One of the primary causes of instability is that the octave pip for D2 serves several other tone holes. What we are fighting isn't that the D2 tone hole is too low on the body tube (or the pip too high), it is that the octave pip placement is a compromise. The idea of creating an octave pip for every key has been done, but it has its limitations (hence the article's term Frankinsax for the "pipped out" horn). The body tube octave pip on every normal saxophone is too far from D2 and too close to G#2, all of which area the second pip is supposed to service. The pip being too far or too close effects the pitch. Too close makes the note flat and too far away makes it sharp. The size of the pip opening, the size of the tone hole, and the height of the pad can also alter pitch.
Before I get back to a sharp or stuffy D2 issue, I'm going to effectively "move the octave pip" for E2. First, blow low E1 and then use your octave key. Your low E might be a couple of cents sharper than E2. That's because the pip is also too high on the tube for E2. We know that by comparing the pip location to where the pad for E3 is located. The E3 tone hole is actually the correct mathematical and acoustical placement for an E2 pip, but since we have only one pip serving several notes, a compromise is made. (One could argue that it isn't the number of octave pips that is the problem, it is the player's limited number of fingers.)
We can use the palm E3 key as though it were a correctly placed octave pip. Play E1 using your pinky and ring finger to push down F1 and E1. That leaves your index finger to operate the side E3 key as the new octave pip. Play E1 and press side E3 instead of the octave key. It should work perfectly for E2. Actually, it works too good because it over-vents because of the pad size. If you just barely crack the side E3, you will get a note that is in tune. If you open it completely, it goes a little sharp, or it goes sharper. So the size of the pip opening also affects pitch.
We now see what happens when the octave pip is too high or too low on the body tube. Play E1 as before and crack open the F3 palm key. Instead of a nice E2, you now get a sharp E2, which is the result of the "octave pip" being too far away. Play E1 and crack open the palm Eb3 key. Now instead of E2 you will get something considerably flatter. That's the acoustical problem in sax design that is compensated by pip placement, pip opening size, tone hole placement, tone hole size, key heights , and who knows what else. But it is always a compromise. Also notice that each of these is just some form of "venting." More venting, less venting, venting higher or lower on the body tube.
We can do similar experiments for an unstable D2. If D2 is unstable and you press the C# LH pinky key (a common remedy), that is adding additional venting lower on the horn. It is kind of a clunky solution for the player, but workable. In an attempt for a less clunky solution, some raise the low C pad as another way to increase venting lower on the horn without pressing additional keys. This works, but it doesn't really help if D2 is also sharp, in fact, it often makes the note louder and sharper. Less stuffy, but not really an improvement. One of the other low tube venting fixes is to put a "cresent" in the C tone hole chimney to effectively make the body tube longer when sounding D2. Of course, this also lowers the pitch of low D1, and then compromises must be made with the pad heights to try to get D1 sharper while getting D2 to remain flatter. Sometimes this works.
If D2 is stuffy and you press the D3 palm key, that is adding additional venting higher on the horn. This fingering is even clunkier, but often works better. Some have drilled out the upper pip hole as a way to increase venting higher on the horn with just the standard fingering. I've seen some claims of success, but I tend to be skeptical of many of these improvements. For one thing, many who initially have a stuffy D2 issue report that it goes away after some hours (or days) of playing. Practice, practice, practice actually has an effect. That make it a little difficult to be certain that a drilled out pip or piece of something glued into a tone hole is actually the fix. It could be that getting familiar with the horn was the actual fix.
A third solution, not often mentioned, is changing the mouthpiece. Because D2 is the least stable note, that is a spot where an acoustical mouthpiece miss-match will often show itself. Spread octaves can also result, but this is often worked around with practice. A mouthpiece that effectively magnifies the instability of D2 is a more time consuming work around.
As noted above, sometimes stuffy D2 seems to go away on its own. Or, you can try a long list of "folk remedies." We all know practice, practice, practice. But there are others like blow warm air, or pretend that there is honey under your tongue, or push your chin forward, or flair your nostrils, or think of England, etc. (Do not try these all at once). I think that through adopting these various fixes players can reinforce a Pavlovian response so that every time they get to D2 they radically change their embouchure and breath support. Don't worry about those people who swear by these fixes being offended by me calling them "folk cures." Those people aren't reading this, they are too busy practicing.
There is nothing wrong with practicing. However, I think that there are more important things to practice than getting a stable D2 or eliminating a warbling D1 if there is another way (i.e., a mechanical way) of eliminating the instability. And I don't mean to imply that D1 and D2 will ever be exactly the same when doing an octave trill, just close enough that you don't have to think "embouchure and breath support" every time you play D2.
Usually all we need is to get D2 and D1 closer together. Play D1 and slowly trill back and forth to D2 by using the octave key. You might have a 15 cent change in pitch and a big change in resistance and tonal quality on a problem horn. D1 tends to play in tune with the lower stack and is more in tune with the upper stack than is D2. That means that D2 is the outlier and you will need to remember to change your embouchure and breath support every time you hit that note and back again every time you play a subsequent note after D2. But if we can get D1 and D2 within 5 cents, then we can effectively ignore the difference, which is what we want.
