In Search of the Optimum Bore

[AvienMael]

Yeah see, that's just it... too much urban myth floating around about what makes a whistle work, too much repetition from people who only think they know. Yes, a good high F will have a larger bore diameter and a thinner wall than a high D with the same tonal characteristics.

[Daniel_Bingamon]

There are certain tone characteristics derived by the bore, the voicing parameters, tonehole diameter.
I think Hans is just simply doing research to focus on one element.

Bore does play a role in these characteristic. In addition to making Tin Whistles, I also make Native American Flutes - the bore is almost always wider than a Whistle in the same key. The desire is for the overall characteristic derived from the bore and you sacrifice the 2nd octave for the desired tone.

A Tin Whistle is generally a wider bore than a flute but narrower than a Native American Flute.
A Boehm Flute or many Irish flutes are narrow bore and play a much greater range even into the third octave and beyond (sounds like Buzz Lightyear <g> )

So, what is really perfect has to do with desire. On one instrument range is greatly sacrifice for a deep haunting ethereal sound - NAFs. The Tin Whistle tries to balance range and tonality.
Flutes can do a lot of things that whistles can't because they are not limited to a mechanical duct.

[DrPhill]

I am following this discussion with interest; theoretical interest only, maybe, as my whistle making skills are very limited. One point jumped out at me from your post AvienMael, and that was point four in the following list:

........................ - the whistle don't care which or what. How much is resonates, what it resonates, or how little it resonates depends heavily on four things: 1.) the force of the airstream entering it, 2.) the focus of the airstream entering it, 3.) wall thickness, 4.) the material the bore is made from. ..........................

Could you give a bit more detail, please? I have seen some posts on this forum stoutly maintain that the material a whistle is made from has little effect on the tone and other posts just as vigorously promote the idea that the material has a big effect. The discrepancy may arise from the fact that different materials place different constraints on, or possibilities for, the final shape of the whistle - wall thickness being one such difference that springs to mind.

Or, were you actually referring to the material the bore is made of (ie air in most cases?) .

[hans]

Thanks Daniel, a good general summary! Interesting that the NAF uses a relative wide bore, but quite a narrow windway and window for a quieter but more fluty, fuller tone.

Yeah see, that's just it... too much urban myth floating around about what makes a whistle work, too much repetition from people who only think they know. Yes, a good high F will have a larger bore diameter and a thinner wall than a high D with the same tonal characteristics.

Can you show a pic of this high F beside a high D? I can't imagine how this F whistle could possibly work, unless it works only from the second octave up.

I am not sure if there is any point to responding to all your allegations against me, but you are wrong in what you think I think! - Okay, I try to respond to some:

First, your premise that tubing width alone is responsible for tonal character is incorrect.

I never made such a premise. Relative tubing width is one factor amongst many contributing to the overall tone. I am just focussing on investigating this one factor. Of course voicing is hugely important, the most important thing really. Choosing a suitable bore size is really the easiest part.

Most accomplished whistlesmiths design a "D" whistle, for example, based on the lower octave "A", and this gives you a comfortable medium.

Yes, I agree, and I said something similar right in my first post: But then whistles are not organ pipes, and operate over two octaves. So the lowest note is not the optimum (acoustically), the optimum is found up the whistle scale, around the fourth or fifth note. The fifth note is of course the A on a D whistle. So that is the frequency I am aiming for max Q. A or G on a D whistle.

Second, your premise that "voicing" the head only serves to remove or preserve lower frequencies is also incorrect - very incorrect, I think.

I never said anything like it. I can more or less agree what you wrote after that, but like to have demonstrated or find out myself, that a wider bore whistle and a narrower bore whistle can be voiced to sound just the same, overcoming the tonal differences introduced by the bore. It would be interesting if that is possible.

Third, and we have butted heads on this in the past - you need to account for wall thickness - by this I mean give it more merit than you do. Wall thickness affects resonance - and resonance is what you are after.

