Thank you for your insights, WhistlingGuitar!
My embouchure is also weakish, so I Imagine I’d get similar results to yours.
And yes, the Midgie is sadly not very in tune with itself, in my opinion. If it were, it would be a very good whistle. I was relieved when I tried out my friend’s MK low D that it didn’t seem to have any of the tuning issues of its higher counterpart.
You’re welcome!
It’s also dependent on the day; I know I can get somewhat louder low notes, but my lip muscles are tired at the moment. I’m sure you’re familiar with that feeling too… 
Just out of curiosity, do you know if your friend’s MK is newer or older? And how did you find the high notes, were they stiff or were they pretty good to your feel?
I didn’t play higher than a high B, but the notes I played seemed fine to me! And as far as I know, he had a brand new Kelpie.
WhistlingGuitar, I like your approach to quantifying the volume difference between octaves. The figures you posted for the MK low D whistle are consistent with my experience. I have a low D MK from about 6 or 7 years ago. I have kept it because it is one of the best low D whistles I’ve played. However, I would like it better if the volume was better balanced between the lowest and highest notes. I say this not as a criticism of Misha’s whistles, but more as a criticism of whistles in general. The reasons, I think, are self evident in both the data you just posted, and the methodology you settled upon for gathering that data.
Before you all flame me for such a contentious statement on a whistle forum, let me try to explain what I mean by it. Your data shows that the loudest you can play the low notes is significantly quieter than the quietest you can play the high notes. This sounds like the very definition of an unbalanced instrument!
You then discuss preferring a disparity closer to 19/20 rather than the 23/24 of the MK. I would agree with this statement, but only in the sense that a smaller disparity is better than a larger one. But ideally, there would not be a positive disparity at all. Surely, in the ideal world you should be able to play all notes as loud or as quiet as you want. I think this notion of balance is worth keeping in mind, because that is the benchmark many other musical instruments use. I mean, ideally, it should at least be the case that when you play one note as loud as possible, it should be louder than when you play another note as quietly as possible … regardless of which notes we are talking about.
But we know that with whistles we are basically stuck having to blow harder in order to get the second octave, and that just puts more energy into the instrument. So, the higher octave notes are going to be louder than the low octave notes. But even taking this as a given, I’d prefer it if the difference was minimal. So yes, 19/20 is better than 23/24, but 9/10 would be better still, and 0 would be even better … so long as I can actually master the skill needed to keep the whistle playing in the octave I want it to play. Here, I think there is essentially a relationship between the sensitivity of the whistle and the skill/sensitivity of the player. My ideal notion of balance would have the disparity be a negative number, but its not clear how you would get such a whistle to jump octaves!
Flutes do not have this restriction though. A good flute player, with a well developed embouchure can play very quiet, delicate, high notes, or very loud, blasting, low notes. They can certainly play the bottom D very much louder than the second octave B, if they choose to do so. Also, relative to a low D whistle, a good flute player can play the low notes on a flute much louder than the low notes on a whistle. I can certainly play the bottom D on my flutes much louder than I can play the bottom D on my MK whistle. But having the capability to do this is all about embouchure development. And deciding whether or when to do it is about musicality.
A good flute player has the ability to change the speed, volume, and direction of the air flow, dynamically. Their embouchure adjustments determine the energy that goes in to the instrument for any note being played. Skilled flute players do not just blow harder to get the higher notes. Instead they tighten their embouchure to increase the air speed and adjust the direction without increasing the amount of energy being input. How much energy to input is an independent dimension of conrol.
I’d love to find that holy grail of a whistle that allows that kind of control, so that I can keep the loudness of the high notes down, and also play low notes very loud when I want to. But there are some aspects to whistle design that make such an instrument very elusive.
Sure it is, an octave vent hole is standard on multiple wind instruments with a 2+ octave range, including the most closely related instrument to a whistle, the recorder. But you already know this 
I’d love to find that holy grail of a whistle that allows that kind of control, so that I can keep the loudness of the high notes down, and also play low notes very loud when I want to. But there are some aspects to whistle design that make such an instrument very elusive.
Elusive? I’m not so sure about that: “Elusive” implies that a significant number of makers have actively tried to solve the “problem” by prioritizing the desired result of balanced octaves and they failed. I don’t recall, over the years, having seen or heard any credible whistle makers say that they experimented with octave vent hole in a serious effort to balance register volume on the whistle. Though in the back of my mind I have the thought that this is something Colin Goldie and I may have discussed years ago, but I can’t recall any details as my memory isn’t what it once was. Also wouldn’t surprise me if he had been successful.
