The facing is the continuous curve starting from the break and ending at the tip rail. The reed sits flush against the table, and first separates from it at the break. The facing is the surface the reed vibrates against while the musician blows into the mouthpiece. The facing curve can be seen on any mouthpiece by looking at it from the side.
The facing varies greatly among mouthpiece brands and plays a crucial role in the response each mouthpiece has. The facing dictates how free blowing or resistant a mouthpiece is, as well as the type of response the mouthpiece gives in the upper, middle, and lower registers of the instrument.
In general, facing curves come in short, medium, and long:
Manufacturers that have used short facings include: Selmer in their vintage mouthpieces with tip openings from E to H, and all Brilhart mouthpieces.
Manufacturers that have used medium facings include: All Otto Link mouthpieces, and most Meyer mouthpieces ever made.
Manufacturers that have used long
The short facing emphasizes the upper register, making it respond easier. This is partially due to the fact that only the forward, thinner portion of the reed is vibrating. A short facing creates less resistance and back pressure when playing as well.
On the negative side, the low end can feel weak, making it harder to fill up the horn, and sub-tone as well. At first one may feel a short facing mouthpiece is easy to play. However, after some use, most people find them rather tricky. It is a lot like riding a race car on the city streets - just too hard to control.
The long facing curve accentuates the lower register of the horn. The sound becomes especially lush and reedy sounding across all registers. Because more of the thick part of the reed is now vibrating, there is also more resistance and back pressure while blowing into the horn. A long facing makes the mouthpiece feel like a larger tip opening than it actually is. A lot of people who like a warm vintage and reedy sound love long facing curves. Anyone wanting a quick responding mouthpiece though will not want a long facing curve.
Another benefit, or drawback, depending on how you look at it, is that the long facing curve allows notes to be bent easier. This is because more of the reed inside the mouth is susceptible to jaw pressure
A lot of saxophonists from the 40s and early 50s played mouthpieces with small tip openings and very long curves. This set-up produces a fat sound with good resistance that sounds much like our current larger tip openings with a medium curve. The long facing also allowed them to easily bend notes, produce a nice reedy sound, and fill up the horn at the same time.
The medium facing is the balance between the short and long facings and is what the majority of mouthpieces made use. A medium facing creates a quick responding upper and lower register, and is also easy to play. Reeds are less picky with a medium curve. You will find more reeds work with this facing. Many players have chosen larger tip openings with medium facings in order to get the big sound of the long curve but the ease of playing afforded by the medium curve. Elongating the length of a medium curve very slightly (approximately one millimeter) on a modern tip opening mouthpiece (say a 7* in a tenor mouthpiece) creates a very vintage sound. Still, most players like the ease of control, and easy responding sound of the standard medium facing, choosing to get the sub-tone, and reedy sound, etc. more with their jaw, instead of being forced into it by the mouthpiece.
The medium facing is the most common facing for good reason. Overall, it is the most versatile and easy to play. An exception, though, is with very high baffle mouthpieces. Because of the shape of the baffle, a longer curve is actually needed to get the mouthpiece to respond appropriately. A high baffle mouthpiece with a short of medium curve will choke the airstream passing through it. Hence, high baffle mouthpieces with a long facing tend to play like medium baffles with a medium facing.
Also it is important to note that different manufacturers name their facings differently. For example the Berg Larsen 'M' or medium curve is actually a long curve, and their SMS, or short curve, is actually a standard medium curve.