jridge gave an answer quoted from aa.com, which asserts that a musical instrument, regardless of size, is your one carryon item, meaning that you may still bring a personal item.

Redhead's answer is inconsistent with aa.com. Maybe you'll have a lucky day and be allowed to bring a violin plus a standard carryon bag, but I wouldn't count on it. Better (IMO) to bring a violin plus a personal item and then be prepared to argue in case an employee doesn't know the rules and tries to prevent you from bringing a personal item along with your violin. You'd be in the right, and you'd win the argument.

Bring a standard carryon item plus a violin and then try to argue in case an eagle-eyed employee stops you: you wouldn't have the facts or the law on your side, and you'd lose, and thus have to check one or the other.