Regardless, I can’t help but wonder if there is a perception that the market won’t bear whistles with thumb holes, which is one reason why you don’t see effort going into producing such a “device” - a term Glenn Schultz sometimes humorously used in reference to a whistle.
Paddler, you have the tools and skills, get cracking! Crank out a few bodies to fit your favorite whistle head and start drilling octave thumb holes man! What’s the addition of one measly little air column node? Child’s play I say!
Question for those of you who currently own or have previously owned whistles with a thumb hole for the Cnat or equivalent scale note: Have you ever tried using that hole as an octave vent hole to avoid over blowing the 2nd register? NOTE: For this to work you’d likely need to just barely vent the hole, leaving it around 90% covered. I doubt the Cnat hole is in the correct location for proper tuning in the 2nd register, but I’m curious if, with proper technique, venting that hole avoids the need to overblow. I’ve never owned a whistle with a thumb hole, otherwise I’d have already tried this myself.
I think the use of an octave vent hole is a great idea Loren! Basically, attack the problem by (a) building a properly balanced instrument that has the potential to play louder low notes than high notes, and then (b) require venting to get the high notes. It has been such a long time since I played any recorders that I had actually forgotten about this approach being an option. Of course, I am very familiar with venting to get second octave D on whistles and flutes, and to get certain third octave notes on flutes, by opening a small keyed tone hole high on the bore, but I’ve been operating under the assumption that the proper location for such a hole is very much note dependent, i.e., needing to be located close to the pressure node for the note, which varies in location from one note to the next.
The other approach to the problem is to build a whistle that has the window positioned such that the player can shade the window with their lips when they want to pump more air into to the lower notes and have them not break up to the next octave entirely. An example of this approach is the fipple based kavals that Winne Clement makes, where the windway is short and the window is rotated underneath so that it can be shaded, as much as is necessary, by the player’s lower lip:
https://www.youtube.com/watch?v=XTSEEL7jRrw
This gives the player some minimal amount of dynamic embouchure control, allowing them to access low notes in a way similar to the hard D on the flute, where you can crank up the energy while retaining enough of the lowest partial to allow the human ear to resolve the note low even though a lot of energy is in the higher partials. I think this can add to the options for expression when playing the lower notes.
I don’t see any reason why both strategies could not be used together to get more balance.
FWIW a cane pinkillo/pinkuyo (https://en.wikipedia.org/wiki/Pinkillu) that I have has a thumb hole up the tube from the top hole by a little less than the spacing of the top two holes. I assume it’s an octave hole though the little book I bought with it makes no mention of it and instructs to get the second octave by overblowing.
I got a ‘same brand’ quena at the same time (late 1970s in Buenas Aires) which is exactly the same but with a quena notch rather than the whistle-like windway-window-ramp setup on the pinkillo.
I suppose they could be tourist items, but they came from a music shop rather than a stall at the airport.
I personally would love a whistle with a venting hole. Clover Flutes makes one of these, but I’ve never tried it.
I think my ideal whistle would be something like a Busker, but with a thumb hole to make the second octave less harsh. I’ve even thought about modifying my Busker some day, if I can get the tools.
Well, in that case, the MK would seem to be well suited to you. I’m still really curious though, if anyone has a Goldie, would they mind testing it? I want to know, just for my own information, how they compare in volume difference to the MK.
Thank you for the kind words, paddler! Just my initial thoughts on your search…
Before you try modifying whistles to add a thumb-hole, can someone with a recorder verify that they do indeed produce a high B with consistent volume to the low D? I thought I had a recorder lying around, but I searched around and couldn’t find one. Just from what I remember, I’d hazard a guess that there’s going to be somewhere between a 13 to 15 dB difference, but that it will still be louder than the low notes. My (potentially mistaken) impression was that the octave vent reduced the air requirements significantly, but that the upper notes still took a bit more of a push than the bottom ones. Perhaps, like you said, you could design a mouthpiece in conjunction with the thumb-hole that could be changed while you’re playing it. I seem to recall that some other members have shown similar interest in such an endeavour too…
Since we’re already modifying the whistle so substantially (making an adjustable mouthpiece, adding a thumb-hole), why not use a fife? Tony Dixon and I’m sure other makers sell a fife head for a high D, and it seems to me that on a high instrument, tonal qualities should be fairly similar to a whistle, only now with the possibilities of adjusting the embouchure with a lot fewer moving parts. Obviously if you don’t want to play a fife and would prefer a whistle-ish instrument, that’s fine, but I just wanted to throw it out there as a simple option for those looking for more control of the octave volumes.
