So it turns out that Fugue has the same battle effect as Djinnfest. In other words, it will put one djinn in recovery per target! This is utterly pointless in the main game because enemies don't actually carry djinn around with them, but it could have potential in linked battles depending on your setup. And before anyone asks, it isn't because of the animation although leaf and I were both pretty shocked that this had never been discovered sooner for that and other reasons.
(http://i.imgur.com/fRvgYJb.png)
Feel free to discuss!