Can anyone help me understand the relationship between the size and placement of holes on whistles? Even just a pointer to theory somewhere on the web would be helpful.
I have just made prototype-2 bass A, and would like to reduce hole sizes next time round…
Many thanks in advance for any help you can give.
Geewhiz, DrPhill, that’s not a simple subject. I could give you a lot of links to read (example: http://www.phy.mtu.edu/~suits/fingers.html ) but… Ok, here’s what I think is meaningful. First point, the holes need to be large enough to allow the highest notes they produce to speak. You can determine this by using a calculator that shows the cutoff frequencies for each hole (like TWCalc). You want that cutoff frequency to be higher than the frequency of the highest note that hole will produce which is usually the second octave note. This is most important to the highest second octave notes. You can usually just double the frequency for the first octave note to get a minimum cutoff frequency for a particular hole. The good news is that the frequencies produced on your bass whistles are comparatively low. So no need for really large holes. Second point - holes size effects your finger spacing. Again a calculator that shows the measurements between holes helps you monitor this in designing your layout. You can play with a calculator like Flutomat and see how a particular hole would move up or down the tube as you change the size of that hole. Also the tone, response and volume of a note is effected by hole size. So you have to do a dance weighing hole efficiency and playing comfort. That’s why we make a lot of different whistles. I could go on…and on…
Feadoggie
Thanks for the reply Feadoggie.
I guessed as much. I also guessed that it is not an exact science…
Could I ask you for clarification on a couple of points? I might be able to learn enough to achieve my goal with a little extra information:
What do you mean by speak? And what is it about hole size that ‘allows the note to speak’? Is this something to do with non-ideal placings of the tone holes?
Except that the holes had to be made large to get the notes in tune. If I could reduce the hole size 20% I reckon I have a playable instrument. It is just about playable now, but the holes are difficult to seal reliably at jig speed ( 
ha ha ha, read: ‘at any speed’ ) because of their size.
That is not bad news. I am using thumb-holes, and the reduction in stretch needed is considerable, though learning another hand pattern will slow me down a bit. The plus side is that I could cope with a wider or narrower span for either hand. Putting a 45 degree bend in the pipe relieved the strain on my wrists, and I have the option of more extreme geometries.
I was hoping the theory would say roughly moving the holes like this will require smaller holes. But If I have to use Flutomat and experiment, then so be it.
I guess no one has researched the effect of putting a bend in a pipe? the bent pipe has second octave notes flat and I was expecting them to be sharp…
Thanks for the help, though, it is appreciated.
Let’s move to PM’s DrPhill.
Feadoggie
I read Phill’s original post and thought, “Gosh, I wish I could help”. But I’m a bear of very little brain in such things, and you’ve already moved way beyond my capabilities. Sounds to me like Feadoggie’s help via PM is going to be of great value. I’d love to see the results, Phill, but the intervening maths, despite my maths background is, I know, going to be beyond me.
Good luck!
I never had trouble/ bothered with cut-off frequency values.
Probably because if the tone hole got so small to cause an undesired effect on cut-off frequency, I deemed the note was already too weak to be useful. A hole being a quarter or less of the bore diameter was too weak, as a rough guide useful tone holes were bigger than a quarter of the bore, and smaller than half the bore. Probably still are, don’t know why I wrote that in past tense 
I have a primitive but (I hope) practical understanding of the relationship.
If you start with a whistle with holes all the same size, it will/may/might sound okay for one octave.
Assuming it’s okay for a low blow, then if you overblow, the next octave will sound wrong. Enlarging the holes makes a difference in both octaves, but has more of an effect on the higher octave - the overblowing one. That is, in my experience anyway.
I ought to add - because someone is sure to point out - that this is so for a cylindrical bore instrument. Conical bores behave in a different way. I’m strictly a plumbing-pipe bodger, so I don’t have experience of conical bores in manufacture.
You can - just - get away with making all the holes the same size except for the “E” hole (on a D whistle).
I just cant resist posting a clip of second whistle attempt. The playing is a bit suspect as the thumb holes put me off a little, as does the need to keep hold of the whistle.
I have a whistle head that I am happy with, and it is attached to the body by a coupler, so that I can remake bodies cheaply and easily as I sort out the tuning.
to answer your original question -
enlarge a tone hole and the pitch will go up, same as moving the hole up (away from the bell)
as someone else mentioned the effect on the second octave is slightly different than the first octave
if you enlarge just the top (or the bottom) of a hole to tune a note it will have a different effect on the octave relationship than enlarging the hole evenly - give it some thought, or even better try it.
remember start tuning from the bottom
holes have an associated cutoff frequency which effects the timbre of the whistle and if is too low will prevent the instrument playing in the second octave - I have only had this happen with one whistle with the top hole, it made the high C# a bit dodgy to get, though I don’t remember it being any quieter (all the notes) than a tube with bigger holes.
