Every system falls short. This is a music theory post.
That was the lesson of Kurt Gödel, whose Incompleteness Theorem proved that every possible mathematical system will fall short of perfection. (Either it will prove untrue things or it will leave true things unproven.)
In my experience, it’s just as true of musical theoretical systems. My beloved jazz theory works well in many contexts, but it fails to label some things and has some necessary inconsistencies that can’t be overcome, at least in any system I know. Other theoretical frameworks work well in other contexts but still fall short. They might fall short in description, or in clarity of communication, or in some sort of consistency. Whatever the reason, they fall short of perfectly describing music.
First, that’s a good thing. Music is so complex and multifaceted that no system could possibly describe it all.
Second, we don’t do a good job of laying this out for students. Too many theory teachers tell their students some version of this: “Master this system, and you will have mastered music.”
No, you’ll have mastered one system of description – one that necessarily falls short.
It’s my opinion that if students knew that information, they’d much more readily be excited about what any system gives them, rather than becoming disillusioned in how it falls short.