In other words, is it a continuous 'round/circle' like curve or a more complex one like the power of y, y being anything over 1. The question is how fast does the slope increases leaving the table and how it decreases reaching the tip. I found descriptions of short, medium and long facings, but that's far from enough. The Concept series has a round chamber and small tip opening. Trying to develop a system for sailing boat hulls for some time, I have been trying to get a feel for curves, that I have applied to other topics along the way, but it lead me to try and understand how the mouthpiece curves that produced good results looked like. Henri Selmer Paris Soloist Mouthpiece for Alto & Tenor Saxophone. I would be curious to see if there are mathematical formulas describing these curves.
So far, unless I'm wrong, this has been an empiric trial and error process.
There must be some very clever physics behind the reed vibrations and the influence of the facing curve to help it being the perfect tone generator that we expect it to be. Later I reused the same scheme to write a VB program that draw and printed the hull in 2D and 3D. In this video Theo Wanne at 1:22 shows a chart of facing curve numbers in his book taken from measurements of different makes and models of mouthpieces that play well. That mouthpiece has a 2.04 mm tip opening with a medium facing. Your tenor mouthpiece (T101) is most like a T25 of the V5 Series. He will usually be advised to buy a particular brand and size (Selmer C, etc.) or, more vaguely, a medium. A young saxophonist usually purchases a new mouthpiece during his junior high or high school years, either because of damage to his stock mouthpiece or the desire for an improved tone. This mouthpiece features a 1.86 mm tip opening with a medium long facing. Mouthpiece Facings, Chambers, and Materials. The following year I built a scheme using a combination of functions that enabled me to define a very convincing sailing boat hull all programmed into my HP41CV calculator. Your alto mouthpiece (A101) is most similar to the A25 of the V5 Series. But a few months later, the idea had worked its way into my tiny skull and I started to play with the concept. Many years ago, when I was in high school, I had an argument with one of my best friend who wanted to design sailing boats using math functions. Is there a function that would describe it perfectly? The real question that keeps haunting me is what should that facing curve look like?
I even tried to thin the side rails but it's not easy to do as the side walls are both very thick and coming inwards.