Question : "What is the deal with the so called mouthpiece popping theory and it's connection to pitch always being constant?"

GR : I don't buy into the mouthpiece popping theory. You shouldn't buy into it either unless someone can prove it to you. Telling you this is a fact means nothing. Go to a physics lab and ask them.

Here are my thoughts based on science and personal experience. Hitting the mouthpiece rim and producing a pitch with your hand will have no relationship to how that mouthpiece will play when you put it to your lips. Why? Because your lips penetrate into the cup and remove mouthpiece cup volume, therefore, the first natural pitch/pop frequency will be raised and this can be different for each player. Thomas Moore did tests and found lip engagement will raise the first natural pitch. I made two mouthpieces the same and reduced one using an estimated lip penetration and it raised the natural frequency of the mouthpiece from about 650 to about 730 Hz's.

Next thought, as the mouthpiece is put into the trumpet the backbore becomes part of a system that is connected to the lead pipe until you reach cylindrical tubing. Look at the some trumpets with the integrated mouthpiece/leadpipe. The mouthpiece is now about 11 inches long and the mouthpiece length includes the backbore/leadpipe taper. This certainly will not pop the same on both ends so why would some manufacturers do this? What is the reason for this? It is a conflict to the popping theory.

In conclusion, the intonation of a trumpet has no relationship to the pop pitch frequency when using your hand. The intonation is greatly affected by the amount of lip in the mouthpiece. That is why one player can play a certain mouthpiece well in tune from top to bottom and another can not. The lip engagement subtracts from cup volume and changes the overtone series on the trumpet, therefore, each person will have a different overtones series depending on the amount of lip in the mouthpiece. Take a given trumpet and mouthpiece. Have 10 of your friends play low C, Middle C, and High C, record the intonation, tune on middle C, note the differences on pitch between the low and high C, as well as, the tuning slide position for each player. The tester should not be allowed to see the tuner while testing. The pitch will only be constant if the mouthpiece, player, and horn are a match. Use the same mouthpiece and horn for each player.