If you mean that the pipe itself is resonating, along with the air in it, and that this is an important factor, I'd say we don't want that kind of material vibration, and better choose a pipe which exhibits less of it, or choose thicker walls to cut down on this kind of vibration. So, yes, we probably differ in our opinions on this.

Resonance is all that a whistle achieves (or fails to). It is nothing but a resonator.

Not true. Even though I am only concerned with investigating resonance in relation to bore in this topic, I must point out that whistles are far more than resonators, there is far more going on when one plays than resonating. For instance part of a whistle's tone is made up of wind noise. One can do a little experiment: take perhaps a mid-range whistle, to hear this better. Now with all fingers on blow very very gently, so the whistle does not yet sound the bottom note. What you hear is wind noise. If you increase the pressure very gradually, you can hear the bottom note starting to sound, beside the sound of the wind, and gradually getting stronger. But the wind noise is always there, present in the complex tone. And the wind noise is not a resonating sound. And there are other non-resonating sounds present, for instance transition sounds, going from one note to another. And other noise due to edge turbulences. All very important contributors to the complexity of tone.

[Tunborough]

For instance I made four different width high C whistles, all playable, from 12.7mm bore to 15.7mm bore

Just to be sure I know the facts: were these made of wood?

Assuming yes, does anyone have comparable figures for CPVC: either the smallest pipe that you can make a high-C or high-D whistle from, or (almost as good) the lowest playable whistle you can make from 12 mm I.D. CPVC pipe?

[hans]

For instance I made four different width high C whistles, all playable, from 12.7mm bore to 15.7mm bore

Just to be sure I know the facts: were these made of wood?

No. From aluminium tubing.

[Daniel_Bingamon]

Yeah see, that's just it... too much urban myth floating around about what makes a whistle work, too much repetition from people who only think they know. Yes, a good high F will have a larger bore diameter and a thinner wall than a high D with the same tonal characteristics.

Can you show a pic of this high F beside a high D? I can't imagine how this F whistle could possibly work, unless it works only from the second octave up.

I am not sure if there is any point to responding to all your allegations against me, but you are wrong in what you think I think! - Okay, I try to respond to some:

Maybe he is referring to relative bore size.

Let's talk about resonators for a second.
A pressure built-up in a wider bore has a greater opening of area into atmosphere. In having this, the discharge cycle can occur quicker.
A big opening will depressurize quicker. In any conduit that is carrying a gas, there a certain amount of non-used space to the bore called the "boundary layer". (We have to think a lot about this at my day job, we make machines that measure the flow rate of jet/turbine engine parts)
The ratio of the bore area to the boundary layer has a certain curvature to it and flattens out after you get to a certain area. This would map out as a parabolic function (probably is connected to what Boehm was trying to describe about his flute headjoints).
Naturally, on a smaller instrument, this parabola will have greater effects on things because of the physical diameter of the instruments bore is closer in range to the boundary layer. I think this probably what Hans is seeing as well.
But, anyway - the big question is "Do wide bore instruments operate at a lower pressure than narrow bore instruments?" If they do, this would influence the charge/discharge cycle and create varying waveforms, like comparing sine wave vs an asymmetric triangle output.
So the rise time occupies a greater portion of the duty cycle and fall time is very short.
I suspect they do - a well voiced contra bass recorder (and whistles some day) can use less air than a poorly voiced low-D

Of course, going back to AvenMail - the width of the windway can also influence the amount pressure that it's operating at and possibly a normal bore whistle with an undersized window might
behave like the wide bore - maybe not as loud since there is less molecules of air crossing the window to carry oscillation. Oh, one more thing - the boundary layer gets smaller as pressure increases. One whistles which are vibrating, the boundary layer has to narrow and widen with pressure - at lower pressures, the amount of change is greater in it is greater. -- That also is part of the reason that the flute changes it's tuning slightly in the second octave

Wall thickness on a closed tonehole basically contributes to the overall area of the bore. To the air column depending on the note being played behave much like bore pertubations (sp?)
Personally, I like them thin - less to worry about. On NAF's I do however let them get to about 3/16" thick on average - have to have enough material for structural integrity.

