A bandmaster is the person who conducts a military band, a brass band, or a similar marching or ceremonial band. They keep the players together, set the speed, and are in charge of how the music sounds. The word has a slightly older, official feel — armies, town brass bands, parades. Though actually, the job is cousin to a conductor’s and to a bandleader’s, but the labels are not free to swap. You would not usually call a jazz bandleader a bandmaster, and you would not call the conductor of a symphony a bandmaster either. Master here means the person in charge, not a schoolteacher.