Depending on the sentence content, there are four ways to puncuate a compound sentence with two independent clauses -
Use a semicolon
Use a semicolon and a transition word (however, therefore)
Use a colon
Use a comma and coordinating conjunction (and, but, for)
In general, classical drama does not have to include irony or soliloquy, but it should be noted that there are many shades of grey with it comes to classical drama, and the rules were frequently "bent".