So, I looked into this a bit already. Not actually making anything, but researching a bit into how recorders actually work. The octave vent thumb hole does not, by itself, solve the problem … especially for the highest notes. The effect of venting is more complex than it may appear. The thumb vent hole is not like a switch that can be used to jump all the notes up to the next octave.
The way venting works is as follows. Every note has its own wave pattern of vibrating air in the bore. There are points along the bore where the pressure fluctuates but the air does not move (these are pressure nodes) and there are points where the air moves back and forth but the pressure remains constant. When you place a vent hole at the location of a pressure node the pressure in the bore can not increase, and this prevents the note that has this wave pattern from forming/playing.
Roughly speaking, when you play the bell note of a whistle or recorder, the air moves in and out of the window, and in and out of the foot. But roughly half way between these two points, about half way along the bore, the air isn’t moving at all. At this point the pressure is rapidly rising and falling (at the frequency of the note). By placing a thumb hole at this location it gives the player the option to vent that pressure node and hence prevent the lowest note of the whistle/recorder from playing. The whistle will then play the next note that will resonate at this bore length, which happens to be the next harmonic, one octave up.
But when you take a different note, like B on a whistle, say, the location of its pressure node is not in the same place. Again, roughly speaking, it will be about half way between the window and the first open tone hole. So it would need a vent hole much higher up the bore. The same is fundamentally true for all notes .. their pressure nodes are all at different positions along the bore. Hence, to cause them to jump a harmonic will require vent holes in various different locations.
So how does a recorder work then? Well, for some notes you vent in order to jump up an octave. For others you over blow to jump up an octave. And for yet other notes you vent by opening a different hole (one of the regular tone holes) to jump an octave, i.e., by cross fingering, (because that other tone hole just happens to be located where the pressure node lies). And for some notes you blow not the first harmonic, but a higher harmonic, and then also vent to reach the note you want. Interestingly, because you are blowing a higher harmonic, that note has more than one pressure node in the bore, and hence you can vent at the one nearer the foot.
So it is a very sophisticated design in which the bore profile is carefully designed to tune the harmonics, and the tone holes also carefully placed, based on that bore design, to allow a wide range of different venting options, via cross fingering patterns, to hit the pressure nodes of notes, with various different harmonics, in order to reach the full range of notes that the instrument supports.
So, even though a whistle is not fully chromatic, it would definitely not be as simple as just drilling one small thumb vent hole and using it as a switch to jump the whole instrument up an option.
And, by the way, Loren, I know that is not what you were implying by suggesting utilizing venting. For those of you who don’t know Loren, let me just point out that his career was spent making very high-quality recorders, so he knows far more than I do about how recorders work!
I do think the idea is worth pursuing, though, but it won’t be easy to design a whistle that works this way. It would not only require a careful bore design and tone hole lattice design (perhaps involving two thumb holes?), but it would also require players to be open to using cross fingering for a variety of notes in the upper octave. I think this latter issue is probably more of an obstacle to acceptance than the thumb hole.
So just to try to pull this back to the topic of the original post, I believe we were talking about low D whistles, not high D. So the alternative you suggest would be a flute head not fife. But this last part of your post reminds me that, even though I am primarily a flute player and maker, when it comes to pitches up around high C or D, I would actually rather play a whistle than a piccolo. On the other hand, for pitches lower than G, I would definitely rather play a flute. I’m not entirely sure why this is, but I will say that the embouchure requirements for playing a high D piccolo well are fierce. I also think that whistle makers have found it easier to balance high whistles than low ones, and I’m really not sure why this is the case. It might simply be that low whistles are a relatively new instrument and probably haven’t gone through as much refinement in their design, particularly balancing bore size, window and windway parameters.
And to come all the way back to the original topic, I find it interesting, but not surprising, that Colin Goldie offers a variety of options in terms of windway height etc. I don’t actually have a Goldie low D, but I have played several of his other low whistles, and every time I encounter one of his instruments it is clear to me that he is right at the leading edge of whistle design. If I were going to buy a low D whistle I’d probably go for a Goldie. It seems like a safe option for getting something close to the best available.
Wow! The nerd in me can’t stop grinning as I read your explanation, thank you!
