The Müller Formula or Predictable Color Preferences (2007)
colourlovers.com
colourlovers.com
Suffice it to say: unfortunately the lightness (a.k.a. value) of the color stripes varies tremendously from one example to the other in this post, which makes this a basically worthless comparison, as in general lightness contrast dominates other visual effects. If you swapped the lightness (e.g. in CIELAB or CIECAM02 color space) from the left and right examples while leaving the hue/chroma the same, you’d get the opposite results inre what looks “good”, which would reveal this “Müller formula” to be bogus (or at any rate radically oversimplified).
More generally, I’ve never seen a convincing exposition of similar color preference effects backed by data collected in a scientific paper with reasonable study design. It’s always handwavey 19th century nonsense, sometimes with a handful of preferences expressed by a tiny sample of homogenous survey respondents tacked on the end. Bad examples are endemic to the pseudosciency-color-theory genre, because most people work with terrible color models which are only marginally relevant to human perception.
The key to making color schemes for graphic illustrations or data visualizations look good is to use enough contrast (especially lightness contrast) between intentionally separate shapes so that distinct elements don’t accidentally blend together. (Note that sometimes you want certain elements to have lower contrast, but that should be an intentional choice, made for some obvious reason.)
http://www.hcs.harvard.edu/~jrus/ycnews/nonsense.png
http://www.hcs.harvard.edu/~jrus/ycnews/nonsense2.png
http://www.hcs.harvard.edu/~jrus/ycnews/nonsense3.png
Also, past discussions of this same example (apparently at different sites?):
https://news.ycombinator.com/item?id=156683
https://news.ycombinator.com/item?id=618881 (this one includes discussion context for the images linked above)
If the “Müller formula” worked the way the author of these example images thought, then the color combinations at the right side after my lightness switcharound should still be “good looking”, but to me at least, with low lightness contrast, they instead start to look very muddy. Likewise, in my opinion the color combinations at the left of each example are improved dramatically by the increase in lightness contrast, even though they still have low chroma contrast and aren’t exactly my favorites.
Currently we use I Want Hue (http://tools.medialab.sciences-po.fr/iwanthue/) which works far better then it should :).