you know how to go sharp or flat with your lip? It`s like that, I drop and raise my jaw to do vibrato. there are a few different ways to approach it, so you can try doing whati said or wait till some hotshot explainer comes in and explains everything like perfectly.

You can use jaw vibrato, which is recommended for saxophone (and clarinet, I believe), where the vibrato is caused by the rapid (and sometimes not so rapid) raising and lowering of the jaw to cause the pitch to waver. The other way is by using the diaphragm to cause the air stream to waver, as used by flutists and singers. Here`s a nice post of SotW the goes into a bit more depth: http://www.saxontheweb.net/vbulletin/showthread.php?t=34458&highlight=vibrato

I've just started my individual tuition at uni, and I hate my tone as well. My teacher explained it as moving your jaw up and down subtley - almost as if you were saying "Wha Wha Wha"

Also, if your embrouche isnt right, like if the muscles around your mouth are too tight it won't come naturally.

Think "ya ya ya" don't actually move your jaw up and down. It's more your tongue.