You're welcome. For those who haven't seen Shooshie's mouthpiece exercises, here is a link:
2.6 The Mouthpiece Exercise. For the record, I don't have a clue who "Shooshie" really is and I know this information did not originate with him. He is just the one known for widely dissemination the ideas on the web. Here are a few of my thoughts.
1. It is important to note that he starts on the suggested mouthpiece pitch for each saxophone and goes down---never up.
2. Basically what changing the pitch the mouthpiece sounds by changing the shape of the oral cavity is learning what is called "voicing". Voicing is particularly important to playing harmonics and altissimo.
3. One can change the "voicing" of the note and lower the pitch on notes from high F down to about A on the saxophone without "lipping down" (relaxing the embouchure). It is easy to try, just raise the middle of the tongue on one of those notes.
4. Acoustically what happens on notes A and lower is that the resonances of the body tube of the saxophone are the strongest and control what Benade calls "the regime of oscillation" which is simply the fundamental along with all of its overtones below the cutoff frequency which is around F#3. This means simply that the sax dictates what note/pitch comes out.
5. On notes A2 and higher the resonances of the shorter body tube become weaker allowing a skilled player to use the resonance of the oral cavity "take over" the "regime of oscillation" from the body tube. Notes can be bent down in pitch and altissimo notes can be played using what are called "cross fingerings".
6. The whole point of practicing "Shooshie's" (for want of a better name) mouthpiece exercises is to develop the flexibility to "tune" the oral cavity in order to have a better command of the highest register of the saxophone.
7. Many professional classical players profess to having the ability to use "voicing" to change the timbre of notes in the middle and lower registers. This would mean that the oral cavity can somehow be used to control the harmonics of a note. This is one area where the jury is still out for me. It may or may not be the case. I will need more acoustic research data on this before I can say for certain that this has validity.