings are not understood, you might as well use a neural net to replicate those ratings, using the palettes and ratings as training data. Black box either way.