The last time I looked, the performance of improvisation in jazz entailed, for a significant part of its history, utiilization of existing popular songs of varying measure length - from Darktown Strutters' Ball to I'll Remember April, from Sweet Sue to Night and Day - I Got Rhythm to Always. At least some of the time, the melody line was integral to the performance and would surely constitute a third 'dimension'
I don't think African music is, or was noted for any strong and memorable melodic content, at least in the idiom of the songs I've just cited. Harmonic sequence first? or the tune? In the case of Irving Berlin I understand that he knew little about harmony - he wrote the tunes but someone else then figured out the chord sequence.
When we were getting our chops around Body and Soul or All the Things You Are I don't think any of us thought we were plumbing the depths of structures derived from Africa. Pity we hadn't known, it would have made all the difference!