In Search of the Optimum Bore

[hans]

I'd like to make a distinction between the "optimal" bore for a single whistle, and the scaling factor for a "family" of whistles so they all have a similar sound (a "consort" of whistles, if you will).

For the optimal bore, we can't look to organ pipes, because different organ ranks will have different bore:length ratios. String pipes are generally narrow, flute pipes are wider. For a given whistle, you probably want to be close to the maximum Q, but you then choose to be one side or the other, depending on what kind of sound you want.

Yes, I agree. It may be interesting to note that for whistles, unlike for organ pipes, there is only a narrow range of widths which work sufficiently successful. For instance I made four different width high C whistles, all playable, from 12.7mm bore to 15.7mm bore. Not a big range. 11mm proves too thin, and anything above 16mm too wide. Within such a range there is a golden middle with maximum Q.

For the scaling factor, organ building is a useful guide. Fletcher and Rossing note that doubling on somewhere between the 15th and 18th pipe is generally satisfactory, and modern design generally uses doubling on the 15th, consistent with what Hans' prefers. They also calculate the optimum scaling factor for a set of pipes that have the same relative Q values among the different harmonics, so they all have the same timbre: this works out to doubling every 14.4 pipes. "This should give tonal similarity across the whole rank, though the basses may be rather loud compared to the trebles."

The scaling factor determines only the slope of the red line in Figure 3. Its absolute position depends on what your "standard bore" is. Doubling at the 15th would give a slightly steeper line, which I think would match the peaks on the Q lines better.

I have not got Fletcher and Rossing's book. Doubling every 14.4 pipes is very interesting. This works out as an octave factor of 1.7818, or a half tone step factor of 1.04931. I mentioned in my OP that an octave factor of 1.77 seems to be right for the highest Q line, and used that for the "optimal bore table" later. It is close to 15 step halving (octave factor of 1.7411). The factor of 1.77 was just a rough interpolation using the graph in Fig 3. I shall take it from Fletcher and Rossing's authority that an octave factor of 1.7818 or 14.4 step halving is more precise. I will post another table. Setting high C to 14mm bore is of course somewhat arbitrary and reflects my subjective preference.

There's a 2001 paper by Michael Moloney and Daniel Hatten on Q factors in cylindrical pipes, if anyone's interested.

I'd love to read that, do you got it in electronic form and can send me a copy?

BTW: thanks, Hans, for the juicy thread.

Thanks for engaging! But pretty boring really . A much juicier thread would be about lips, mouth and ears (in pipe organ speak) and the behaviour of jets.

[Feadoggie]

Might this be the Maloney and Hatton paper referred to above?

[hans]

Here is a scaling table, calculated using a halving ratio of 14.4 steps, or a semitone width ratio of 2^(1/14.4)=1.04931, for a maximum Q line according to Fletcher and Rossing, and a base of 14mm for high C:

Code: Select all

Whistle bore scaling 
width doubling every 14.4 semi tones, 
octave ratio = 1.7818, 
half tone step ratio = 1.04931,
and a base of high C bore = 14mm
key     bore (mm)
G# 	   9.53
G        10
F#       10.49
F        11.01
E        11.55
Eb       12.12
D        12.72
C#       13.34
C        14
B        14.69
Bb       15.41
A        16.17
Low G#   16.97
Low G    17.81
Low F#   18.69
Low F    19.61
Low E    20.58
Low Eb   21.59
Low D    22.66
Low C#   23.77
Low C    24.95
Low B    26.18
Low Bb   27.47
Low A    28.82
Bass G#  30.24
Bass G   31.73

[/size]

As a rough guide, a narrow bore whistle could be defined as having a width up to about two steps up, and a wide bore whistle as having a width of up to about two steps down. I imagine going three steps (or more) up or down will give problematic results.

[rhulsey]

Hans, this is really interesting what you have going here.

I'm not familiar with the book mentioned here or its authors, but if the numbers presented mean halving on the 14th or thereabouts being 'normal', I'm not sure about that. In my 30 plus years in the organ business, I don't believe I've never run across a set of pipes that halves that quickly, at least not as an entire rank. Garden-variety halving for a Principal stop is generally 17th, but many tonal designers/voicers employ empirical scales that vary at any number of point in the 61 note (+/-) keyboard compass to achieve whatever results they are after. It is, however as subjective as something can possibly get, and what works for one may not even be possible for another.

Of course, it would matter if you are scaling for a Principal sound, which isn't imitative of any given instrument, really, or a flute rank of some variety, which would very often 'grow' as the notes ascend, and employ halving ratios, at least in ranges of notes, on the 20th note or even greater. That's a remarkable difference in diameter from 14th halving if I'm reading this correctly.

