I can't believe this idea hadn't been capitalized on yet!

As of now, the Thunderer BGM from Lahabrea/Twintania/Nabriales plays when you fight them. However, Ascians should have their own BGM that fits with their Ivalice summon/esper theme; they are important story bosses after all and SE has been on a roll with including old beloved themes in the game as of recently.

Well since they are derived from Ivalice summons, why don't they have a remix of the Esper Battle theme from FF12? There's already a version in Dissidia that would work quite well, but an original FF14 ARR rendition (ala Terra's theme for Magitek armor) would be a nice addition and a throwback to the Ivalice games (which, in my opinion, are pretty darn lacking in tributes, in FF14).