Mouthpiece Shank Bores

Some information about Morgan mpces in particular and sax mpces in general...

The Morgan Classical alto sax mouthpiece has one of the largest chambers Morgan sells for an alto.
On some saxophones, particularly Selmers, they got complaints that it was hard to slide the mouthpiece far enough along the neck cork to get them to tune. They had to be pushed way down the neck for that particular mouthpiece.
For a period, they reamed the bore of each mouthpiece. This had an unintended consequence for more modern saxophones, most notably Yamahas, where the mouthpiece would fit too loosely on the cork.
In fact, they got more complaints about the loose fit than they had ever gotten about the tight fit, so they quit reaming them.
However, if someone complains about a tight fit, they have them return the mouthpiece and they use a reamer to enlarge the bore.

The bore on their current alto mouthpieces is about 0.625 (5/8").

Below are a couple of pictures of a reamer made to slightly enlarge the bore of alto sax mouthpieces.
This reamer was made (yes, made) by a private individual who decided to take matters into his own hands.

As far as the taper of the mouthpiece bore, all Morgan mouthpieces are tapered to about 0.010 tpi (taper per inch).
This is in contrast to the taper on the reamer they use which is 0.020 tpi, twice the steepness of the normal taper, which may have been unintentional.

As far as the out-of-roundness of the bore of some other mouthpieces...that is not intentional.
Some mouthpieces are made in a mould and as they cool, they are placed on rods so that their roundness is maintained.
It is not possible to maintain a perfectly round bore during the cooling down process, so there is some distortion but it is usually quite small and one tends to find it on the cheaper mouthpieces.