There has been a great deal said about calculating the volume and length
of the missing cone.  My best efforts to do show have been shared on
this forum and have been commented upon at length by the participants in
this discussion.

There is an obvious disagreement between Lance and myself with regard to
this topic.  My understanding of the disagreement is as follows:

-Lance believes that the missing cone should somehow be extrapolated
from the geometry of the body.

-I believe that using the slope-length formula prescribed by Ferron with
measurements from the neck produces satisfactory results for our
purposes.

-Lance believes that the natural resonant frequency of the missing cone
(without the neck) can somehow be calculated and tested by blowing on a
mouthpiece with the part that goes on the neck cut-off and a narrow ring
replicating the neck opening (he calls the constriction) inserted in the
end.

-I believe that the calculated natural resonant frequency of the missing
cone added to the length of the neck can accurately and adequately be
derived from the formula Frs = xo/2L  given by Benade.  I also believe
that the frequency of the mouthpiece plus neck when played with a
"normal embouchure" can be accurately compared to this calculated
frequency when and adjustment for end correction is made.  I also
strongly believe that this method of testing the frequency by  playing
the mouthpiece  on the neck is far more practical and allows a much
greater degree of player control of the pitch than playing on a cut-off
stub of a mouthpiece with a narrow ring inserted in the end.

-Lance believes the 1 mm gap between the base of the neck tenon and the
bottom of the body tenon socket has significance in the calculation of
the missing cone using the geometry of the body in the missing cone
comparison study
<http://jbtsaxmusic.homestead.com/Missing_Cone_Volume_Comparison_Study-R\
evised.pdf>   that I conducted.  He thinks it should be treated as part
of the neck for length and volume.

-I believe that the regardless of how the 1mm "gap" and its .445 ml
volume are treated, that it makes no significant change in the findings
of the study which were that the (large) missing cone extrapolated from
the taper of the body minus the measured volume of the neck produces a
missing cone that is far too large.   In fact, if the mouthpiece
replicated a missing cone that size the played pitch on the mouthpiece +
neck would have to be  close to Gb concert---a whole step lower.

It is clear to me that Lance and I cannot agree on these details and
that further argument and bickering on these items of disagreement  is
pointless and is beginning to annoy the neighbors.

That said I would like to invite Lance (or anyone else for that matter)
to take whatever instruments they have available and to
try to find a way to calculate the volume and length of the missing cone
for that saxophone as I have. To test that missing cone calculation I
suggest that Lance come up with a way to play test the missing cone
substitution and see if the frequency of the played substitution is a
good match for the calculated frequency of the missing cone.  If he
needs some old mouthpieces to cut up I have tons of them.  Just let me
know.

Once this is study and testing is completed and the results posted here,
I will be more than happy to review and discuss those findings with him
at that time.  I am not dropping out of the discussions entirely on this
forum (sorry Steve) merely stepping aside from the circular arguments on
the above topics that are going nowhere.

John