This is probably a question for the makers out there. According to pancelticpiper, and I’ve no reason to doubt him, second octaves, relative to the first, sometimes play flat sometimes sharp. I’m curious to know how a maker goes about tuning a second octave relative to the first. If he drills and tunes a hole for a certain note, how does his manufacture of the whistle determine how the second octave will relate to the first. I don’t think I’ll ever make a whistle . . . but I would like to understand more how they work.
About the making I have no idea but it’s simple enough to compare where two whistles overblow.
About the relative pitch of two whistles’ 2nd octaves, tune two whistles so that when you stick them both in your mouth and blow, the low octaves are right in tune, say on the note G. Then overblow them to get G in the 2nd octave and the difference will be clear. Of course it’s a rough test, but it’s valid, I think.
It doesn’t matter, really, as long as the octaves can be blown into tune by the player. At the extremes playability suffers. The sharpest 2nd octave I’ve seen was the Optima I tested, so sharp that you had to blow the 2nd octave so soft that the notes were on the edge of falling to the low octave, and blow the low octave so strong that the notes were on the edge of breaking to the 2nd octave, to play the two octaves in tune. Really, on that whistle, when I was blowing the low octave notes strong enough to match the 2nd octave at its lowest possible pitch, the low octave notes were fluttering on the edge of breaking.
One of the flattest 2nd octaves was the Dixon I have. To play the octaves in tune the 2nd octave has to be well blown out, and playing very loudly. The low octave, being relatively sharp, has to be very underblown, giving a volume and tone far below what the low octave is capable of, if fully blown. Trouble is, if you blow the low octave so that it plays at its full potential the pitch is higher than the 2nd octave is capable of (the notes breaking to higher harmonics before they can get sharp enough).
Anywhere between those extremes the player can make things work.
You can likewise test the relative pressure required to make the 2nd octave speak by sticking two whistles in your mouth and increasing the pressure until one whistle breaks to the 2nd octave and the other doesn’t. Some whistles have an easy nimble 2nd octave, on some it takes a huge increase in the blowing to force out the high notes. Just yesterday I tried a friend’s V3 and the 2nd octave was amazingly easy and light… I could triple-tongue high B and each note spoke cleanly and effortlessly. (Of the Low D’s I have the MK and the Lofgren have the easiest 2nd octaves… this V3 blew them away in this regard. However its low octave had a rather lower volume than the others.)
Thanks, Richard. But it’s the theory I’m interested in. I know that slightly shortening the window (lengthwise) makes for an easier second octave and weaker first e.g. Ian Lambe & Reviol Low Ds, and possibly the V3. Large holes also make that second octave easier but I really want to understand, in practical terms, how a maker determines the relative tuning of the two octaves. It interested me in a previous posting (actually probably a PM) that you said you found Overton Low Ds to to have a flat second octave requiring a lot of blowing to get in tune whereas your Goldie Low D had a more balanced tuning. Given the marginal differences between the two whistles, why is that I wonder?
Interestingly, according to Guido Gonzato, “. . . with cylindrical whistles the second octave is slightly flatter than the first octave.” Just found that. Fairly dogmatic statement . . . but experience doesn’t seem to bear that out.
Interestingly, according to Guido Gonzato, “. . . with cylindrical whistles the second octave is slightly flatter than the first octave.” Just found that. Fairly dogmatic statement . . . but experience doesn’t seem to bear that out.
What experience doesn’t seem to bear this out?
Does the experience include careful examination of the whistle design?
Is the whistle truly cylindrical?
Perhaps the statement is dogmatic because the theory says its true.
Deviations from a pure cylindrical (or conical) bore can effect the octave tuning, in either direction.
Hole size and depth also effects octave tuning, though this cannot make 2nd octave sharper, only less flat
There is even math that describes it, though the common calculators on the web approximate the solution to the equations, and the approximation throws away information on the difference of tunings of the octaves/harmonics.
Perhaps you might find this page of interest http://tippleflutes.com/the-tipple-fajardo-wedge/
Thanks for your interesting post. I was acknowledging panelticpiper’s not inconsiderable experience in playing whistles. And I would have thought that the tubing used in making the likes of MKs and Goldies would be truly cylindrical as you put it . . . but perhaps not.
