Your graph of the Zinner is interesting in how it relates to a radial 
curve but.....This is radically different from most North American 
clarinet mouthpiece curves....I can't see how it would suit reeds.  
I 
would guess the development of mouthpiece facing was empirical and
not 
based on any theory.  The reed element is a big factor here....reed 
taper and vamp length etc.   I'm not criticizing here....I'm just 
confused..    I take it the radial curve comes from a circle....are 
there parabolic curves?  I would assume they would be generally
longer 
in facing length for a given opening...Looking at your chart however 
the Zinner clarinet curve is already too gradual compared to North 
American standards...The parabolic clarinet facing would have a facing 
length 
of60 or 70!      Point me in the right direction here.    John

That Zinner is Steve Fox's personal piece. It's a German facing, 
designed to work German bore or Oehler clarinets. These are usually 
played with very hard reeds. Vandoren's Black Master reeds go up to 5++
to suit players who use these pieces.

--- In MouthpieceWork@yahoogroups.com, "John Price" 
<john_w_price33@h...> wrote:
> 
> Your graph of the Zinner is interesting in how it relates to a radial 
> curve but.....This is radically different from most North American 
> clarinet mouthpiece curves....I can't see how it would suit reeds.  
> I 
> would guess the development of mouthpiece facing was empirical and
> not 
> based on any theory.  The reed element is a big factor here....reed 
> taper and vamp length etc.   I'm not criticizing here....I'm just 
> confused..    I take it the radial curve comes from a circle....are 
> there parabolic curves?  I would assume they would be generally
> longer 
> in facing length for a given opening...Looking at your chart however 
> the Zinner clarinet curve is already too gradual compared to North 
> American standards...The parabolic clarinet facing would have a 
facing 
> length 
> of60 or 70!      Point me in the right direction here.    John