Of course you start to experiment because it's obvious that a mouthpiece has a great influence on the sound produced. Behold the fascination.
It is a fascination that's shared by every musician. Read the reviews of reeds, mouthpieces and instruments and you read about sonority, preferably about a very special one which you surely won't find anywhere else. Patents likewise include claims on improved sound. But if you start to experiment more seriously, your sound (I prefer to use the term 'sonority') appears to be a magnitude that's not that easy to measure and a rather vague one as well, one that constantly varies under the influence of the register you play in, your breath, your reed, your temper. Instead it's wiser to focus attention on correct intonation and this appears to be measurable quite well. A tuning indicator and especially the patience to graph out everything shed much new light on the matter. Otherwise nondescript mouthpieces suddenly attract attention because they do just nicely.
Another facet of the mouthpiece is an easy and especially reliable respons. This is not directly a measurable feature, but it is a very recognizable one, and one which is of great practical importance. Handling your breath in an efficient way in the sense that not your mouthpiece consumes the air for you, but that it converts it efficiently into sound, not to mention the response to slap tongues, multifonics and top tones. It is an approach that has brought much good. It demythologizes sound and leads to the acceptance of how a saxophone really sounds. It frees your hands to search for how – apart from the myth – a mouthpiece works and should be designed to execute that job as well as possible. The requirements are simple:
The instrument must speak both forte and piano and we want to play nice crescendos and decrescendos. Downward intervals and register changes should be produced correctly, the lowerst range should respond just impeccably, likewise top tones, and intonation should not be adversely affected. Also, we don't want to hear too much accompanying noise. Easy enough.. And guess what? If everything works well it sounds well. Your material should primarily work, the rest will follow.