A melodrama; the genre comprising musical drama of this type. Also (occasionally): the musical accompaniment of any variety performance.
Now chiefly a theatrical term, in which the notion of a musical element is retained. The word appears not to have developed the wider application of melodrama to sensational drama of any kind.
Late 18th century; earliest use found in untitled. From French mélodrame from mélo- + drame, after Italian melodramma.