About resonance: the trumpet is an open tube system with characteristic modes of vibration that it naturally ‘likes’ to vibrate. These characteristic modes are determined by the characteristics of the trumpet, especially the length of the tubing. For example, in open position, every trumpet player know that the characteristic modes are C-G-C-E-G-C, the trumpet naturally vibrates to these notes (because they are probably solutions for the homogeneous equation that governs the open position trumpet), so they sound better because they dissipate energy in the form of sound waves with maximum efficiency. We, as players, drive the trumpet system with our breath, so now we’re dealing with a forced system. It can be shown that such a system will dissipate energy in an optimal way when the frequency of the drive-system is equal to a characteristic frequency of the driven-system – when this happens we have what we call resonance.

To achieve resonance we have to provide a flow of air with a frequency equal to one of the characteristic modes, this is where the vibrating lips come about. Now, how you, as a player, can make your lips vibrate with maximum efficiency as to achieve the desired frequency (and support it with high quality) is where the teachings of Greg comes. I think what tension does is to diminished the quality, it gives you less control, less mastery os what you’re doing. With tension everything is tight and responds too quickly to small changes, we don’t have room to control.