Point taken about the high vs low whistle and piccolo vs flute. Perhaps to simplify the design of this quasi-whistle one could combine overblowing and a thumb hole? Most whistles I know are quite sweet up as far as octave G, and really ramp up the volume quite significantly from there. It would be an imperfect compromise, but if there’s only one octave vent for, say, the high B, or even the high A and B, since I imagine their pressure nodes are pretty close together, then that should simplify the bore design and reduce the cross-fingerings quite significantly, I would imagine.
My apologies if my suggestions are somewhat rudimentary and have already been considered. I’m still learning a lot about woodwind acoustics, though I’m enjoying it immensely!
Also, I agree. The next time I get a low D, I plan on it being a Goldie, they just seem to be consistently great.
I like this line of thought. I think the challenge, though, is mostly ergonomic. For example, when you plot out the location of the pressure nodes for notes such as A or B, they are quite a long way up the bore. As a rough estimate you could measure the distance between the window edge (labium) and the second tone hole (which is what vents first octave B), and then take half that distance measured down from the labium and make a mark on the back of your whistle. This is roughly where the high B vent would be. Now see how comfortable it is to play your whistle while always keeping your thumb over that mark. As the whistle key gets lower, the distances get larger and the vent hole seems more out of place.
Of course, a lot depends also on the size and flexibility of your hands.
A different approach would be to abandon the idea of getting high A and B via the second harmonic and instead try to get them via the third harmonic, perhaps by venting tone holes or an additional lower thumb vent, lower down the tube. A lot of flutes allow you to do something like this, playing the second octave notes by leaving your left (upper) hand tone holes covered, and only opening or closing the right (lower) hand tone holes. To go above G you have to jump up to the third harmonic with your embouchure.
Another aspect of all of this has to do with the method you employ to make the lowest notes louder. For example, if you do this by making the bore fatter, it may be the case that the high B is going to be loud/uncomfortable regardless of whether it is overblown or vented. Fatter bore aspect ratios make it harder to blow the harmonics. This is why overtone flutes/whistles have a bore aspect ratio of 1:50 or so. So I think some experimentation would be necessary to explore different strategies for making the low notes louder, to see what impact they have on vented high notes, and the ability to utilize higher harmonics.
Then why is it that recorders use a venting hole about halfway down the entire bore to play high A? High A won’t even play on some recorders without partially uncovering the back-D, which doubles as a venting hole. If that’s not the acoustically correct position for venting A, why does it work so well on the recorder?
So how does a recorder work then? Well, for some notes you vent in order to jump up an octave. For others you over blow to jump up an octave. And for yet other notes you vent by opening a different hole (one of the regular tone holes) to jump an octave, i.e., by cross fingering, (because that other tone hole just happens to be located where the pressure node lies). And for some notes you blow not the first harmonic, but a higher harmonic, and then also vent to reach the note you want. Interestingly, because you are blowing a higher harmonic, that note has more than one pressure node in the bore, and hence you can vent at the one nearer the foot.
This is confusing. I’m no expert when it comes to recorder, but I played it seriously for a couple of years, and it never seemed to me that it worked like you’re saying. The recorder seems to use the same venting hole for most notes in the second octave. As I mentioned, you use that back-D hole to vent high A. But you have to use that same exact hole to vent second-octave G, in order to play it quietly and in tune. And while venting that hole isn’t necessary for E or F, it makes those notes quieter.
For notes above high A, of course, you have to use a different harmonic, so you end up using cross-fingering, as you say. But for all the notes below that, you use the same hole. (Of course, the hole needs to be covered different amounts, depending on which note is being vented; but you still use the same hole for all of them.)
So unless I’m missing something, it seems like the same hole can be used to vent a bunch of different notes. And if all this works on recorder, why couldn’t it also work on whistle?
A different approach would be to abandon the idea of getting high A and B via the second harmonic and instead try to get them via the third harmonic, perhaps by venting tone holes or an additional lower thumb vent, lower down the tube.
Interestingly, using third harmonics already works on some whistles, and it sometimes produces a more in-tune note than using the second harmonic. I use recorder-fingering for the high B on my Kerry Busker whistle (which, correct me if I’m wrong, is some kind of vented third harmonic), and it produces a much more pleasant high B than the normal fingering.
So, even though a whistle is not fully chromatic, it would definitely not be as simple as just drilling one small thumb vent hole and using it as a switch to jump the whole instrument up an option.
And, by the way, Loren, I know that is not what you were implying by suggesting utilizing venting. For those of you who don’t know Loren, let me just point out that his career was spent making very high-quality recorders, so he knows far more than I do about how recorders work!