I'm not going to move the pip. Moving it closer to the low D tone hole would make D2 flatter, but make G2 sharper. I'm not going to drill out the pip, although some claim that it can be a remedy for stuffiness. I'm not going to move the tone hole. That leaves me with adjustments to tone hole size and key height.
We can flatten the pitch of D2 by adding a cresent to the "up stream" side of the tone hole used to produce D2 (the C tone hole) That effectively moves the tone hole further down the body tube. If the problem is that the tone hole is too far away from the body pip, a cresent overcomes the sharpness by overcompensating on the tube length. It will also make D1 slightly sharper, but maybe not enough to be objectionable.
What if, instead of making the tube effectively longer, we made it effectively shorter? Well maybe not shorter, just sharper. If we put the cresent on the furthest edge of the tone hole (i.e., on the down stream side), it reduces the size of the tone hole but it doesn't increase the effective distance between the pip and the tone hole, which we have sort of determined as too long for D2. So what does just reducing the size of the tone hole do for us? This is where things get wonky. Reducing the size of a tone hole has the effect of lengthening the tube. Again, a smaller tone hole will also have the effect of making D1 slightly sharper, but again, maybe not enough to be objectionable.
Here I am halfway through this blog and I'm still talking about octave pip positions and gluing stuff in tone holes. I haven't even gotten into adjusting key heights, another "fix" that might have an effect. As I said above, unless every player that has your model of saxophone has the same problem, we are probably "masking" a problem, not "fixing" a problem. What we need to examine is the "cause," not the fix. If other players don't have the issue with pip placement and tone hole size, then those are not really the cause even though monkeying with that stuff can improve things.
What is weird about the two common, and to seemingly opposite, solutions often working (fingerings that increase low vent or increase high vent) is that neither one of them is likely the actual cause. They might mask the problem, making us think that lower (or higher) venting was the issue when it wasn't actually the problem. These fixes are the same as changing pip size and location, adding cresents, and adjusting a key pad heights.
Saxophones being what they are (a tube with an effective length adjusted by sealing consecutive openings), it is safe to say that the "seal" part of the adjustable length is going to almost always be the issue. If your brand of sax is common enough, and other players don't have the same issue, then you cannot blame the design of the sax. Maybe you can blame your mouthpiece if it is radically different from what other players are using. Maybe it's your personal embouchure, oral cavity, lung capacity, etc., but now we are getting pretty far afield from what is likely causing your pitch problems.
My experience has been that, sooner or later, I will come across the actual cause of a stuffy, weak D2 or a warbling D1 (and below). And the root cause has always been a leak. For some reason when told this a player's first response is "My horn doesn't leak!" Maybe it just got back from the shop and the tech told them that it doesn't leak. Maybe it has a couple new pads or all new pads. Maybe the player spent hours with a leak light. Fine. But far and away the number one cause of a weak or unstable D is a leak.
If you are lying in bed and find that water is dripping on you, is there a leak? Your roofer says there isn't a leak and water is still dripping on you. Is there a leak? If the Google solution is to cover your roof with a blue tarp, have you fixed the problem? How about just covering your bed? Fixed?
If we accept that the cause is a leak, then here are some places to look (in no particular order). As I said way back at the start of this blog, when I started making a list it got very long and often included some of the "blue tarp" solutions that I have already mentioned. Here are places where a surprisingly tiny leak can wreak havoc on D2. Keep in mind that these leaks are affecting other notes, it's just that D2 being the least stable is affected the most.
I've found that the leaks that are most likely to affect D1 (warbling) are those near the "would be" correct position of an octave pip for that note. Leaks further down the sax tube can make for a weak response, but not unstable warbling. The most difficult to detect is a neck tenon leak. Because of the distance the air travels (actually vibrates) out from the neck tenon, the effective leak is further along the neck than you would think. In fact, the leak around the neck tenon might not be in a straight line, meaning that air could travel around the back of the tenon and out the top of the tenon on the opposite side. A leaking neck tenon may have the same effect as a leaking lower pip, even though the lower pip is several inches further down the horn. (Although further down the horn, it is the "air path distance" that matters, so a tenon leak has the acoustical effect of a pip about 2 inches below the joint).
The lower pip is placed where it is most effective to break the harmonics and cause low notes to jump up an octave. A tiny leak there (or effectively there) can cause warbling from E1 on down. If the warbling starts low or is only low, then I would be suspicious that a leak is acting as a "false octave pip" or "ghost vent" in a corresponding upper key. For instance, if the side Bb2 key not sprung tight enough that can cause Bb1 to be unstable and warble (because it almost wants to jump an octave).
Likewise, if D1 is unstable and shaky but the surrounding notes seem better, first check the upper D palm key, the natural place for the D2 octave vent. I fought with a warbling D1 on an old tenor. I just could not play softly without a soft pulsating vibrato (that wasn't me controlling the vibrato). A small chamber mouthpiece helped, but that's not what I wanted to play. It turned out the the palm D3 key had a very light spring on it. The pad didn't leak light, but apparently playing D1 caused enough vibration at that point such that the pad leaked just enough air to cause D1 to almost jump to D2. One would think that playing at volume would really make D3 leak, but that didn't seem to be the case. At volume, I was in control of the D1 pitch. At ppp, it always felt like D1 was in control of me. A new, stiffer spring changed that.
Probably enough rantings about warbling D. Hopefully, it can give somebody a clue where to start the search.