Thanks to Gary Kern for alerting me to this information from woodwind.org's clarinet forum:
It should be born in mind that I have used only modern mouthpieces to test the vintage instruments I have reviewed. Gary K has seen significant improvements on a Selmer Centered Tone, for instance, with a different barrel and a more historically correct mouthpiece.
Date: 2013-12-06 15:17
Stephen Fox, "Basic Clarinet Acoustics":
1.The mouthpiece bore affects both the overall pitch and the balance between the top and bottom of the playing range. It is usually conical (tapering towards the top), more rarely cylindrical.
It is essential to use a mouthpiece with the correct bore size and shape for a given clarinet. A mouthpiece with a bore smaller than ideal will play sharp up to about A in the second register, then flat above that; one with an oversize bore will behave in the opposite way, flat up to the same point and sharp above.(This is rather a moot point when discussing modern equipment from major manufacturers since virtually all mouthpieces currently manufactured have essentially the same bore, within a few tenths of a millimetre at least; it is crucial to consider it, however, when dealing with historical instruments, and clarinets with now-uncommon bore sizes.)
2.The barrel bore affects the tuning of the upper part of the second register and the lower altissimo notes; these are sharpened if the barrel bore is enlarged.The size and shape- cylindrical, reverse taper, compound taper, etc.- of the barrel bore also exert a disproportionally large effect on the playing feel and resistance of the entire range of the instrument.