And, as most any organ voicer will tell you, a narrower mouth is easier to bring into speech and control than a wide one. I think the widest mouth whistle I owned was a Grinter, and the other end of the spectrum would be Pat O'Riordan.

Reggie

[AvienMael]

Having a read through Maloney and Hatton's paper, and I noticed this:

"...was positioned at the center of the pipe by inserting it from one end. This eliminated the need for drilling a hole through the pipe wall at the middle of the pipe to allow microphone
placement. Leaks around such a hole were found to seriously affect the Q value."

Pretty much what I would have expected, and alluded to earlier. You'll get the bell note - IF and only if all the tone holes are well sealed, but the moment you move one finger, it's all dependent on how you voice the head, because THAT is what determines the "quality" of any given oscilation in a whistle.

[Peter Duggan]

but the moment you move one finger, it's all dependent on how you voice the head

And whether or not the bore/voicing combination lets you get harmonics from any given fingering?

[david_h]

... but the moment you move one finger, it's all dependent on how you voice the head, because THAT is what determines the "quality" of any given oscilation in a whistle...

How significant is that compared with the large change in bore to length ratio once you start lifting fingers ? The voicing applies to the bell note as well.

[hans]

Having a read through Maloney and Hatton's paper, and I noticed this:

"...was positioned at the center of the pipe by inserting it from one end. This eliminated the need for drilling a hole through the pipe wall at the middle of the pipe to allow microphone
placement. Leaks around such a hole were found to seriously affect the Q value."

Pretty much what I would have expected, and alluded to earlier. You'll get the bell note - IF and only if all the tone holes are well sealed, but the moment you move one finger, it's all dependent on how you voice the head, because THAT is what determines the "quality" of any given oscilation in a whistle.

What do you mean by quality? The tonal character of a whistle or organ pipe is depending on relative pipe width. There are aspects of the tone which depend on window and tone hole geometry, but the relative width determines how wall losses and radiation losses combine and have an effect on the fundamental frequency and the harmonic overtone frequencies. And this effect is not even, but leads to a more prominent fundamental relative to the harmonics if the pipe is wider, and vice versa to more pronounced harmonics if the pipe is narrower. This has nothing to do with voicing. Voicing introduces or tries to keep low additional frequencies, like hiss and the "breathy" tone of some whistles.

Just to demonstrate you can listen to a sound sample I recorded using four different width C whistles, playing first a G and then a F on the four whistles in succession. The whistles are of similar construction with a rounded windway and blade, and similar relative window dimensions, although the wider whistles have wider windows and as a consequence play louder. So if you are not distracted by the differences in volume and some hiss you can discern the tonal differences I keep talking about.
tone comparison mp3

As to your point about tone holes making Q value measurement meaningless: you are misunderstanding the point in the quote you give. The point made is this: A small hole in the wall of a resonator will affect Q measurements, but not the resonating frequency. A small hole will lead to some extra loss. But open tone holes in a whistle affect the resonating frequency, that is their purpose! The effect of open tone holes is to reduce the effective pipe length. The effectively reduced pipe still has Q, in fact it may have a higher Q as it is shorter with the same width, and there is less wall loss. Therefore it plays louder using the same driving jet force, the same wind. It is still a resonator and obeys all the acoustical laws regarding to resonators!

[Tunborough]

Might this be the Maloney and Hatton paper referred to above?

Dat's da one.

I'm not familiar with the book mentioned here or its authors, but if the numbers presented mean halving on the 14th or thereabouts being 'normal', I'm not sure about that. In my 30 plus years in the organ business, I don't believe I've never run across a set of pipes that halves that quickly, at least not as an entire rank. Garden-variety halving for a Principal stop is generally 17th, but many tonal designers/voicers employ empirical scales that vary at any number of point in the 61 note (+/-) keyboard compass to achieve whatever results they are after.

Fletcher and Rossing never suggest 14.4 is "normal". According to them, 15 to 18 is, "generally satisfactory for diapason ranks, but in fact the scalings used historically generally depart from such a rule over at least part of their compass." More or less what you just said.

I don't know much about Thomas Rossing, but you can find more on Neville Fletcher, and many of his papers, at UNSW. I don't agree with all of his conclusions, but if you like this thread, you may find him interesting reading.

[Tunborough]

Just to demonstrate you can listen to a sound sample I recorded using four different width C whistles, playing first a G and then a F on the four whistles in succession. The whistles are of similar construction with a rounded windway and blade, and similar relative window dimensions, although the wider whistles have wider windows and as a consequence play louder. So if you are not distracted by the differences in volume and some hiss you can discern the tonal differences I keep talking about.
tone comparison mp3

Hans, I'm not sure that proves your point on the effect of tube width. I listened to it with a "Bars and Waves" visualization in Windows Media Player (spectrum analyzer as eye-candy). It shows whistle 2 and 4 with lower levels of even harmonics than whistles 1 and 3. For what it's worth, Fletcher (and Douglas) would attribute that to the position of the blade in the wind sheet; I can't say whether he's right or not. 3 has the most second harmonic, 2 has the most third harmonic. 1 has more harmonic content than 4, but unless 2 and 3 are out of order, I don't see a steady progression from 1 through 4.

