The low pitch vibration spreads in the ground and in space from your posture stabilized on your roots, as if you were sitting on the sound source. Keeping concentrated on this balanced position, you release then your whole body at the very end of your exhaling, to let your spontaneous inhaling come in, maintaining this fat and low voice on a full vibrating pitch : you develop this fat and vibrating sound from practicing the overtones control, as recommended by Joe Allard and by David Liebman.
Next you quietly play upper and upper notes in the pitch range, reaching the higher register and the related overtones, still driving this low vibration from your heels, and above all, without modifying anything between your embouchure and your diaphragm : any unwanted alteration of the sound must be avoided by letting loose and relaxing down to your breathing center point, even reaching down to your heels !
Doing so, the high register sound can be kept rich and homogeneous by extending the downwards feeling to your roots : keep thinking low in the highs ! This way, and counter to some misconceptions, carefully dismissed by Alfred Tomatis in The Ear And The Voice, you ensure the sound fullness by maintaining this body configuration of your air column and of your embouchure throughout the whole range from lower to higher pitch : among other benefits, this brings a gratifying comfort feeling and allows legato playing between the end-notes of the tessiture, as Dominique Hoppenot precisely describes it in her Inner Violin / Le violon intérieur.
Musically, you go up and down, but physically you must always go down. The pitfall is that a sound may look nice but not be a good one.
Thanks to the work achieved (low and fat breathing, vertical pushing), you can now play much more backwards, so you can avoid playing your way up when you hit high notes.
(…) You are going to learn how to feel down in order to better go up. (…) But you should obviously never go back up !
Always pack down and vertically push down.
Michel Ricquier, Traité de pédagogie instrumentale
(translated by Guy Robert)
Low note articulation and tone production are two of the subtle challenges confronting saxophonists, as is the opposite problem of the tendency to go sharp in the high register. A saxophonist should not sound like he has a different tone for each register. The overtone matching process may go on for years.
David Liebman, Developing a Personal Saxophone Sound