Regarding fipple design (whistles, organ pipes):
What determines at what wind speed a note is sounded, and at what wind speed the octave above it is sounded?
I am looking for some good physical (acoustical) science answers.
I know that roughly the airspeed doubles going from a bottom octave note to its first octave equivalent. But what is the precise relationship, and what influences this (windway factors, window factors, chamfering, labium shape and angle etc.)
Has anyone looked into this closely, or can give me any pointers (preferably freely available on the web)?
I can try to answer your question in terms of organ pipes, having spent nearly a lifetime as a voicer and organbuilder. However, physics is one thing, and music is another as you know!
Bear in mind, there are lots of exceptions, and few rules! A pipe of any given scale (diameter) can have a mouth of virtually any ratio to its circumference, though this is normally 1/7, 1/6, 1/5, 2/9, 1/4 or 2/7. This relationship will partially determine the overall volume and tone color of the pipe, but that depends on the cutup (height of the window), pressure, alignment, etc. There are limitations, of course, but a pipe, say with a diameter of 1", with a mouth width of 1/5 cutup 1/3 will only make so much sound, regardless of pressure. As the cutup goes higher, the volume (generally) will increase as the need for volume (or pressure) increases and the tone will broaden and become more flutey. In my whistling experience, a narrow mouth whistle would be O’Riordan, and a wide mouth whistle would be Grinter. There are the two extremes that I myself have seen.
Different tone qualities are also achieved through variations in scale, mouthwidth, material, pressure (which is constant with any given organ pipe), i.e., the toe of the pipe is open and the air volume is adjusted at the flue (windway), which is only possible with low pressures, or the toe is variable and the flue plays less of a role.
As for the overblowing, the languid (block) and its bevel and its relationship to the upper lip (blade) make this determination. Since the languid of an organ pipe will move within its solder joints enough to quicken or slow the pipe, (up for slow, down for quick) the upper lip is best left square to the lower lip - again there are exceptions. However, if you don’t move the languid, the upper lip can be moved forward to quicken the pipe and thus hasten an octave jump if that is your goal, or pushed back to slow the speech.
Beveling is also done according to taste. Most pipes are left blunt, but some sounds require (again depending on your goals) that the upper lip be beveled or ‘skived’. This will in effect help to narrow the tone, and also make the alignment of the flue and upper lip and languid position become more and more critical.
As I’ve said before, my hat is off to the whistle makers. The ‘exceptions’ to the rules that I apply to organ pipes that are used to make whistles play more than one note amaze me, for certain!
And this goes on and on and I’ll be glad to share my experience with you here or offline. You can PM or email me if you like as this just might put everyone to sleep!
Thanks Reg! I’ve been reading your post carefully, translating what I could to whistle-making theory, or at least try to see the analogies. I’ve also been busy reading up on organ flue pipes. I found the following on the web:
So back to your post: Are you saying that by quickening the pipe’s response the pipe can also be overblown easier, with less pressure, if the pressure is increased? Translating that into whistle design:
I get an easier overblow,
a) if the jet hits a sharper blade,
b) if the window height is smaller relative to the width (what you call the “cutup” ratio),
c) if the block protrudes less into the pipe, i.e. is more flush with the upper windway edge (lower lip).
And what are the effects of bevelling the block or the upper windway edge (I think you answered that, but I am having difficulties to see it in the whistle design)?
In the whistle design I have been following the wind is pushed through a narrow curved windway, and the bottom of this is aligned with the curved labium/blade edge, the top is aligned more or less with the outer pipe. So the windsheet does not hit the blade full on, but is mostly directed outward. I assumed that the bevel on the block has the effect of pulling some of the wind down into the pipe (initially), so helps starting interaction with the edge.
