I was taught to tighten up for the higher notes/loosen for the lower ones.

My gut feeling is that much of the whole sound coming from a sax is due to the human blowing down the top end.So, this idea that mouthpiece internal length is the main factor in tuning the upper notes, while the cavity size is a factor in intonating the lower notes... Given that the mouthpiece cavity also seems to influence the general tone of the instrument (bright, dark), would it be fair to say that, all other things being equal, a given sax will tend to have a characteristic tone as a result of which type of mouthpiece lends itself to good intonation on that sax?
Well said. The player's concept is the overriding factor over the equipment in my experience. All the set-up and saxophone do is to facilitate the sound in the player's mind without the player having to work as hard.My gut feeling is that much of the whole sound coming from a sax is due to the human blowing down the top end.
You could give exactly the same set up to 10 players and get 10 (or more!) different sounds coming out.