Hole size and depth also effects octave tuning, though this cannot make 2nd octave sharper, only less flat
Perhaps you would expand on this please. Do larger deeper holes make the 2nd octave less or more flat?
Dougle Tipple’s comment that “one of the inherent shortcomings of cylindrical bore flutes is that the upper part of the second octave begins to go slightly flat,” bears out what Guido Gonzato says and I was taken with the idea of his wedge that mitigates against that tendency, I wonder if any low whistle makers have thought of playing with that idea.
I’m curious to know what you make of this, pancelticpiper. It occurs to me that a maker tunes a whistle in accordance with the way he plays whether that be blowing soft or hard, or somewhere in between. A player may approach that whistle with a very different way of blowing. I wonder if that has any bearing on the perceived relative tuning of the two octaves.
I’m still left with the question of how much control the maker has over the relative tuning of the two octaves if, for example, the size and depth of the holes makes a difference.
I believe that might be the purpose of the block on Carbony low whistles. Instead of coming straight down from the windway, it comes down for a very short distance and then it angles forward, and it slopes, extending at a steady angle into the shaft of the head. The block angles forward until it meets the floor of the head, going completely under the window and meeting the floor beyond the area where the ramp is. I have difficulty explaining stuff like this, but hopefully you get what I mean. I posted some photos of this in the Whistle and Flute Makers Exchange Facebook group, as I was asking about what the purpose of this was. Some suggested that this was to give the same effect as a Fajardo wedge, or the tapered head on a Boehm flute. Not sure if this photo will show up for everyone or not, since I am linking it from a closed group.
Sorry for the poor quality, but I only had a flip-phone camera at the time and was in poor lighting. Shaws also have a block that angle forward, but it is a steeper angle, doesn’t extend very far out at all, and starts immediately at the top of the block, immediately under the windway exit. I am not sure if it is that way for the same reason as on the Carbony (if the reason is indeed as others had told me in the first place).
The main thing that affects the tuning of the registers is the bore. The tuning of a cylindrical bore is progressively flatter through the octave. The tuning can be adjusted by changing the bore at, or near, the pressure nodes of the standing wave. Constricting the bore at a pressure antinode will sharpen the note (or the same is achieved by widening the bore at a pressure node). If you know the wave function for your whistle (and who doesn’t?), you can work out where to narrow the bore. Failing that, it’s experience and trial-and-error. A good explanation may be found here: http://www.navaching.com/shaku/tuning.html. Although it is for shakuhachi, the principal is the same, so it is worth the effort of wading through it.
Thanks, Chris. Maybe I’ll write to Carbony and see what they have to say. Couldn’t hurt. Of course Carbony whistles are tapered so may not suffer from the same problems that Tipple outlines. But Carbony’s reply might be interesting.
BTW Could you PM me on how you’re finding their Low D, given the comments you sent me about their Low G.
P.S. Thanks for the posting PCL. That’s an interesting but heavy article. I’ll come back to it later.
The WIDesigner program, https://github.com/edwardkort/WWIDesigner, does treat the octaves independently, and can handle tapered bores and bore sections.
For strictly cylindrical bores under normal blowing conditions, the second octave will tend to be flatter than the first. You can mitigate some of the difference by adjusting the size and spacing of the holes, but not a lot. The difference is less if the whistle is designed for someone who likes to blow hard in general, so that notes in both octaves are in tune near the top of their range.
Yes, the angled tail on the block serves the same purpose as the Fajardo wedge. Both help even out the tuning on the octaves.
There are other things the maker can do in the design of the head to alter the tuning difference, but I don’t know what they are.
You can mitigate some of the difference by adjusting the size and spacing of the holes, but not a lot.
Can you enlarge on that please? Larger holes further apart mean less difference or what?
Highwood also referred to the depth of holes making a difference. Again, I would like to know which way.
There are other things the maker can do in the design of the head to alter the tuning difference, but I don’t know what they are.
I suspect that, in shortening the window slightly to bring the octaves closer together and make the second octave easier, that the tuning difference will also be reduced.
Now I need to go back and measure the bores.
But a mere glance shows me that the Burke Low D, with a bore bigger than several other Low D’s I compared, was in the middle 2nd octave pitch-wise, and three other Low D’s, with bores roughly the same, had very sharp, in the middle, and very flat 2nd octaves.
