Jbtsax's Moving The Mouthpiece - Derin Insert Tests
This is an interesting topic. I hope you don't mind my migrating it here from over there. It seemed to have bogged down. Understanding why your instrument/mouthpiece behaves the way it does can only improve your musicianship and your music. Here's jbtsax's summary:
"A - The alto saxophone is tuned to A=440. A 1/4" wide delrin ring the same dimensions as the end of the neck is inserted into the shank of the mouthpiece. The mouthpiece is set onto the neck 1/4" lower than before.
The saxophone's tuning is exactly the same on the A=440 tuning note, and the pitch relationships up and down the scales are the same as when the mouthpiece was in the original tuned position on the cork.
Conclusion: Adding to the physical length of the saxophone as measured from the tip of the mouthpiece to the first open hole has no effect upon the pitch produced by the instrument or its intonation provided the volume inside the mouthpiece remains constant (unchanged).
B - The saxophone is tuned to A=440 with the delrin insert in the shank of the mouthpiece. The pitch relationships throughout the range are the way the saxophone normally plays (see above). The insert is removed from the shank of the mouthpiece and the mouthpiece is pushed onto the cork an additional 1/4". Again the saxophone plays in tune to A=440 and the pitch relationships (intonation) remains consistent with the way the sax normally plays.
Conclusion: Subtracting from the physical length of the saxophone as measured from the tip of the mouthpiece to the first open hole has no effect upon the pitch produced by the instrument or its intonation provided the volume inside the mouthpiece remains constant (unchanged)."
I duplicated jbtsax's findings on a tenor sax using a similar insert and his conclusions are good, but one needs to go a little deeper in order to see what is happening and why. We are assuming that the truncation is at the small end of the neck.
The conical instrument needs the following in order to function:
1. a body tube
2. a mouthpiece chamber
3. a constriction between 1 and 2.
The total volume of the mouthpiece chamber AND the constriction should equal the missing cone piece of the truncated cone. As the end of the neck is the smallest point of the bore, that is obviously and effectively our constriction, but as the neck is not part of the truncation, our constriction has no length. It is effectively 2 dimensional - for now. The mouthpiece chamber and throat are all considered chamber volume, and regardless of shape, they behave as a cylindrical tube (with perturbations).
When we add to the physical length of the saxophone as in "A" above, by inserting a 1/4" long cylindrical tube, the same diameter as the neck opening, into the throat of the mouthpiece, and then pull the mouthpiece out 1/4" to get our tuning right, we have reduced the volume of the effective mouthpiece chamber (chamber+throat) and given our 2 dimensional constriction 1/4" of length and respective volume. The total volume of chamber + constriction remains the same. One can vary the chamber/constriction volume ratio this way (A) and that (B), and as long as the combined volume AND the resonance frequency of their combined length matches that of the theoretical truncation, the tuning will be OK, both in low and high registers.
What is going on? While the mouthpiece volume + constriction volume=truncation volume, the mouthpiece and the constriction are still 2 separate parts. One is not the other. Changing the length will always affect the pitch. No explanation necessary. Changing volume will always affect pitch as well WHEN IT OCCURS AT A COMPRESSION ANTI-NODE (or displacement-antinode) AND the mouthpiece chamber is a pressure anti-node for every note on the horn. In "A" we inserted the 1/4" constricton into the mouthpiece throat and pulled the mouthpiece out 1/4". The extra length made the general pitch lower, but the constriction displaced some of the mouthpiece volume. Since the mouthpiece chamber is a pressure anti-node, the pitch general pitch of everything was raised. So the intonation did not change. Same thing in reverse for B.
In one of my tests I enlarged my link chamber to where it would not play in tune at all, regardless of where the mouthpiece was placed. While I could push in to get a good A=440, the upper register was sharp of course. Even though the volume of the mouthpiece/2 dimensional constriction was right, the resonant frequency of their combined lengths was too high. By inserting a 1/2" constriction insert into the throat of the mouthpiece and pulling back out appropriately, both the combined mouthpiece/constriction volume and their resonant frequency matched that of the theoretical truncation, and the intonation was as close to perfect as it could be, in every register.
Notes:
1. In actuality, the constriction tube wall volume displacement/constriction tube bore displacement ratio is never exactly 1/1, so putting a 1/2" constriction doesn't equal pulling out 1/2" exactly.
2. The effective mouthpiece volume in playing conditions is significantly larger than the hard-walled, closed reed, geometrical measurement. Add the volume of the reed and it's arc at it's widest point at least.
3. Amplitude (pp - ff) and embouchure variations (vibrato, bends, etc) also change the effective mouthpiece volume. One need look for a mean volume, that takes this into account to base everything on.
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