Yes, I had wondered about that. Undercutting as a way of raising the second octave relative to the first has come up several times in discussions here. IIRC one experienced PVC flute maker says to undercut the side away from the foot to get this effect.
I haven’t seen an explanation of this. Is it something to do with pitch-dependant end effects, or cutoff freqencies?
Bore diameter must play a part in this. I have seen information about impedance but that maths is above me. I see talk that a smaller bore makes the second octave easier to play, but does it make it sharper bringing the tunig up to meet the first octave, getitng both in tune?
If it’s a matter of getting the right internal bore diameter to achive perfect, or at least very good tuning in both octaves, then how on earth does a maker get the second octave in tune with a wide bore, without pertubations and other modicications.
I would love to have another go at making a pvc whistle, but right now I would just be wasting material.
Currently, I stand by my original statement at the start of the post since there, so far, don’t seem to be any explanation on how this tuning is achieved.
You mean other than blowing harder for the second octave? Works for me. I don’t like it which is why I mainly play flute.
Yes indeed, pushing 25-30 cents out of a large bore is not feasible way to get an instrument in tune in the second octave.
As I said earlier, you can raise the second octave tuning by either acoustically enlarging the tone holes or by blowing harder. Reducing the wall thickness and undercutting are two ways to make the tone holes acoustically larger, the other is to actually make the holes bigger. The tone hole size required to terminate the bore for all frequencies is bore diameter dependent, so reducing the bore diameter while holding the tone hole size constant, does change the second octave tuning somewhat.
You have to understand the effect each of these changes has relative to the others and then balance them all to achieve your goal. If you fix something, such as tone hole size, or wall thickness, or bore diameter, it may well become impossible to achieve all your goals in terms of tuning, dynamic balance, and ergonomics.
In my opinion, achieving a perfect balance between all these issues is much more achievable with a flute where you have more embouchure control to manage the dynamics.
When you undercut a tone hole you are making it larger on the bore end, which makes it acoustically larger, which sharpens the notes it vents but more so in the second octave, because different frequency waves perceive it differently. Undercutting also repositions the point at which the tone hole intersects the bore. If you don’t want to move this point further up the bore, then undercut only on the foot side of the hole. This will mostly sharpen the second octave and minimize the impact on the first.
Why not just make a whistle with said perturbations? Or a wedge?
Nearly all of my favorite whistle brands have perturbations anyway. It’s a method that works, so go for it.
(Interestingly, there’s also nothing ahistorical about this approach. I’ve found images of cylindrical whistles from 100+ years ago that have perturbations in the form of pinches in the head.)
But this has all kinds of secondary effects on other things, such as tuning.
It seems to me it can’t be the case that every flat-in-the-second-octave whistle could be easily corrected simply by “making the holes bigger.” If the solution were that simple, the problem wouldn’t be so ubiquitous.
So is it possible that a lot of whistle makers can’t find a way to make the holes big enough while, say, preserving tuning, leading to this problem existing in most cylindrical whistles?
It is the case that making the tone holes large enough will terminate the bore for all frequencies, meaning that the second octave is not inherently flatter than the first, due to the bore shape and dimensions. But this doesn’t guarantee anything about the ergonomics, volume balance, or effects on tuning balance of blowing harder in the second octave than the first. All of these things need to be balanced, and they all impact each other.
So I’m not claiming that there is an easy fix. I’m really just shedding some light and explanations on the OPs original claim that it was not possible to achieve in tune octaves with a cylindrical bore whistle. That claim was false, but there are constraints and tradeoffs. I was just trying to be explicit about what these are.
Enlarging toneholes to the extent of correcting a flat second seems to make the instrument unbaringly shrill
Thanks paddler, very succinct.
Yes, and this may be a motivation to look either at a smaller bore size ( so bore termination can be achieved with smaller tone holes) or bore perturbations so that second octave pitch can be raised independently of first octave pitch.
Trade offs and constraint, thanks thta makes sence. So really the original claim is true to the most part, and you are saying there are unfortunate compromises to be had. Some great info in this thread 
I think your original claim was overstated, but I can relate to the underlying sentiment.
Fundamentally, I think it boils down to having to make tradeoffs among a set of constraints that lets you achieve what you want in almost all dimensions, but not all.
If you want to have your cake and eat it too, use a flute instead of a whistle, but accept the fact that you will have to learn to play it well.
If you stick with whistles, then be prepared to go down the rabbit hole of experimenting with many almost identical bore sizes, tone hole sizes, and head designs, searching for that magic sweet spot that might well not exist. And even if you find it, or get close to it, the player will still have to learn to play it well to achieve the desired result.
Time to get some material and start some experiments
Yes, I’m a maker. As to how I get the octaves in tune, the answer is I dunno. I measured a bunch of whistles and took the bits of them I liked, modified so as not to be copying anyone, and went from there. I did science for a living for a few decades, so deliberately haven’t thought too scientifically about the whistle. As I said above, probably half of my whistles turn out very in-tune across the octaves, most of the rest require a little lipping, and the occasional whistle just winds up in the dustbin. I don’t know why.
One challenge with using PVC is that you are very limited in your choice of bore diameters. If you get set up to bore your own material, you can buy or order gun drills in whatever custom sizes you want. Then the fun really begins. It incurs large up front costs though.
I think one of the reasons so many makers struggle to find a good balance, and end up with a shrill top end, is because they use whatever tubing or drill size they can easily acquire (say 1/2”) and start from a bore that is too big.
Even a change from a bore of 11.9 mm to 12 mm makes a noticeable difference in what kind of balance you can achieve on a high D whistle.
I was talking to a whistlemaker a few years back and he said he was limited to brass tube size and had to compromise. Same with all materials I guess, standard manufacturing sizes
It would be really useful to have the tools to anneal and redraw tubing over a mandrel or through a die to make small adjustments to the bore size.
To do a good job of these kinds of experiments, you really need to be looking at bore size increments on the order of 0.1 mm, centered somewhere around 11.9 mm for a high D whistle, in my opinion.
I had tuning issues with the second octave of the first quenas I made, primarily because my hole placement was entirely experimental with no calculations, but a top Chilean maker, Domingo Uribe, was insistent that you can get all three octaves in tune with a cylindrical or conical bore, so I kept working on it until I made ones that worked. I also attach a whistle converter with a windway to the top end and the resulting whistles play in tune across the range too, but I am using big tone holes: small ones certainly do go flat in the second octave. This works for C (high), low G (standard quena, 16 to 18mm bore) and low D (standard quenacho, 20mm bore). I use thick walls and no undercutting, as does he. If you want it to play quieter, restrict the windway size.
This makes me think about length/ bore ratio and what could be considered the ultimate number