The term 'band instrument jug' can be broken down into four crossword solutions: kazoo (5 letters), OBOE (4 letters), SAX (3 letters), and TUBA (4 letters). The kazoo is a small, handheld instrument made of metal or plastic with a membrane that vibrates when air is blown through it. The OBOE is a woodwind instrument with a double reed mouthpiece and a conical bore. The saxophone is a brass instrument with a single-reed mouthpiece and a conical bore. The TUBA is the largest and lowest-pitched brass instrument, with a conical bore and three to six valves.