I also want to mention that the perturbations in the bore introduced by your coupler will effect the tuning and if you make a whistle without the coupler you will have to change the hole position and/or sizes to get the same results - if the same results are even possible!
Have fun
I’ve never had a note refuse to speak in the second octave, except for B and above. I have found the the shape of the cutoff ratio (as defined b Dan Bingamon) vs. hole position (hole #) can have a significant effect on timbre. You can experiment and make smooth transitions from note to note or peak this ratio at certain notes. You’ll find that not all sets of tonehole diameters/spacing produce the same result.
The link for TWCalc (which can produce this graph) is: http://www.kingsmills.us/twcalc/twcalc.zip
Thanks for those replies.
I really need to do the mind-work calculating before getting the hacksaw out… but my ‘design’ does mean that is is very easy to make new bodies to fit to the head. And I do relate better to the heuristic approach.
I see this as an iterative process. First I needed to find a way of reaching and spanning the holes (done). Then I made a reasonable first approximation of a whistle head. Nowhere near perfect, but good enough to start with. Now I can concentrate on hole spacing/size - I need to be able to close the hole easily and completely which gives me a maximum size slightly less than that on my current model. Then I will go back to the hardest task of refining the head.
The essential point that I hear is ‘to make the holes smaller, move them towards the head’. I am using the ‘rubber band’ technique for placing holes (based on a low D), so my next experiment will be to stretch the band (from the bell end) by 10% or 20% more than the 4/3 ratio suggests and see what effect that has.
Oh and I deleted the sound clip - it was awful 
I’ve been wondering about something related to this topic. One of my peeves concerning low whistles is when the B2 hole is too large to cover easily or cleanly. So I’m curious, what would the trade-off be for making the B2 hole a little smaller?
Ah, Susato syndrome? I think there are a couple reasons why you might see this on a few whistles. All of this is conjecture on my part so humor my ramblings please. Not all of this is serious. 
I’d like to think that one reason is that low whistle makers have large hands and fingers so they don’t notice a problem having a big BH2 hole.
I suspect some makers scale up/down a successful design as they make whistles in new pitches. So if you have a high D that works well and you want to make a low D with similar characteristics then it seems logical that you scale everything up. So if you had hole sizes expressed as percentages of the whistle bore you would get equally large holes in relation to the bigger bore whistle. Does that make sense? And it does work to a point. The point is where it becomes impractical to cover the resulting holes.
The second reason is perhaps more common. When you design a low whistle you end up with a finger spread between BH1 and BH3 that can be pretty large. If all three of the BH holes are of similar size there is a significant distance between BH2 and BH3. The distance between BH1 and BH2 is fairly close. So to make the overall stretch more playable, you move the BH2 hole down towards BH3 and the BH2 hole gets larger. Of course one could move the BH3 hole higher but then it would get smaller and the E note would become weaker.
So to answer your question “what would the trade-off be for making the B2 hole a little smaller?” You can make the BH2 hole smaller but it moves up the tube and farther away from BH3 and the F# becomes weaker or at least less rich in timbre. You can make the holes any size you like but volume, response and tone may be uneven. The trade-off is up to the whistle maker. If you make your own whistles, it’s up to you. Guitars are so much more simple!
One of the curious ways that the numbers work out using the accepted calulations is that the BH1 hole is usually the smallest hole and the BH2 hole is usually the largest.
I’d be interested in how others see this phenomena.
Have you ever looked at a good low Bb flute? You’d expect big holes on one of those right?
Feadoggie
Make a key for the lowest note. A Normally open key is not too hard to make. I’ll see if I can round a picture of one.
Its the only pair of holes with a semitone between the notes that vent through them. Does the size difference allow B1 - B2 to be similar to B2 - B3 making it easier to spread the 3 fingers to their maximum (try it on the table top) ?
You’re kidding, yes?
Feadoggie,
Thanks for the thorough explanation. I kind of understand the reason now for the larger B2 hole. I’ve never seen a low Bb so I’m not sure what you’re pointing out at the end there. The lowest whistle I own is a low C which I’m currently trying to sell because it’s just too big for me to play. The whistle that gives me the most trouble with the B2 hole is my Copeland F. I think it’s the combination of it being a large hole and a conical bore. The hole being at the thin end of the whistle is deeper than the B2 hole on a straight bore whistle is a lower key and it’s a fairly constant source of irritation to me when I play it. The conical bore doesn’t bother me at all on the higher whistles (D & C), but on that F? …grrrrrrrrrr.
Just an update for any interested.
A tune with echo on my bass A and the tune before echo.
Thanks for all the help and encouragement.