Hi Keith and all--

Here's something relevant from Nederveen (Acoustic Aspects of Woodwind Instruments, pg 83):

"The mouthpiece cavity and the reed compliance are essential factors in the tuning. As was shown in Section 27, the sum of the real and fictitious cavity volumes must approximaely be equal to the volume of the cone-truncation, to ensure purity between first and second register. The application of this simple rule of thumb is obscured by the influences of diameter perturbations in the crooks and upper parts of the instruments." ...

..."For at least two of the three [tested] sporano saxophones, theory predicts that correct tuning for both registers seems to be unattainable--and it is indeed so Many soprano saxophones are seriously out of tune. Instrument makers, well aware of this, tried to do away at least with some of the sharpness of the upper register by a device for improving one note, B5 [high C#]: when the register key is pressed, a spearate key keeps a small hole closed (which hole stays open for B4). Thus the sharpness of B5 is indeed reduced, but unfortunately too much so, which makes the device equally annoying. On the Selmer, very ingeniously, the key is perforated so that the venting for B5 is reduced less drastically. It can be seen form the tuning diagrams that this measure is satisfactory. The best cure for the soprano troubles, as it evolves from the present investigations, would be to make the bore purely conical, reduce the truncation and leave out the above-mentioned coupling for B5. The Selmer comes very close to this ideal; its bore is the straightest and its truncation is the lowest; it was found to be the best-tuned instrument of the three."

"If the angle of conicity of the lower part of the bore of a conical instrument exceeds that of the upper part, as does the Schenkelaars saxophone, the mutual uning between registers is stringly influenced...."

He goes on to mention (and show) that reed compliance is not a large factor in saxophone tuning except in the very lowest notes.

What strikes me as interesting about all this is that he seems to be saying that mpc-cavity-related tuning effects are only one is a plethora of factors that affect the tuning, and deviations can serve either to compensate for or exaggerate deficiencies in other areas. 

Nederveen does say that deviations from the ideal mpc cavity volume "strongly influence the high register and the upper part of the low register, whereas the lowest notes are altered less."

FWIW,

Toby