This one was tricky. It surely sounded like the Ennio Morricone’s soundtrack from “Once Upon a Time in The West” (the man with the harmonica) because it was inspired there.
This music appears in the scene in which Barbossa, Elizabeth, and Jack confront the representatives of the East India Company just prior to the ship battle is an homage to the “spaghetti western” style of director Sergio Leone, particularly in the gradual approach and use of alternating extreme closeups of the characters’ faces, as well as the choice of music, which is reminiscent of the Harmonica theme from “Once Upon a Time in the West”.