The key to this is using HSL (Hue, Saturation, Lightness) instead of rgb or hex. If you use HSL, you set the saturation/lightness of the colour and then use an expression to drive the "H" - the hue. The hue will then shift colour according to whatever you feed it. In this demo I just used the text of the div, you can use the array count or whatever magic number system you'd like.
Why not set your un-mouseovered colour to 15% Saturation of the element?
(Note : These are using HSL in pure CSS, so if you inspect the element it won't be converted to RGB like the rest of the Jquery elements)