In the underlying representation, acute marks high tones, unmarked marks low tones, and H marks variable-toned vowels — the tone of variable-toned vowels depends on position with respect to the word boundary and to high toned vowels. Basically, it's normally low in odd-numbered syllables from the beginning of the word or most recent long vowel, or when adjacent to a high tone vowel, and is high otherwise. (But underlying high and variable-toned vowels can still surface as low when preceding consonant clusters or certain affixes that condition low tone — marked with a preceding <`>, as in oᴴkííθ-ha+háačí-`yóo-oᴴkoᴴ > hokíiθhaháačiyóoko.)

And yeah, the aesthetic feel is meant to be fairly Arapahoan.