From your statement, is it correct to assume that you are adjusting the "length" of the saxophone by getting the long tube D octaves in tune with one another and adjusting the "mouthpiece volume" (missing cone) by bringing the short tube B octaves in tune with one another?
Not quite. You're finding the correct missing cone volume first by matching the Ds. Then you're adjusting mouthpiece pitch (by adjusting chamber length for that volume by changing chamber size) to get the B and above in line with the rest of the horn.
It is not clear to me whether "if top B is sharp" means above A=440 or sharp in relation to the B an octave lower. Can you clarify your statement? In other words, at what point in the process is the tuning done to a standard pitch and not just bringing octaves in tune?
In relation to the octave below it. We're checking the 'width' of the octave.
I find mouthpiece volume and the "missing cone" totally fascinating and have studied Benade's writings on the subject. In fact, I have taken part in numerous discussions that address the importance of mouthpiece effective volume vs length of the instrument as measured to the tip of the mouthpiece in saxophone tuning. Any information that you can share in this area would be appreciated.
I also find it fascinating. Have a good look at Rocaboy. His study on the Basson reed cycle makes all of this obvious. I'll try to sum up how I think it works (but lets try not to retread old ground only with me standing in for Lance this time):
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The sax is shaped like a cone with the end cut of to put a mouthpiece on it. It will play mostly in tune when the volume of the mouthpiece matches the volume of this cut of end of cone. This is what matching the Ds fits.
Everybody knows there is a standing wave that reflects from the reed to the end of the sax. There is
another standing wave from the reed to the end of the mouthpiece (which behaves as a helmholtz resonator, with some length of the neck being the port). This wave influences the lengths of the open and closed portion of the reed oscillation, but it doesn't hugely affect the pitch of the sounded note until that note is at or above the frequency of the mouthpiece. Which, on most horn-mouthpiece combinations, is somewhere around B above the staff. So if the mouthpiece pitch is higher than required, it will make the top end sharp. So it needs bringing down. How do you make a mouthpiece pitch lower? Lengthen it. How do you do that and keep the volume the same? Narrow it.
I think it isn't just the perceived pitch, either. The mouthpiece pitch should pull up or down all the overtones in is vicinity as well, which will make pitch and tone less stable, reed response more sluggish, it affects everything. You'll know everything lines up properly when the horn sings effortlessly.
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I don't think this is any more info than what we have been talking about for a couple of years now, I just hope its concise and clear enough (and correct, FTM). I have made pieces like this for several professional players and serious students, and used while designing my own mouthpieces that I manufacture. So whatever the reason it works, it obviously works. I feel like I should reiterate that this isn't much of a solution for developing players. Until you can produce a professional sound your chops will hold you back more than a slight acoustic mismatch between horn and mouthpiece.