That talk of "harmony" is only a metaphor. You're comparing emotional contentment or how things might work constructively, to the musical combination of tones into a chord that's pleasing to the ear.

The whole thing is doubly subjective. Musical harmony depends on the human ear, and the extended sense of a person's "harmonious" relation to nature is more subjectivity on top of that musical subjectivity.

So harmony exists but only in that the claim is poetic, metaphorical, subjective, and therefore not empirical or falsifiable. It's just an expression of feeling, of the sense that you're doing well in the world, that your life "agrees" with deeper levels of reality. It's not an objective proposition that's factually true or false--unless you're implicitly appealing to theism.

I have similar issues with the correspondence theory of truth, by the way. The so-called agreement between human symbols and natural facts is dubious because it's subjective and metaphorical. Ultimately, most statements in natural language are similarly metaphorical and anthropocentric. We should just be aware of that fact, especially when making grandiose claims about something like God or cosmic harmony.