I know nothing of the technical aspects of whistle building, but I do know a bit about mixing music. For an instrument to “cut through,” that instrument has to claim it’s own frequency space with regard to the other instruments around it. I’m not sure if that’s what you were hinting at or not.
Interesting thread that seems to boil down to the length of the whistle determines its its pitch, and the smaller the diameter, the longer the whistle must be for any given pitch.
The diameter is a determining factor not only in timbre, but in power as well. A smaller diameter, all factors being equal, will make a smaller sound than a larger diameter. But even that can be altered with width of window, height of blade, etc.
You might try this: take a small diameter wooden dowel and cut it to the length of the inside of any given whistle. Insert it into the whistle and play the bell note, and you will find it is slightly sharper because you have effectively decreased the area of the body, which would require more length to play the same pitch.
That’s a technique that organ voicers use when working with older pipes. While there is a limit to the effectiveness of doing this, afixing a dowel inside a pipe will reduce its ‘scale’ and thus increase the brightness of the tone or give it more power. If your whistle has a difficult upper end or seems to require lots of air this might be a solution.
Reg
For a “professional” instrument, it isn’t possible to just change the bore diameter between bordering keynotes. Once you begin to change registers you will get very poor results. Changing bore diameter changes the spacing of the Anti-nodes and therfore the tonehole placement and size. Increasing bore diameter brings the toneholes closer together, while reduction of bore diameter spreads them apart. If you leave the tonehole spacings the same and don’t change their size, you will get flat or sharp pitch in the upper registers by changing bore diameter. You can’t “cheat” and have the perfect whistle.
Tried this, have you? It’s mostly an exercise, but at least it is not theory alone and provides a demonstration of the subject at hand. Actually, it is surprising to me how much it can change the character of the tone without too much note re-arrangement.
Reg
I have now. 
Reg, this is very interesting. It’s such an obvious thing to try that I never thought to try it. And you know I simply can’t resist Rube Goldberg tweaks. I’m going to call this the Reg Hulsey “Hot Rod” tweak. 
So I now have round bamboo skewers stuck up inside several of my wider bore whistles. And I quite like what I’m hearing so far. I didn’t even cut them to length, so they’re just sticking out of the bell - which, for all I know, enhances the end effects. A small piece of tape at the bell keeps the rod from sliding out, and makes it easy to experiment positioning the distance of the rod up the bore.
It’s not so much the pitch and tuning as the change of timbre, volume, and playing characteristics that intrigues me.
And Thomas: What you say may be true in theory. But I’m not finding any problem playing these Hot Rodded whistles perfectly well in tune, including across registers. After all, big old fingerholes are not zero dimensional antinode points. And intonation is a matter of active control anyway.
Hot Rod, huh? I’m flattered 
!
Truth be known, there are probably a lot more wooden dowels glued in organ pipes around the country than any organbuilder would lay claim to! It simply works. It is easy, cheap, non-destructive and yields results. How much better can it get? Good to know 32 years in the organ biz have paid off in such a way!
I have a brass Burke session d here that becomes clearer, sweeter and plays perfectly up to the 3rd D with an 1/8 brass rod in it - without affecting the note-to-note tuning. Amazing!
Reg
Reg, is this a contradiction, or maybe I misunderstand what you mean by power?
Keeping in mind that an organ pipe gets a constant supply of wind - and a mouth blown musical instrument does not, generally. By adding a dowel to a pipe, you decrease the scale (diameter, area, etc…), the mouth width (window in whistle speak) thus becomes a larger portion of the new “diameter”, i.e. wider, and without closing the pipe’s toe and cutting off some of the air supply, the pipe plays louder. Did that make sense? That might not be what you are after, but in a nutshell, it is what happens with ‘volume’, at least.
OK, I thought it might be something like that. Constant air, larger window relative to the now-smaller bore, more power compared to a pipe made for that smaller bore in the first place. I think I understand.
Yessir, that’s it. I suppose when you ‘Hot Rod’ a whistle, I’d imagine your musical ability takes over and compensates for the very small reduction in air needed as a result of the tweak.
Bamboo skewers sound much more ‘official’ than wooden dowels, too!
