There are some interesting parallels between the CoF and the color wheel, the most obvious of which is that pitches opposite each other anywhere on the CoF are the most dissonant when juxtaposed against each other - similar to complimentary colors opposite each other on the color wheel. (Think orange and blue). Besides that invariant, the tones are permuted in the CoF a bit, which differentiates it from the standard 12-color wheel, which keeps neighboring tones together.

I wonder if one permuted the color wheel to be more like the CoF if it would make the basis of an interesting music visualizer, such that the harmonic relationships between tones correspond to the harmonic relationships to colors shown.

Here's an old visualizer that attempted something like this, but they didn't permute the color wheel in the manner I'm suggesting: http://www.musanim.com/mam/circle.html