I theorize that Hunting Horns are nothing more than typical musical instruments encased in hard shell. However, that doesn't explain the way the notes are played.
So, I believe this. With each swing, a part locks into place and air is pumped in. The part is whatever would cause sound. When you finally have a viable combination, the hunter automatically knows. When you play, each part releases in progress from first to last, and the air is pumped out, hence the sound and color produced.