TubeNet

What effect does mouthpiece OD/ID taper (new Euro, American, old Euro, etc., etc.)[/i], the thickness of the mpc exit, and the diameter of the receiver have on play?
There are steps of a millimeter or so involved, and those should affect wave propagation down the bugle.
Have tuba players:
1. analyzed this? . . (not likely)
2. commented directly on it? (I was told to use tape to fit)
3. had experiences indicating effects one way or the other?

Rim

Wide: Increases endurance.
Narrow: Improves flexibility.
Round: Improves comfort.
Sharp: Increases precision of attack.

Cup

Large: Increases volume, control.
Small: Relieves fatigue, weakness.
Deep: Darkens tone, especially in low register.
Shallow: Brightens tone, improves response, especially in high register.

Throat

Large: Increases blowing freedom, volume, tone; sharpens high register (largest sizes also sharpen low register).
Small: Increases resistance, endurance, brilliance; flattens high register.

Backbore

Combinations of size and shape make the tone darker or brighter, raise or lower the pitch in one or more registers, increase or decrease volume. The backbore's effects depends in part also on the throat and cup.

I apologize for my imprecision. . . should've said "mouthpiece shank taper", as I'm interested in the match or mismatch between the mpc shank and the receiver.

There are so many variations in the way tuba parts are manufactured and put together at the receiver and leadpipe, that it is nearly impossible to predict the effect of different tapers or thicknesses at the end.

Some receivers transition smoothly into the leadpipe; some go into a leadpipe that is slightly or even significantly larger than the end of the receiver; and probably some meet a leadpipe that is smaller than the receiver.

It pretty much comes down to trial and error to see what works best in any particular tuba.