How come natural tones can be played on a brass instrument? And why can you play all tones on a mouthpiece?

Answer

We must first agree on what we call a ‘natural tone’. In my opinion, a natural tone is a tone that can be played on a wind instrument, without the aid of valves or valves.

Then it is ‘by definition’ that you can play a natural tone without using the pistons.

Then why can you play multiple tones on the mouthpiece? This depends very much on the skill of the player.

Simply put, a wind instrument is an interaction between a resonator and a source. The resonator is a standing wave in a pipe that imposes a specific frequency. You can influence this frequency by making the tube longer or shorter (sliding trumpet) or by using valves.

The source is something that adds energy to the resonator for a loud sound. So it is important that the source adds energy at the same frequency as the resonator. With a trumpet, ‘the source’ is the mouthpiece and the player ensures that he adds energy to the ‘natural tone’ of the trumpet by making his lips vibrate with the correct frequency. He can regulate this by playing with the tension of the lips and the air pressure in the mouth.

In summary: the trumpet can only reproduce frequencies that correspond to the length of the instrument (and its harmonics). It is a purely passive element. The frequency the mouthpiece produces depends on the tension and pressure of the player’s lips. Since it has many more degrees of freedom, it can play more tones.