This is very detailed and chock full of great visualizations, but I still can't figure out how harmony search is fundamentally different than your run-of-the-mill genetic algorithm. What am I missing?
It's not different. Both are random search algorithms packaged in a (somewhat complex) human abstraction. The convergence properties are the same as for other search algorithms using meta heuristics, including the classic simulated annealing algorithm.
It looks to me like a GA that can mix and match chromosomes from a set of fit candidates instead of just mutating them individually. In other words, sex.