[AvienMael]

Hans - I will take a couple of pictures of whistles I have here at this house ( I live between two cities) and post them later this weekend. They will show you what you have asked for, with respect to bore size. I will use aluminum whistles, since that is what you build with.

I think Daniel said it pretty well, and it echoes what I have been trying to say in at least one respect. We choose a particular bore size based on personal preferences. I would expand on that by saying that often our preferences are based on what we know, and how we do things - these things all shape each other, much like the different aspects of the whistles we make shape each other. There is a range of bore sizes for any key that will work and work well for most keys, provided you build and voice the head appropriately to that bore, and a variety of tonal characteristics or properties available to you with any bore size - provided you know how to tap them. I can a standard 1/2" tube and make at least 6 whistles that sound entirely different from one another simply by making 6 different heads for it. Even with regard to your own sound samples, the question was asked if those whistles were made of wood - was that due to bore size?

Take for example, your basic feadog whistle. It has a bore constructed of 1/2" brass tubing with a wall of @.014". Now contrast that to a brass Burke narrow bore whistle. It is also built with a bore consisting of 1/2" tubing with a wall of @.014" These are two entirely different whistles with nearly identical bores and wall thicknesses. The Burke is louder, clearer, more articulate, and a lot less "breathy" than the Feadog. Overall, most people would agree that it is "stronger" - and that is precisely why people buy them. Obviously these differences have nothing to do with the bore, the difference is in the whistle head.

The whistle head, or fipple, or whatever else one may call it, is what is going to determine the strengths and weaknesses of any whistle - especially the quality of the tonal oscilations that occur within the bore. Moreover, the person playing the whistle will have a lot of influence over this aspect as well, depending on how they manage the breath they are delivering into the whistle. This is why I say, it is not the same as a tube in a pipe organ. In a pipe organ, everything is more or less constant. A valve opens, a predetermined amount of air enters at a predetermined force and velocity, and the result is more or less, always the same. Not true in a whistle - not true at all.

And as for your statement about the whistle tube being brought to resonance serving as an undesirable characteristic - again, I have to disagree with you. A whistle is basically nothing more than an acoustic resonator... which will have it's own resonance based on material and wall - should you choose or prove able to achieve it. Actually, it is this resonance that whistlers like and look for... when the whistle sounds and actually feels alive in the hands - this is what makes one whistle stand out among all others. This is a whistle which achieves "maximum Q". John Sindt makes whistles like this, that's why he currently has a 14 month waiting list. There are the fabled and obscure "1 in a 100 Gens" out there. Colin Goldie can make whistles like this. Some Copelands are like this. Jerry Freeman's new Bluebird comes very very close. The Lon Dubh also comes very very close. It is what makes them preferred whistles of choice. It is I think, even after all of this discussion, what you are trying to achieve by exploring bore possibilities - possibly without even realizing it.

... and honestly Hans, I hope that you do.

[Tunborough]

Ok, I have an answer, but I don't like it.

I took the range of diameters Hans got for high-C whistles, and scaled it to other pitches, based on the quality factor equations in Moloney and Hatten. It doesn't say anything about tone colour, just what's playable. The minimum diameter is the smallest tube that has Q >= 43 at the playing frequency. The maximum diameter is the largest tube that has Q >= 43 two octaves up from the playing frequency. (43 because that's what gave the results I got from Hans.)

Code: Select all

Pitch   Min Dia (mm)   Max Dia (mm)
E5          11.4            11.5
D5          12.1            13.5
C5          12.7            15.7
Bb4         13.4            18.0
A4          13.8            19.2
G4          14.6            22.0
D4          16.8            30.6

I don't like it, because I've got high-D and Bb whistles here with 12 mm tubes that play just fine. It may be because Moloney and Hatten looked at CPVC and Hans used aluminum, but I don't think this would make this much difference. It may be because it isn't sufficient to just measure Q.

