I’d like to hear some comments on wall thickness.
I play a black diamond which I like, and it has thicker walls than the cheapie whistles like Generations.
I am wondering in how far this contributes to me liking the black diamond better (other than that the diamond can be pushed harder and is better tuned).
Just curious 
berti
The effect of “wall thickness” or “chimney height” on playing holes is found in the upper registers. When a player “overblows”, the internal pressure increases and the aircolumn pushes up into deep playing holes. The extra cubic volume flattens the scale. This is not too much trouble in the first overblown register, because a player subconsciously blows harder to correct flat pitch. This does make the sound more shrill and piercing on the higher notes though.
Timbre: Instruments with deep voicings and toneholes suppress higher harmonics and have a more mellow or reedy tone color, like a Recorder.
When I tested several Low D’s, recording myself playing them and listening back, I noticed that the Susato had the most flutelike sound, and also that it retained the most tonal colour in the 2nd octave, both of which I attribute to its having the greatest wall thickness of any of the Low D’s I tested.
Um, my Black Diamond has about the same wall thickness (@.020) as my low end whistles. It does, however, have a larger diameter - very close to the same as my Dixon Trads, and the heads between these two whistle makes are interchangeable. I don’t detect a difference in any of my traditional style brass whistles that I can attribute to anything other than the heads and the bore size. They are all basically thin-walled ranging from @.014" - @.025" (on plated bodies). Now my Dixon Pro brass whistle has a body with both a larger bore and a wall thickness of about .065", it does sound different from the thin walled whistles. It is often described as warmer, mellower - both of which I would agree with. It still has a bit of chiff, but it’s less “tinny” sounding - if that makes any sense. I have another brass whistle that I made from tubing with a wall thickness of .049", and again, this thicker wall has a mellower, warmer tone. Of course this is all coming from a guy who has spent 20+ years on construction sites and 4 years in mine where we blasted around the clock, so what I hear may be different from what you hear 
I have a Black Diamond C (which I like very much) and just compared it to other C whistles, including the Gen; the BD is certainly no thicker in the walls and is also of slightly lesser bore diameter actually(which I can tell scientifically, as it fits inside the Gen). Thomas’s great explanation notwithstanding, there are lots of variables and lots of threads on most of them - wall thickness, bore diameter (thinner often said to be more responsive, etc.), materials (often said said to be the least contributor to variation in tonal qualities), the all important “voicing” of the head piece, internal perturbations, etc.
You’d think perhaps you could track the physical attributes of your favorite whistles and just go out and buy one with a tape measure, but it doesn’t seem to work that way - I have favs of varying physical characteristics, all over the charts. I’m guessing voicing and the way each characteristic fits into the whole are key (no pun intended).
Philo
As far as the difference in sound with your Black Diamond…I think the difference you are hearing is owing entirely to the mouthpiece. It has a shorter and narrower window, and a curved wind split. I’ve tried this mouthpiece on other tubes. On the Dixon Trad tube, it sounds the same as it does on its own tube because it’s basically the same tube. I’ve also adapted it to a tube I made from 316L stainless with a wall thickness of .050", and a small inner diameter of 13/32", and it sounds amazingly sweet and is very responsive, but no other whistle head in my collection makes that tube sound anything like it. So in this case we have a thicker wall with a much smaller bore, but it only sounds good with the Black Diamond mouthpiece. Everything else I’ve tried on it thus far makes it sound exactly like a bone-stock Feadog.
the short answer:
Yes
the slightly longer answer is complicated because the whistle is a sum of its parts
an example (unfortunately with little to do with wall thickness) - I took a head off a Generation D and stuck it on an Eb, same id/od tube just shorter with holes in different places (obviously) Its a much nicer whistle IMHO plays better, sounds sweeter/more focused/more bird like would be reasonable description - I find it amazing the same head can sound/behave so different on a different length tube.
I have made only thick walled whistles, from plastic and wood - maybe I should try a brass tube with a wood or plastic head and see what happens, thing is I really like wooden whistles, and plastic ones are nice too. My walls for a high D whistle are about 0.063 in (plastic) to about 0.075 inch for wood.
I’m confused by the 2nd posting, not trying to be smart - just understand.
I have never read an explanation for why blowing harder sharpens a note (I know it does - works for many (all?) wind instruments)
I am presently exploring ways to tune octaves with thicker walled whistles - 'cause that’s what I’ve been making. I have not experimented with thin walls with my heads.
So back to the 2nd post:
1:
When a player “overblows”, the internal pressure increases and the aircolumn pushes up into deep playing holes. The extra cubic volume flattens the scale.
OK
But then:
2:
a player subconsciously blows harder to correct flat pitch.
So blowing a little harder (overblowing) gets you a flat octave because of (1)
And blowing a little harder than this then sharpens the note (2) ?? does this not just (according to 1) just increase the internal pressure more and so would we not expect the not to go flatter still… or what else is going on?
Well, this is a guess based on my own tinkering but, The initial tone for any note is created at the windsplit. The tube shapes this tone into a note, but in the case of over-blowing, I think the initial tone as it is produced at the windsplit is what becomes sharper, therefore the resultant note produced by the tube is sharper.