Huh. In that case, I really wonder how David Furman from Clover Flutes makes his venting hole work. As I mentioned, David makes a whistle with a venting hole, which he says is to make the second octave quieter. I always imagined it worked like a recorder’s, and made all the notes up to high A quieter and sharper. Maybe it only works on one or two notes?
I second this. Even if a venting hole only worked for high A and above, it would be very beneficial.
The quena has a thumb hole that works for venting, but quena players don’t use it that way as it provides no advantage - it introduces additional low hissy sounds that are off the note instead of them being an octave lower than the note being played, and once you’ve heard the difference, you notice the recorder producing those ugly hisses off the note too when venting. I was experimenting yesterday with a quenilla with added fipple to compare the volume of vented high notes to their unvented equivalents and there was hardly any difference (and yes, I kept far enough away from the microphone to avoid hitting the 90 decibel limit that you get on a phone). I’d prefer to control the volume disparity by having a variable width windway, and maybe the control for that should be sideways movement of it rather than having to push it harder against your mouth which would upset the handling.
The behavior you describe is not surprising. First of all, a vent hole that is not close to the pressure node of the note being played is going to have a very different effect than one located near a pressure node. At or near a pressure node, it will prevent the formation of the lower harmonic without stealing energy from the higher harmonic. A good example of this is venting the highest tone hole on a whistle to get second octave D. You get a nice clean tone with little to no energy loss. Once you are away from the pressure node location it will basically just act as a leak in the bore, leaking energy and creating the opportunity for the bore to resonate at a different frequency, or perhaps a mix of frequencies. I think this is what you are hearing when you try to use a single vent hole for many different notes.
The other thing that is very different about the quena family of instruments is that they have very large tone holes, sufficiently large to effectively terminate the bore length, regardless of the frequency. In contrast, a recorder has much smaller tone holes that are sized such that they terminate the bore for low frequency notes, but not higher frequencies. This is why cross fingering works in the higher registers: the lattice of tone holes below the first open tone hole has a significant effect on higher notes even though it does not on lower notes.
You can clearly see these cross fingering effects, and the sensitivity of higher frequency notes to the lattice of tone holes downstream of the first open hole in this recorder fingering chart:
The second octave A and B are a clear example of what I’ve been talking about. You can see that in order to raise the pitch from A to B, you actually close some lower tone holes while leaving the upper tone holes the same. What you are doing here is creating a longer effective bore length for B, and then causing that longer bore to resonate at a higher harmonic. Closing the lower tone holes enables that harmonic to form when it would not do so with them open. And the remaining open tone holes in the B fingering provide the venting necessary to prevent the formation of lower frequency harmonics that would otherwise be able to form in this longer bore. If the tone holes were enlarged to the size of those on a quena or some modern whistles, this whole strategy would not work, because the tone holes would terminate the bore length for all frequencies that the instrument plays. Boehm’s redesign of the flute with extremely large tone holes was an example of this radically different approach, and since cross fingering wouldn’t work any more, and the tone holes were way too large to cover with fingers, it ended up with a large number of tone holes that are all keyed.
Anyway, the ideas I have outlined are not new or controversial. Recorders share a lot of the same design principles as baroque flutes, which are also dependent on cross fingering and very careful manipulation of harmonics. These designs grew out of practical experimentation over a long period of time. The theoretical foundations that explain how and why they function the way they do came later, but they have also been published and well understood for well over 100 years now. British physicist Lord Rayleigh was a pioneer of the theoretical underpinnings of all this, and he publishing his work on acoustics and resonance as early as 1870, work which still forms the foundations for modern acoustics theory.
Instead of using a thumb-hole, in order to improve the ergonomics it shouldn’t be particularly challenging to design a simple key operated with the thumb, and to have, say, two keys for two different pressure nodes. That should solve the problem both of ergonomics and a limited number of thumbs. Also, it creates the interesting possibility of venting two holes at once. Someone with more knowledge than me will have to say what effect that would have, but would it potentially vent a third pressure node somewhere in between the two established holes?
The possibility of the third harmonic is interesting and potentially a solution to the problems, but in order to keep the fingering as simple as reasonably possible, I feel like it would be best to keep it to two harmonics and use a couple of simple keys to activate multiple pressure nodes.
The traditional tapered bore starts with a wider area near the windway and tapers down towards the bell-note. What happens if we reverse the taper, and have a wider bell-note and a narrower top section?