Does anyone see how to fix this? Does anyone have any other results that I could use to calibrate this: what tubes are playable and what aren't?

[hans]

The figures in your table don't look right. There is only 0.1mm diff for E5, 1.4mm diff for D5, going up to 13.8mm diff for D4! E5 should be more, and D4 not that much I imagine. The other issue is to take my C whistles as a given standard for maximum and minimum bore width. There are no real cut-off points for max and min width, just gradual decline.

I do not understand why you set Q>=43 for different keys. The Q value should increase with lower frequencies, judging from Figure 3 from the Liljencrants paper I cited. With increasing max Q for lower frequencies you would need to raise the "cut-off" Q (acceptable Q for max and min width) I think. And decrease it for higher frequencies. From your premise of fixed Q>=43 you won't have any whistle above E5! At least that is at the base of my idea for determining narrow and wide bore values from the scaling table posted earlier, by going up or down the scale by some steps (I said two steps, but maybe that could be stretched with appropriate head design). That was my non-arithmetical way to estimate what could constitute narrow and wide bore. Or draw parallel lines either side of the max Q line on Fig 3 for some arbitrary maximum and minimum cut-off for width. I am trying to avoid the math!

I am curious as to your 12mm bore Bb whistle. The sounding length would be about 354mm, with a length/bore ratio of ca. 29.5. What are your window dimensions for this? A pretty wide window to get enough power to drive such a long tube I guess? And how much quieter compared to your D does it play?

[AvienMael]

Actually, if you halve the differences in Tunborough's chart, what you get seems to be right in the range of "normal". For example, if I take the min for C5 as 12.7mm, and the max as 15.7mm, and halve the difference, I get 14.2mm - exactly what I would expect for a C whistle. Doing the same thing for the low D gives you 23.4mm for the bore - which will produce a good, solid low D whistle. Bb will give you 15.7mm - my gen Bb measures exactly 15mm.

So if you take it for what it is, with the "mins" being the minimums, and the "max's" being the the maximums, what you get when you look dead between those two values is right in line with what you would expect.

Now, if I take this step further with respect to the low D, and try sizing the bore for the A4 (as has been suggested) using the "middle of the road" value, what I get is a bore of 16.7mm. Can we make this whistle? Yes, and it's going honk all over the G scale, but above and below that range the intonation is going to suck at what would be considered average volume (to put it bluntly). Can we overcome this? Yes, to some extent, and if we build and voice the head appropriately, and choose a tubing with a very thin wall, our task will be easier. Choosing tubing with a thicker wall will only exacerbate the undesirable tonal characteristics of the whistle, and tend to defeat the lower end of the scale in the first octave. We could also further change the whistle head to accomodate a thicker-walled tubing, and change our tuning of the tube, voice the tube to defeat some of these characteristics, but this in turn will result in a further reduction in volume. Either way, a bore that small is going to have a rather "screechy" tonal characteristic unless we can voice that particular characteristic out of it at the head. I know these things because I have done them.

What this means to me is that 1.) the chart proves what I have been trying to point out. 2.) Choosing one key of whistle, and trying to calculate your bore size for other keys, based on your preferences for that key, isn't going to give you the results you are after. There are too many variables at play in a whistle - chief among which is the player - and you are dealing with too wide of a range of physical volume (capacity / width between walls) within the bores to make bore sizing the basis for tone production. It doesn't work that way in a whistle. You achieve the desired tone at the whistle head - the bore can only refine and enhance that tone, or detract from or destroy it, depending on whether it works with the head by resonating appropriately, or against it by resonating in a way that creates additional impedance to the sound wave.

