"American Frontier" includes many decades and many places, so it is difficult to answer your questions with specificity. People brought the musical tastes that they had from elsewhere, so the "frontier" did not stand apart. The West tended to be more international than other places in North America, so the region included musical traditions from throughout the world - sometimes enjoyed by others and sometimes kept within an immigrant group.

In addition, Western theaters exhibited a wide variety of musical performances - everything from opera singers to black choral groups and black-faced minstrel shows. Primary sources describe individuals who played musical instruments at home and for small gatherings, and they frequently describe purchasing the latest compositions (and many traditional tunes/songs) as sheet music mailed from Eastern publishing houses.

Beyond that, books could be written on the subject, so I'm not sure where else to take this. Feel free to ask questions.