I'm thinking specifically of they way words like "frankly" are sometimes used in modern English.
Take the sentence: "His speech was uninhibited, unprepared, and frankly insulting to half of his audience."
Now it could be read that here "frankly" is describing the way that the speech was insulting, saying the speech was openly and obviously insulting. However it seems another reading could be made where "frankly" is describing the tone of the sentence itself, reading almost like:
"His speech was uninhibited, unprepared, and frankly (I am going to be frank about this) insulting to half of his audience."
Is this interpretation of the sentence valid? If so, is there a term for this linguistic phenomenon? How exactly does the word "frankly" fit into this sentence (such as if you were to diagram it)?