This html message parsed with html2text ---------------------------Thanks. I've only dealt with chamber volumes by adjusting them when palm-key
intonation issues arise, but I'm planning on measuring a whole bunch pretty
soon (when I get some time).  
  
I notice that this experiment used a cylindrical tube. So the discrepancy
between calculated and measured values is interesting in that it's a nice,
simple (??) situation without all the variables of a real saxophone and still,
the theory/practice numbers are quite different. Anyone done this with a
simple cone? Or does that get us into a world of complexity in which "all bets
are off"?  
  
If I recall correctly, Keith's chamber volume measurements varied from
calculated numbers (based on the entire cone taper of the horn, yes?) in both
directions (some low, some high). Does the recently discussed multiple cone
taper of the saxophone enter into this?  
  
Dan Torosian  
  
John wrote:

> Some time ago Keith and I communicated about mouthpiece volume and he sent
> me a spreadsheet of some measurements he had done. Being interested in the
> subject, I have tried to recreate the technique described by Benade (FMA p.
> 466) in his study of mouthpiece acoustics with Jim Gebler to determine the
> "equivalent volume" of a mouthpiece under playing conditions.  
>  
>  By using some simple techniques and some easy math, I found that the
> effective or equivalent volume" of a Rousseau classical alto sax mouthpiece
> was approximately 28% larger that the physical volume past the end of the
> tube it was inserted upon. This was in good agreement with the chart in Fig.
> 22.1 on p. 466 showing the equivalent volume of a soprano sax mouthpiece at
> various pitches.  
>  
>  The steps of the study can be seen at this web page: [Equivalent volume of
> a saxophone
> mouthpiece](http://jbtsaxmusic.homestead.com/mouthpiece_effective_volume_study.pdf)  
>

The beauty in the Benade/Gebler calculations is that the use of a simple cylindrical tube allows an accurate measurement of the "equivalent" volume of the mouthpiece.

In other words the volume, when added to the cylinder, would produce a resonant frequency the same as the one played using the mouthpiece added to the cylinder.

Trying to use a cone would not achieve a better result.  It would just make it harder to find or make the components used in the test.  

Finding the "equivalent volume" of the mouthpiece is actually a process by which one can estimate the volume added by the space taken by the vibrating reed and the interaction with the player's oral cavity. 

The comparison of the equivalent volume of the mouthpiece with the estimated volume of the missing cone the mouthpiece is said to replicate under ideal conditions is a totally separate calculation than the one done in my simple study.  For this reason, the shape of the tube used is not an issue.