yes my teacher also talks about air a lot also. and the response the physics aspect. this does not have much to do with playing higher or lower. embouchure, apeture, air and strength along with which direction you move your air is the most important. experience also helps a great deal. if you notice when you play, lower register playing moves the air directly across while as you move up in the register your air consistantly changes to cold air and the direction begins to angle down. when you begin to understand your own horn, you personal horn and feel the pitches and let your mind teach your body to play, then this along with scales, chromatic or whathave you on top of pedal tones and longtones, lipslurs, all this will begin to come together and improve your range. but also, a great misnomer with dci, the best players are not the ones who can play triples c,d, and g's. they arethe ones who can play these and other registers with quality. please dont forget to work on these.