Yes, quickening the pipe will make it easier to overblow. An organ stop called “harmonic flute” or its many variations is a double-length open pipe, usually from about 2’ f or g (middle f or g on the piano) with a hole approximately half way up the speaking length. the pipe will not overblow if blown very softy, but will if fully blown, with or without the languid being down. On the other hand, there are builder who have made harmonic flutes that don’t have a hole - they blow the pipe hard and knock the languid down until you get the octave.
a) sharper blade? I think that’s probably for you to decide. The whistle is such a peculiar beast in that it must play so many notes with only one mouth - as opposed to 16 different pipes, each with progressively smaller diameter and proportionately narrower mouths.
b) a lower cutup will yield generally a smaller sound that will overblow more easily, be quieter in the bottom and louder in the top. I’d think (and I’ve not attempted whistle making) that there is a compromise in there somewhere, where the proportions become magical and you have a decent bell note and a top end that won’t shatter glass! During “tonal finishing” which is voicing on the job (church, auditorium, etc) we will often ‘trim’ pipes (raise the cutup) to get the speech prompt when lowering the languid doesn’t do the job adequately for whatever reason. These trims are often a fraction of a millimeter, and the results are easily heard, and this is usually on pipes say, 1’ and smaller, and a normal D whistle is what I’d call 1’ d.
c) good question this is where there’s a departure in physical construction. The languid in a flue pipe is different than the block because the block has a face that runs to the mouthpiece in a whistle, whereas in a flue pipe it is simply a partition with a bevel on its leading edge. I cannot say what the function of the bevel of the block/languid is in a whistle, or what the result is by altering the height of the block on the mouth. I’ve bought and sold many whistles and looked them over carefully in the past several years, and there are all kinds of ways to do it, just as with organ pipes or any musical instrument. Again, I think it’s a matter of what works for you. The ‘rules’ are very broad.
Beveling - the Grinter whistles (F and soprano D) I owned had wide mouths and curved windways and curved upper lips to match that were sharp. the block had no bevel at all, it appeared to be sawn off square. I have a Burke whistle here (2001) with a ‘block’ that appears to be flush or nearly so and a tiny bevel on it. O’Riordan, and Greenwood whistles are virtually identical, and they have flat upper lips that are fairly sharp, narrow mouths and windways that are D (on its side) shaped, beveled blocks and very open windways on the incoming end. There’s no analog for this in organ pipes that I know of. In fact, in looking at this construction, it doesn’t seem to make a lot of sense from a flue pipe perspective!
As for your design directing the air outward, I would say that no matter what design you use, it must behave that way for a whistle, which is characteristic of a pipe that isn’t too quick, otherwise you’d overblow the bell note from the get-go. At least that’s what I’d think. Maybe one of these days I need to make a whistle!
Again, my lack of understanding the function of the bevel, having seen such extremes in the whistles that I’ve owned, doesn’t really help answer your question. The lanquid bevel (and languid thickness) in organ pipes can be specified to pipe makers by the tonal designer for various and asundry reasons - and there are many interpretations of the results. Probably as many interpretations as there are voicers, I’d say. Generally, supply-house pipes come with 60 degree languid bevels. I was responsible for such details as a matter of policy in one position that I held where it wasn’t practical to be specifying varying bevels and thickness ratios, and settled on 60 degrees, and a thickness that was, as I recall, 1/14th of a mouth width that was 2/9 of the circumference. It worked for us, but others would invariably do something different!
Thank you for the informative links. I think you’ll find, as I have over the years, that the physics and theory are interesting, but are only hints for what you really do and get the results you want. Did any of that blabbering help?
I thought I’d offer a few uninformed thoughts & observations, particularly about block bevels and tapered windways (ala O’Riordan and many others).
I’ve not seen a particularly wide cross section of whistle designs, but have seen beveled blocks on Burke’s, a Hoover whitecap and several Freeman tweaked Feadog-type heads. I also use a slight block bevel on my own homemade whistles. A few trial & error observations:
Beveling the block (at the window end) seems to help “sweeten” the upper notes of the second octave and make the octave break more controllable. I use 45 degrees, only about 1 mm on a high-D.
Too much bevel seems to increase the air speed/pressure (“push” as the players call it) needed to make the second octave break, to the point that the second octave A & B can become real “squawkers”. My opinion is that no bevel is better than too much.
Block “stick-out” - more stick-out sweetens the upper notes, but lengthens the attack time of the notes. In the extreme, this can make a whistle sound “mushy” (for lack of a better term). An extreme amount of stick-out actually shortens the window and can make the bottom D & E play weakly, also.