Very interesting! I guess that’s why venting works on multiple notes (with varying degrees of effectiveness) on the recorder. I still wonder if a venting hole similar to the recorder’s could be added to a whistle with similar effects. The recorder’s strategy of using one hole to vent multiple notes may be flawed/imperfect, but I still love that it allows you to play much of the second octave relatively quietly. I’d love to see this on a whistle.
The second octave A and B are a clear example of what I’ve been talking about. You can see that in order to raise the pitch from A to B, you actually close some lower tone holes while leaving the upper tone holes the same.
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If the tone holes were enlarged to the size of those on a quena or some modern whistles, this whole strategy would not work, because the tone holes would terminate the bore length for all frequencies that the instrument plays.
But interestingly, this strategy does work on many whistles! It actually works best on my Kerry Busker, which is my largest-holed whistle. I can get a much better sounding high B with XXO XXO on it than with XOO OOO.
The odd thing is that it doesn’t seem to work on my whistles that have a small bore-to-length ratio. On my whistles with a larger bore-to-length ratio (including those with relatively large holes), it seems to work. No idea why this is.
But then again, this is without venting, so maybe it doesn’t speak exactly to what you’re talking about. I also suspect that quenas have larger holes than even the largest-holed whistles.
I’m pretty sure that would cause the entire second octave to be extremely flat. My understanding is that taper causes the second octave to sharpen, and reverse taper causes it to flatten. (Correct me if I’m wrong here, paddler.)
To understand the effects of different bore shapes you really need to dig into the acoustic theory and understand Rayleigh’s rules. I can’t give a full treatment of this in a forum post, but I can hopefully give you the gist of what is going on.
So before I was talking about pressure nodes, which are the points in the bore, for a given note, at which the air is not moving, but the pressure is varying. Well, there are also pressure antinodes, which are the points at which air movement is maximal. For first octave notes there will be two pressure anti-nodes, one at the window/embouchure and one at the foot or first open tone hole. If you constrict the bore at a pressure antinode it will have the effect of lowering the pitch. You can think of it as slowing down the air flow which prevents it from resonating at such a high frequency. This is why shading the window lowers the pitch of a note, and why making a tone hole smaller lowers the pitch. But it is also the case that if the bore is constricted at that location it will also lower the pitch.
So, when a conical bore flute or recorder has a reverse taper in the body it has the effect of progressively lowing the pitch of the notes. This allows the maker to move all the tone holes up the bore proportionately to regain the original pitch, and hence improve ergonomics. Or a maker can take into account that a player might want to blow the lower notes a bit harder to compensate for their lower volume, and hence leave them pitched slightly lower than the higher notes on the tube (because blowing harder on a recorder has the effect of raising the pitch). This is one of many trade-offs that a maker can select from, and it will influence how the player interacts with the instrument.
But it is important to understand that tapered body flutes and recorders do not have a uniform taper all the way to the embouchure/window. The head sections are cylindrical. So for high frequency notes that have a pressure antinode located in this head section, there is not a lowering of pitch. In other words, the differential in gradient of taper in different parts of the bore has a selective effect on different notes, and can be used to stretch the octaves. In high quality, highly refined, instruments this bore profiling is taken to extreme lengths and the bore exhibit areas of constriction and areas of expansion that deviate significantly from a linear taper. This is how bore profiling can be used to selectively tune specific notes and harmonics. It is a complex process, but it is used extensively in the best instruments.
So all of this works for cylindrical and reverse tapered bores, but bores that taper in the other direction (getting progressively wider toward the foot) do not behave the same way, and in particular do not tend to have harmonics that are in tune, which is why they are not used in woodwind instruments that have bores open at both ends.
The other thing to look into if you really want to understand this stuff is “end correction”. The acoustic length of a bore is actually a bit longer than the actual length because of the acoustic impedance at the open ends. The end correction, which is the additional length of the bore acoustically, determines where the actual pressure antinodes lie, just off the ends of the pipe.
If you are interested in a visual illustration of what I was talking about earlier with pressure nodes and the use of harmonics in the different notes on a recorder, Philippe Bolton has a very nice illustration here:
Thanks for the explanation, and the link to the illustrations, paddler! That makes a lot more sense now. Looking at where the velocity nodes fall in the diagrams, it would seem to be possible to create a couple of vents at different locations, and use keys to activate them.
I just tested on my MK, and while XXO XXO works, it has a nasty undertone. However, XXX XXO, the same as E, does have an overblown harmonic that produces an in-tune B without any significant undertone. It also is quieter, now with a spread of about 19 dB.