This is a fun game, although I can see we're soon going to run into trouble, given that the only three J countries I can think of are Jamaica, Japan, and Jordan. It extends a little if one uses territories and dependencies, but who wants to be the person trying to find twenty-six composers, A-Z, from the Island of Jersey?
But until then....
Odo of Arezzo (c. 10th century CE)
Very little has survived from him, and there's practically no biographical information on him, save that he was an abbot in Arezzo, a theorist, and composer of religious works.