Neither cared for culture? That's very wrong, even in the Middle Ages Alfonso I of Castlle compiled the cantigas of Santa Maria and probably wrote some of them. Guillem IX of Aquitaine was a duke and a troubadour, troubadors were invited to many European courts. Throughout most of the "barbarian" period all sorts of artists were sponsored by nobles, they were the ones who comissioned works.
How come music peaked in the period 1600-1900? As well as culture in general, all our "classics" came from that time. What was it about that period that made it so special? As far as I can gather before 1600 we were ruled by barbarian warrior elites that just went to war with each other, and after 1900 it became nouveau riche capitalists (whether industrialists, banker jews or tech moguls). Neither groups cared much for culture. In the middle though, despite all the wars, we had a gentlemanly aristocracy that fostered the arts, with direct patronage like from Joseph II or even direct participation like Frederick II playing and composing. Thots?