The sound wave generated by a whistle head is not the same as that generated by a pipe organ or a flute. A whistle does not achieve the same desired frequencies in the same way. We can easily build a low D flute with a bore of 16.7mm without the tonal deficiencies we will encounter in a whistle of the same key, and having the same bore. You make PVC flutes - you've already demonstrated this for yourself. Think about it.

[Tunborough]

The figures in your table don't look right.

I agree.

I do not understand why you set Q>=43 for different keys.

Because that's what I got for your 12.7 and 15.7 mm C whistles, and those were the only data points I had. (I'm actually amazed how close these two data points were: 42.8 and 42.9.) If I get more data points, I'd be happy to do the math again. I reasoned that Q should measure how well a given tube "likes" to resonate. Although you can get to higher Q at lower frequency, I don't know that you have to get to higher Q to make it resonate. (Maybe you do, but without more data, I don't know that.) I'm not expecting these numbers to be absolute boundaries, just a guide to the "useful range" of diameters for a given key.

One of the Bb whistles is 341.5 mm from end to the lip, with a window 6.6 mm wide and 6.1 mm long (fipple to lip). I misjudged the tonehole positions, so they had to stay smaller than they should have to keep it on pitch. It isn't a loud whistle, but not that much quieter than some of the high-Ds I've got. (I wonder if the fundamental may be about as loud, but not as much power in the harmonics.)

Later, as AvienMael suggests, I'll do the math for the "mid-point". It isn't half-way between the extremes, it's the diameter at which the Q at the lowest note equals the Q at the highest note, which should give the best balance across the range. I'd still be interested in getting better numbers for the "useful range" though.

[hans]

I do not understand why you set Q>=43 for different keys.

Because that's what I got for your 12.7 and 15.7 mm C whistles, and those were the only data points I had. (I'm actually amazed how close these two data points were: 42.8 and 42.9.) If I get more data points, I'd be happy to do the math again. I reasoned that Q should measure how well a given tube "likes" to resonate. Although you can get to higher Q at lower frequency, I don't know that you have to get to higher Q to make it resonate. (Maybe you do, but without more data, I don't know that.) I'm not expecting these numbers to be absolute boundaries, just a guide to the "useful range" of diameters for a given key.

The fact that you won't get any "useful range" for a high F whistle if you stick to Q>=43 should be reason enough to question the whole approach. You'll need to lower the Q for higher whistles. As to lower keys: You can get lower Q pipes to resonate, but much quieter. For instance as Daniel said extra long narrow bass tubes.

[Tunborough]

Here are my results for the "optimum" diameter: the inside diameter at which Q at the lowest note equals Q at the second-octave note, and Q is higher everywhere in between. Uses the formula for Q from Moloney and Hatten and a couple of assumptions, which may be an over-simplification for real whistles. Frequency in Hz, diameter in mm. Does this look reasonable?

Code: Select all

Key     f0     Opt Dia   Q
C3     130.8    44.1    73.9
D3     146.8    40.0    71.1
E3     164.8    36.4    68.4
F3     174.6    34.7    67.1
G3     196.0    31.5    64.6
A3     220.0    28.6    62.2
Bb3    233.1    27.2    61.0
C4     261.6    24.7    58.7
D4     293.7    22.5    56.5
E4     329.6    20.4    54.3
F4     349.2    19.4    53.3
G4     392.0    17.7    51.3
A4     440.0    16.0    49.3
Bb4    466.2    15.3    48.4
C5     523.3    13.9    46.6
D5     587.3    12.6    44.8
E5     659.3    11.5    43.1
F5     698.5    10.9    42.3
G5     784.0     9.9    40.7

[hans]

These optimal diameters look remarkably close to the ones obtained using 14.4 step halving in the table I posted. The only difference I can see is that you got high C bore calculated as 13.9mm, whereas I set it to 14mm. If I set high C bore to 13.9mm and use the 14.4 step halving ratio, I get exactly the same figures than you!

What assumptions did you make?