Oklahoma!, (1953) by Rodgers and Hammerstein, is a play in the tradition of the genre called a “musical drama.” It is a stage play with songs, an American spin-off on Italian opera. It is a “comedy” in the sense that it is not a tragedy (the characters are not "high" and do not "fall from a high place"; it is a historical play in that it dramatizes the historical struggles of American settlers over whether the lands should be farmed or whether they should provide open grazing for cattle. It is a melodrama in the sense that the emotions are exaggerated and not very psychologically valid, but “things” turn out the way the audiences wants them to. While there is a “bad guy,” Judd, he is a cardboard villain, not a real antagonist. The play tells its story partly in song and partly in dialogue. The peripheral characters are all fairly stereotypical, rather that carefully drawn figures. So the simple but accurate answer to you question is that Oklahoma! is a typical American musical drama with many elements of melodrama and some elements of history plays.