Toby, etc...
First, I'm not saying that tonal ring is produced by the body of the clarinet vibrating. I was simply responding to Toby's statement about the wood in a clarinet body being static. Clearly, the wood does vibrate. However, I'm not suggesting that's the reason for tonal ring. Frankly, I DON'T know why one clarinet has a vibrant ringing sound and another does not. It's a complete mystery to me.
Second, I don't imagine qualities in my sound. Much of my musical training is in composition and for many years I've paid great attention to listening to sublities in tonal clolor. Thus, I pay considerable attention to detail when I'm playing and listening to my sound.
Tonal ring is a term often used among classical clarinetists. I readily admit that I did not understand it for many years. The clarinets I used for the past 7 or 8 years were larger bore instruments and I cannot say that I experienced much ring with them. Thus, when I heard classical clarinet buddies discussing tonal ring I wasn't exactly sure what they were talking about. However, when I acquired my 70's Monopole it took only several notes to say to myself "Wow, that's what they mean about ring!". Simply put, my .574 bore Monopole has tons of ring whereas my .580 bore Monopole has a beautiful sound but not the level of ring as the other Monopole.
I do not know why one clarinet has more ring than another. It comes down to trying a bunch of clarinets and finding one that -- for whatever mysterious reason -- has a truly exceptional quality of sound.
No, I have not had an oppurtunity to try a Greenline. I'd like to as I've been curious about it.
PS, I agree with Steve that some mouthpiece/reed setups can help to bring out more ring in a clarinet. However, in my experience that goes only so far. My setup on my 70's Monopole is a Grabner K14, #3 Legere Quebec, and a Klassik string ligature. When I use my K14 setup on my 1960 Monopole it doesn't have anywhere the level of ring as my 70's Monopole. I get a bit more ring on my 1960 Monopole with a Grabner K11e. However, it's still nowhere the level of ring produced by the 70's Monopole.
Roger