[Tunborough]

For instance I made four different width high C whistles, all playable, from 12.7mm bore to 15.7mm bore. Not a big range. 11mm proves too thin, and anything above 16mm too wide.

Very interesting. Did you find that 11mm and 16mm were not playable at all, throughout their range, or did they have specific problems at specific parts of their range?

[hans]

When a whistle is too thin, it has a problematic bottom end: the bottom notes get progressively weaker when reducing the bore.

When a whistle is too wide, it has a problematic second octave top end, the top notes need too much push to sound.

These effects are gradual, there is no cut-off point from which a whistle would be unplayable because of too wide or too narrow a bore. It just gets difficult, and more and more difficult.

Sorry if my tone sample is not convincing! I am pretty sure I can hear the effect, and have done with many different whistles and bore experiments in various keys.

Here is another comparison, using four different width D whistles.

[Daniel_Bingamon]

And, as most any organ voicer will tell you, a narrower mouth is easier to bring into speech and control than a wide one. I think the widest mouth whistle I owned was a Grinter, and the other end of the spectrum would be Pat O'Riordan.

I made a tri opening mouth once for a Low-D - loud like a train whistle but also consumed a lot of air.
The basswhistles are currently using 1" wide mouths with a nice gentle slope to deliver the air from the cavity that the mouth pipe goes into up to the duct.
The lower freq. you get, the pickier it is but techniques used on low freq. work makes high freq. whistles speak even better

These effects are gradual, there is no cut-off point from which a whistle would be unplayable because of too wide or too narrow a bore. It just gets difficult, and more and more difficult.

Yep, gradual is the right word. It's surprising that with good voicing you can make a 3/4 long pipe that is way over the the natural length vs bore parameters and still get a very low note that plays but it's very delicate and quiet but it really is there.

[AvienMael]

"Quality" - the "Q" upon which you based this thread.

I will try to explain my point one last time, and then call it quits... lol:

First, your premise that tubing width alone is responsible for tonal character is incorrect. "Q", as I am understanding it, is based on frequency -vs- resonance of said frequency within any given bore, and attempts to define that frequency at it's maximum possible amplitude within that bore. Therein lies your fundamental problem - so back to my original question - what frequency are you looking for? - because you're only going to get ONE maximum Q in any tube. That's half of why this works for a pipe organ - one frequency = one tube. PERIOD. The other half is a regulated supply of air - something a human whistle player is not going to supply at a consistent value. This is what I (and I think Daniel) mean when we say there is a trade-off in a whistle. You shoot for the lower octave, or the higher octave. Most accomplished whistlesmiths design a "D" whistle, for example, based on the lower octave "A", and this gives you a comfortable medium. Whistles that focus on the bell note will have tonal differences in the upper octave, and vice-versa. But does this mean we strive to make the "A" overpower every other note on the whistle? Of course not... and this is where the old trial and error method comes into play...

Second, your premise that "voicing" the head only serves to remove or preserve lower frequencies is also incorrect - very incorrect, I think. In fact, you can change for the better - or even ruin the entire tuning of a whistle by voicing the head, depending on what you do. You can make it warmer, brighter, more or less articulate at each note - and sometimes end up with certain notes that speak above all the rest. If you seriously believe that the voicing of the head does not have a final and defining impact on the tonal quality - be it tuning, timbre, or amplitude of the oscilating frequencies within the bore at ANY frequency, then you are sadly mistaken. Every one of your 4 whistles could have sounded more or less the same, if they had been voiced differently - whether you believe me or not.

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 want your whistles to sound more or less the same, then wall thickness will get you there faster than anything else. In your mind, this boils down to a bore/length ratio - even though you are starting to admit that what you once thought about bore/length ratios is not necessarilty the case in whistles. Resonance is all that a whistle achieves (or fails to). UIt is nothing but a resonator. It will resonate a good pure tone, and it will resonate a thin, unstable tone - and every combination in between - 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. A really good high F, for example, will have a larger bore diameter than a high D, with a thinner wall than that same D whistle. The tonal characteristics - all of them, including volume, will pretty much be the same. Their playing characteristics (back pressure, etc.) may not.

[Peter Duggan]

A really good high F, for example, will have a larger bore diameter than a high D, with a thinner wall than that same D whistle.

Eh?