Hans is right and I am wrong. I knew that info was fuzzy. Still, the concept I described is still OK.
Well that’s more or less all I was trying to point out - for the purpose of the discussion, there was nothing wrong with the layman’s explanation you gave.
To Hans’ credit, he has done his homework on the physics that are employed in whistle design. I remember a series of discussions on this forum (must have been about 3 years ago) in which questions were posed and answers were sought - all aimed at developing an understanding of the essence of what makes a whistle work and how, and Hans was a big part of these discussions. He wasn’t satisfied with general ideas or theories, he really wanted to get to the bottom of these things.
The one thing to remember is that these rules of physics aren’t neccessarily hard and fast when it comes to whistle design, because there are other factors influencing tuning, tonality, intonation (between octaves), and volume that are determined in large part by other factors like wall thickness, bore size, head design, and the volume and velocity of air that actually enters the bore (which again relates to head design). And of course, we can mutate the behavior of the sound column by making changes to the bore of the whistle such as tapering it, stepping it, or baffling it. Beyond that, our choices in material can influence how the whistle resonates, again having some effect on the overall tone.
But as to the original question, here is an every day example of how bore size affects tone to also consider: Take the basic high D whistle - be it a Generation, Feadog, etc. These whistles have both good and bad reputations, depending on who you talk to and what their experience(s) amount to. What is at the heart of this matter is actually the bore size (IMO). Yes, the head does have a lot to do with how these whistles sound and play - and the head is every bit as important as it would be on any whistle, maybe even more so - because what is going with these thin narrow bore whistles is that the inner diameter of their tubes is actually right on the verge of being too small to support the D scale “nicely,” with a desirable amount of volume, and without the whistle having an insane amount of backpressure. So what you end up with is a whistle that requires precise breath control to pull it all off, and which also exhibit a lot of chiff and can be prone to squawking and chirping.
what is going with these thin narrow bore whistles is that the inner diameter of their tubes is actually right on the verge of being too small to support the D scale “nicely,” with a desirable amount of volume,
Excellently observed, thank you. I’d wondered why my “ultra-narrow” D (8mm) didn’t work, now I know
FWIW, my “ultra-quiet” practice instrument is 11mm bore with seven holes, plays a diatonic D scale with a low C. It is quiet, but that’s what I wanted 
The one thing to remember is that these rules of physics aren’t neccessarily hard and fast when it comes to whistle design, because there are other factors influencing tuning, tonality, intonation (between octaves), and volume that are determined in large part by other factors like wall thickness, bore size, head design, and the volume and velocity of air that actually enters the bore
Simplified rules may not include wall thickness, bore size, etc. but they sitll fall under the ‘rules’ of physics - one just has to use more complicated models. What does not fall under the rules of physics is: what is a good sound, what is in tune, how much chiff is the right amount, whether the player likes to have a forgiving instrument or live on the edge and so on.
Just because flutomat and commonly available hole calculators don’t have the ability to deal with stepped bores or tuning of the second octave does not mean that these things cannot be calculated - in fact much of the mathematics has been around for at least 80 years.
In this vein I would like to clarify an earlier post of mine - while I don’t have the time or space to give a detailed answer I certainly do not want to lead anyone astray! I talked about the effect of bore on pitch, what I did not say (and mostly due to just quickly calculating and not delving into it very deeply) was that most of the effect on pitch (at least according to my calculations done with my own spreadsheet) is due to the ‘window’ - the window is smaller than the bore and effectively lengthens the vibrating air column, the amount it lengthens the vibrating air column depends on the ratio of the windows area with that of the bore (as well as on the depth of the window and geometry and …) so that if you increase the bore size the window has a longer effective length. Does that make sense?
What is at the heart of this matter is actually the bore size (IMO).
I think you may be at least partially correct - for example the Gen Eb and D share the same tube size and IMHO the Eb is a much nicer whistle, one possible explanation is that the bore more suits Eb (agreeing that the bore might be too narrow for D) - though it should also be mentioned that the Eb is also tuned differently (IMO - based purely on playing and not studying the hole sizes or playing into tuners or the like)