bloke wrote:There are many things going on with the dimensions of sax mouthpieces
No kidding. One thing we're vaguely aware of that I've never heard mentioned with tuba mouthpieces is the acoustical role the mouthpiece chamber plays in the effective length of the resonating air column. The basic acoustical principle of a saxophone supposes a conical shape, and somehow (apparently "somehow" involves something called Helmholtz resonance) the mouthpiece chamber serves in lieu of the hypothetical continuation of that conical shape where it's truncated at the mouthpiece receiver. So intonation can be influenced by absurdly small adjustments of the mouthpiece, as a small change in chamber size corresponds to a lot of small diameter hypothetical conical bore. Next time I get a chance, maybe I'll try a few notes on the tuba with as much lip as I can stuff into the mouthpiece - could that raise the pitch by making the "chamber" effectively smaller?
But at any rate, sound is a combination of reed, mouthpiece, player and saxophone. Players tend to eventually sound like themselves on whatever mouthpiece; reeds may be good with one mouthpiece and not another; mouthpieces may be good with one sax and not another; and of course what we sound like to ourselves is not what the rest of the world hears. Sounds a lot like the tuba, plus reeds, but range of possibilities is really quite a bit larger - the difference between one mouthpiece and another can be very striking, which I can't say of the tuba.