I'd be interested to see how these convex structures relate to neural patterns... I'm sure these shapes some how mathematically can be traced back to the structure of the neural connection patterns that are fired when we hear these scales.

This idea of scales being the basic patterns that music is based on also reminds of color schemes - scales seem to be to hearing as color schemes are to vision.

Ha put that together and... web app idea! A scale generator for musicians just like the color scheme generators that we have for web designers. :P