You want music to be as reliable and consistent as mathematics. It’s not. Or is it?
Or, it doesn’t seem to be. Music requires a point of view. What’s wrong in one context is so right in other contexts. (Consider perspectives on dissonance in various times.) In fact, I think it’s important to know what your point of view when you interpret music. What bedrock principles do you stand on when you write, interpret, or listen to music?
And that’s where it’s actually more like math than you think. When the Greek mathematician Euclid wrote his extensive works on geometry, he described five axioms. These are the five things that we must assume are true without proving them. Everything else follows from these five true ideas. Change the axioms, and you would get an entirely different system.
Just like Euclid, you must decide what’s definitely true, and then let all your musical decisions stem from those axioms.