That's very cool: DARPA is sponsoring a research on the intelligent software that can play jazz. The article explains the reason for that, but to me it looks more like a smart PR move to attract public attention. The computer writing stories would sound much more feasible, because it involves tracking several characters, their motivations, events, consequences, predicting responses etc. And the application, aside military purposes, could be quite fancy as well (and lucrative!): making an engine to control NPCs in RPGs and create new quests/substory plots. Many companies have claimed that they have a special engine for this, but in reality the implementation is usually very heavily scripted without much improvization.
Or it could be computer that draws pictures, which also requires improvization. HyperNEAT can do that :) And its predecessor was even used in a simulation computer game to command shooting bots.