I am wondering at what frequency the helmholtz resonance of the mouth would have some effect on the tone of the trumpet. Rudimentarily the helmholtz resonance is when a cavity resonates like a spring, for example blowing over the end of the bottle, the bottle is behaving as a helmholtz resonator. Whisteling is also governned by this principle. While I can't whistle into my horn. It seems like the volume of air in the mouth and the size of the opening into the trumpet should behave as a helmholtz resonator. Though maybe only at the higher frequencies that one can whistle.