What kind of music was there when Stephen F. Austin was around?
Since he was around from 1793 to 1836 there are various musicians who were present in the period. They include classical and opera like Adolphe Adam, Mikhail Glinks and Robert Schumann too. There are others like Joseph Haydn and Thomas Attwood who were also popular musicians in the period. You can go to http://en.wikipedia.org/wiki/1793_in_music or http://en.wikipedia.org/wiki/1836_in_music for more details.