[Dr. Bob]

I've often wondered what physical, structural aspects of a mouthpiece determine its in-tune pitch relative to placement on the neck cork? For example, two mouthpieces that perform similarly on my tenor require very different positions on the neck to be in tune: almost 3/4" separates these two when they're in tune, respectively.

Inner diameter of the mouthpiece neck receiver? Interior bore diameter? Baffle height and angle? Is there any way to know in advance of playing where a mpc is likely to sit and play in tune?

Just curious. Thanks for your thoughts.

Bob

 

[MojoBari]

It is mostly chamber volume. You need something close to the chamber volume of the “missing cone”. This is the volume that is missing if you extend the taper of the neck past the cork out to a point. Some will say it needs to be exact but actual measurements show it will be a little off one way or another depending on the tip opening, geometry of the mouthpiece and the player’s embouchure. Long narrow mouthpieces will need to be tuned to have a little different volume than short fat classical mouthpieces. Wide tip openings have a larger effective volume than narrow tip openings. Loose embouchures push in more than firm ones.

Then the shank length can be whatever the mouthpiece maker decides to do. They are just trying (if they try) to come up with a length and diameter that most players get a decent position on the cork for a variety of sax designs. I think every maker does this by trial and error testing. Some refine their new designs after feedback from the market.

 

[saxoclese]

Great answer MojoBari. That really covers it. Tests using a soprano sax mouthpiece by Arthur Benade and his assistant James Gebler found that the "geometric volume" one would measure by taping the facing closed and filling the mouthpiece with water is approximately 28% less than the "equivalent volume" of the mouthpiece under playing conditions. He attributed this in part to what he called the "elasticity" of the reed. A description of these tests can be found on p.466-467 of Fundamentals of Musical Acoustics.

It would be interesting to recreate these test using two tenor mouthpiece of different lengths and chambers to compare the "equivalent" volume of each related to the placement on the cork.

 

[1saxman]

The shank/inner bore is frequently omitted from this discussion as it has been here. There is no standard for any of the saxes, and sometimes mouthpieces of the same brand and model will require a different cork on the neck. This bore, along with the throat configuration, is probably the largest factor in mouthpiece water volume and therefore it's pitch tendency. We make huge changes in this volume when we change the mouthpiece position on the neck for tuning and typically the mouthpiece still sounds and reacts the same - just the pitch changes. With certain flat-playing saxes, I have run the mouthpiece all the way on until the throat stopped it, and the mouthpiece still played the same but the sax was more in-tune.

 

[Dr. Bob]

Thanks you guys.

 

[MojoBari]

The part of the bore that is over the neck cork is out of play.

 

[Benjamin Allen]

It is mostly chamber volume. You need something close to the chamber volume of the "missing cone". This is the volume that is missing if you extend the taper of the neck past the cork out to a point. Some will say it needs to be exact but actual measurements show it will be a little off one way or another depending on the tip opening, geometry of the mouthpiece and the player's embouchure. Long narrow mouthpieces will need to be tuned to have a little different volume than short fat classical mouthpieces. Wide tip openings have a larger effective volume than narrow tip openings. Loose embouchures push in more than firm ones.

Then the shank length can be whatever the mouthpiece maker decides to do. They are just trying (if they try) to come up with a length and diameter that most players get a decent position on the cork for a variety of sax designs. I think every maker does this by trial and error testing. Some refine their new designs after feedback from the market.

That's a really well thought out and well presented answer. Good stuff, Keith.

 

[MojoBari]

Great answer MojoBari. That really covers it. Tests using a soprano sax mouthpiece by Arthur Benade and his assistant James Gebler found that the "geometric volume" one would measure by taping the facing closed and filling the mouthpiece with water is approximately 28% less than the "equivalent volume" of the mouthpiece under playing conditions. He attributed this in part to what he called the "elasticity" of the reed. A description of these tests can be found on p.466-467 of Fundamentals of Musical Acoustics.

It would be interesting to recreate these test using two tenor mouthpiece of different lengths and chambers to compare the "equivalent" volume of each related to the placement on the cork.

28% is a bigger correction than I thought it was. But I knew it was significant.

 

[dexdex]

Interesting post and discussion. Thanks Mojo for the explanation.

 

[Dr G]

It would be interesting to recreate these test using two tenor mouthpiece of different lengths and chambers to compare the "equivalent" volume of each related to the placement on the cork.

