Convex chords

I was just now looking at Honingh and Bod's paper "The Notion of
Convexity in Music", which can be found here:

http://staff.science.uva.nl/~ahoningh/research

It it I found an interesting suggestion, which is that we might be
able to use convexity as one way of filtering out the interesting
p-limit chords. One might ask questions, such as whether it is
possible for there to be a non-convex ASS, or whether a non-convex
chord can be found with no really good convex alternative.