Dynamic music possible in future?

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This already exists to a degree. Many raids and trials change the music as they shift through the various phases, most notably becoming more amped up for later phases.

I don't like music shifting around like that. I'd rather just listen to one consistent version of the song than have bits of it fading in and out all the time.

They already shift between "in battle" and "out of battle" versions of music, and that's enough for me.

I think a boss designed around the music would be cool, each skill adding to the music, tempo and mood to the situation- a creative exercise for the battle and sound team. In general, not sure... sometimes changes can be grating.. like entering FATE rings because of the sounds that come along with it. So I'd be worried if it wasn't done spectacularly well and then also prolifically present in all content lol.

A bunch of Alliance raids already have music that changes between Normal and Battle, but are essentially just other versions of the same song. I don't mind the idea of changes for the amount of party members alive, but that'd take a LOT of time and effort for something pretty unnecessary when you probably wanna be succeeding, not having most of your party dead. :P

this pretty much only exists in King Moggle Mog fight.

They do to an extent, but it would probably be harder to sync up modal music to very specific things with latency taken into account.

It can get extremely messy in very busy fights and technically is very challenging. You've already listed two conditions: party health and boss attack intensity. Mixing the two can be frustrating and lead to inconsistent results with music that is quite bad to hear to if not directly confusing. There are cases where the music dynamically changes but they are based on distinct things like boss phases. Dynamic music is nothing new in terms of software development but as with everything, if you overdo it it can lead to a huge mess that will probably make people turn off music entirely.