Yet another way to compare where the mouthpiece sits on the neck, is to measure the distance from the tip of the mouthpiece to the end of the neck - internally. This would shift the focus away from the arbitrary "How much cork is showing?" method that includes variations in shank length, and the whimsical wide of the cork strip when applied to the neck. Not, perhaps, something that everyone should do (I encourage ignoring the cork, and instead tuning the horn), but a standard caliper in the hands of an experienced person could easily make the depth measurement.

 

[saxoclese]

Yet another way to compare where the mouthpiece sits on the neck, is to measure the distance from the tip of the mouthpiece to the end of the neck - internally. This would shift the focus away from the arbitrary "How much cork is showing?" method that includes variations in shank length, and the whimsical wide of the cork strip when applied to the neck. Not, perhaps, something that everyone should do (I encourage ignoring the cork, and instead tuning the horn), but a standard caliper in the hands of an experienced person could easily make the depth measurement.

Point well taken. An "inexperienced" person could even come close by putting a mark on the cork where the mouthpiece ends, and then remove the mouthpiece and measure the distance from the end of the neck to the mark on the cork. When I attempted to recreate Benade's and Gebler's method of finding the "equivalent volume" on my alto mouthpiece, one of the steps was to first measure the "geometric volume" and then calculate the volume of the cylinder displaced by the insertion of the neck. Subtracting that figure gives the actual "geometric volume" used. For anyone interested in the method used I have attached a pdf of my procedure.

 

[turf3]

Or, you can do what I do, measure from the tip of the MP to any external registration point (octave pip location, for example). The distance from the end of the shank to anything is dependent on how long the manufacturer decided to make the shank. Any of the shank past the end of the neck - in other words, on the cork - has NO acoustical function, it's just there to mechanically hold the thing on the neck.

 

[skeller047]

Point well taken. An "inexperienced" person could even come close by putting a mark on the cork where the mouthpiece ends, and then remove the mouthpiece and measure the distance from the end of the neck to the mark on the cork. When I attempted to recreate Benade's and Gebler's method of finding the "equivalent volume" on my alto mouthpiece, one of the steps was to first measure the "geometric volume" and then calculate the volume of the cylinder displaced by the insertion of the neck. Subtracting that figure gives the actual "geometric volume" used. For anyone interested in the method used I have attached a pdf of my procedure.

I put a mark on my neck cork (or my mouthpiece does it for me) where it plays in tune. The only thing that affects whether I place the mouthpiece on that mark or away from it is my calculation of how the lead trumpet player's current divorce proceedings are going to affect his pitch. That's more complicated than the missing cone calculation.

With regard to the OP's question, while all these discussions on missing cones and chamber sizes are correct they don't completely answer it. One other factor to consider (strongly) is embouchure pressure and position. Additionally there is t the effect of the player's physical makeup - your throat and mouth interact dynamically with the mouthpiece and reed, so what "in tune" looks like can be markedly different for different people.

The missing cone concept DOES come in to play with the procedure I use - I try to adjust the mouthpiece so that my horn is in tune with itself. I do this by matching the pitch between B2 (LH index finger alone) and B1 (low B) overblown. I "slur" between these fingerings until the two pitches are in tune. Then I try to play in tune with the mouthpiece there. Theoretically this is the point where the "missing cone" is replaced by effective mouthpiece volume.

In practice, this meant (for me) that I had to relax my embouchure, the side benefit being that my tone was better. It may not result that way for everyone, but usually people that have tried this approach end up pushing in a bit.

 

[MojoBari]

That is good. I sometimes check the B’s. Especially on sop sax.

On tenor and alto, I usually check D2 with my palm key D with no octave key. D2 can be sharp but this helps me lower its pitch. But if you tend to bite your palm D sharp this can be a problem with using D2. Also if this makes much of your lower notes flat, you need to compromise some. I check low Bb played as the harmonic F2 with the actual F2.

 

[skeller047]

I check low Bb played as the harmonic F2 with the actual F2.

I use that fingering on alto when I really really want to play that note loud. I particularly remember a chart in Sammy Davis Jr's book, "Birth of the Blues", it's in Ab, and in the shout chorus (band standing up) there is a whole note "F" on the lead part - I used to play it fingering low Bb, so that it rang out with the rest of the band. It doubled the trombone note and was an octave below the trumpet note, it was a great sound (great arrangement!), and the darkness of the tone helped it blend with the bones. Plus it felt bluesy I get shivers remembering that chart...