Tapered windways - wide at the mouth/narrower at the window: I’d offer a relatively simple explanation for this one. If you are using a (head) design where the windway is cut into the tube wall by hand, you want to avoid creating a choke (constricted area) in it. One way to help avoid a choke is to noticeably taper the windway roof and floor (=block top surface) from entry to exit. A choked windway can make much of the second octave unreachable or very hard to control.
Thanks, that is all very useful. Yes, learning by trial and error is most important, and the theory lags behind in many ways. But it is also good to learn from the accumulated wisdom of organ builders and tuners.
Henry, 1mm bevel at 45° for a high D whistles sounds a lot, but if it works for you… I am happy with 1mm bevel at ca. 60° on a low D. This corresponds to the figures Reg gives (bevel of 60 degrees with a thickness of 1/14th of a mouth width, and width of 2/9 of the circumference).
My low Ds have a pipe of 25.4mm OD, 23mm ID, and the windows are about 13mm wide. 2/9 would give about 16-18mm window width (16mm using ID not OD). 16mm/23mm is about 0.7. That ratio would produce a rather loud whistle (I used it on narrow bore high whistles). For the low D it will get too air demanding, you run out of breath very fast! Therefore I settled for a narrower window.
The “cut out” window height is indeed crucial for tone. I have been experimenting with this, and the bevel protrusion, on a new low D right now. From many variations I get these figures for an acceptable tone (which is of course subjective) and for manageable high B and strong low D notes: 6-6.5mm height x 13mm width with 1mm bevel protruding 1mm, windway 1.2mm thick. The 6mm window height gives an easier high B, and a little less power overall, than the 6.5mm.
As to my original question: I will do my own blow pressure tests and see if they can tell me more. At least I should be able to get some objective figures for different pressures for different notes. Then I can observe minute design changes easier, I hope. Still, the proof is always in the playing, and the playing by different players.
Reg, if you like to build a whistle one day, you can always start with a a flue pipe. Only don’t use zinc and lead, but some more agreeable material for human contact! Then add finger holes, and in sizing and placing these lies another box of mysteries, partly solved by acoustic theory. Equations and computer programs to solve these come in very handy here.
Hans when you refer to the term “window height” are you referring to the height of the surround that forms the window or the longitudinal measurement of the window (from the end of the airway to the blade)?
I used the term as for organ flue pipes. So from blade edge (upper lip in a flue pipe) to top edge of windway (lower lip in a flue pipe). As pipes stand upright usually, this is the height of the “cutout” mouth or window. The height of the surround would be the height of the ears or box ears. I like box ears on the low whistles, for giving a more stable and stronger tone. Mouth, lips and ears are nice descriptive terms when you look at an upright flue pipe, with the foot underneath admitting the air.
Maybe window length and width could be used for the whistle, length being the longitudinal dimension. Only the length will be shorter than the width, which is not so intuitive.
Hans,
I never thought much about this question, but I believe I can tell you how to get an exact answer, without any theorizing or pontificating.
Get a plastic bag and measure the volume with calculations or some displacement process. Alternately, get a large cylinder of known dimensions whose piston will seal the bore. You may even consider using the capacity of your own lungs, whose capacity can be measured by displacing water from a container inverted in water. In any case, connect to the whistle under test. Squeeze all the air through while timing the process, while holding the desired note steady. Measure the windway and calculate cross-sectional area at the exit. Simply divide: (cc/sec) / (cm^2) = cm / sec. Here are sample calculations:
Lung capacity, 1 gal = 231 in^3 = 3785 cc.
On my WD Sweet Pennywhistle, the windway is about 0.048" thick x 0.350" w = 0.108 cm^2
When I played a low D, I could hold it for 40 sec before running out of gas.
Now (3785/40) / 0.108 = 876 cm/sec, 8.76 m/sec, about 20 MPH
Walt Sweet,
Master of Arts in Mathematics for Teachers, 2006
Western New England College
Springfield MA
I really like Walt’s idea - simple! You might be able to modify a bicycle pump to provide a known air volume and basic pressure measurements, if it has a gauge attached, as many do. (You might have to find a gauge with a lower pressure range, though.)
Hans - the 1 mm dimension on my block bevels is along the diagonal. At 45 deg, the axial bevel length would be ~0.7 mm. Curiously, the same amount seems to work just as well on larger heads (3/4" CPVC). I’ve also found that a small radius works, too.
