A while back I wrote a small package in Javascript for computing area proportional Venn and Euler diagrams: https://github.com/benfred/venn.js . The 2 circle case here is relatively easy, but the problem gets tricky when you have 3+ sets. I wrote up my approach here https://www.benfrederickson.com/venn-diagrams-with-d3.js/ and https://www.benfrederickson.com/better-venn-diagrams/
In the music example, it has to give up on rendering all intersections since the layout isn't feasible with area-proportional circles - is there anything else that could be done? Is it possible to use ellipses or curved-shapes instead?
But then I guess searching for a solution could become too computationally expensive for client-side JS.
Venn/Euler diagrams don't work all that well past 3 sets, not all areas will be shown if using circles - so unless some of the sets are disjoint it will be a misleading diagram (like in the music example). However, I think it works well for 3 set diagams, I have an interactive example on last.fm data here https://www.benfrederickson.com/distance-metrics/ in the context of explaining some simple distance metrics.
I thought it was pretty neat