Of course the Burke has several “perturbations” and a number of Burkes I’ve had had one oddity: B in the 2nd octave was considerably sharper than B in the low octave, the rest of the notes being good.
For what it’s worth, here’s what WIDesigner says about hypothetical changes to a hypothetical Gonzato-style PVC high-D whistle. The baseline has an inside diameter of 11.9 mm, 1.9 mm walls (hole depth), and a 5.4 mm long window. For each of these trials, I re-optimized the whistle to make it as in-tune as possible over the full two octaves.
- Reducing the walls to 1 mm or even 0.4 mm (more like a brass tube) can give an octave spread maybe 5 cents narrower on some notes.
- Increasing or decreasing the diameter by a few mm doesn’t really help the octave tuning either way. Some notes are better, some are worse.
- Making the window half a mm shorter or longer didn’t make it significantly easier or harder to make an in-tune whistle.
- Designing a whistle for someone who prefers to blow both octaves near the top of their range doesn’t seem to do much for the octave balance.
Anything else you want me to try?
Thanks for that link - I’ll have to check it out, though I do have a spreadsheet that I developed that predicts octave tuning.
Its not so much the bore size that matters but perturbations in the bore.
It does not take much to make significant changes - we’re talking thousandths of an inch
edit: - just reread pancelticpiper’s post perhaps he was meaning to measure both size and perturbations, in which my second comment is more relevant. It is difficult to measure a bore variations accurately enough, also consider tuning mechanisms by their nature will alter the bore.
A whistle with a bore of 0.490" v 0.480" will not be much different however widening a section by 0.002" can make a significant difference, or not, depends…
Interesting fact, the equation (1st published ~1930) that describes a wind instrument bore, holes and frequency produced (there has to be a better way to say that - but I’m tired) is the same for cylindrical and conical tubes. I’ve never played with conical tubes so I have no practical experience.
As to tone hole size - a deeper hole (due to a thicker tube, or a chimney (think modern metal flute)) is more or less equivalent to a smaller hole.
Making a hole larger or less deep will raise the pitch of both octaves but will raise the 2nd octave more than the 1st
Of course there are other factors involved in picking tone hole size besides fine tuning of octaves.
Also the size of the head window effects tuning of both octaves (not that this would be a primary reason to choose a particular dimension), a flute is a more flexible instrument because the player has control of the size of this hole and can alter the stream of air’s size.
For such a simple instrument - a tube with 6 finger holes, and a contraption to direct an airstream over 7th hole - the whistle is quite a complex design problem, if one wants great results.
Can you model the effects of a Fajardo-style wedge?
Can you model the effects of a restriction of the cylindrical bore near the window, say a narrowing of the bore to about 80% to 90% of its diameter, starting down from the labium one bore diameter and one bore diameter long?
I would be very interested if such “perturbation” could be mathematically modelled to assist second octave tuning. In reality it seems to work reasonably well to lift some upper second octave notes from inherent flatness, meaning the upper second octave notes can be blown softer than if the whistle bore is left entirely cylindrical.
To be more precise: such tube narrowing will lower all notes, but the upper second octave notes less, thereby lifting these relative to the others from their inherent flatness.
The hypothetical whistle I’m using was based on a very real PVC whistle that does have a Fajardo-style tail sticking out of its wooden fipple block. Exactly the same principle as Sirchronique’s Carbony, although I wasn’t aware of the Carbony when I carved it.
To model it, I reduce the diameter at the windway to 10 mm, tapering in from 11.9 mm at 19.6 mm above the splitting edge.
If you look at the average octave spread of all the notes, the wedge doesn’t offer much improvement. However, the wedge does allow you to produce a whistle with:
- Noticeably smaller octave spread on G, A, B.
- C# and C-nat much closer to being in tune in both octaves.
Out of curiosity, I tried tapering in the other direction: from 11.9 mm at the windway and 19.6 mm above the splitting edge, down to 10 mm or 8 mm at the bottom end of the whistle. To my surprise, that didn’t work nearly as well, offering almost no improvement on the straight cylinder. I’d begin to suspect the model, except Edward Kort reports that WIDesigner models the tapers in his NAFs very well.
Hi, I have noticed when I make whistles that the second octave will be always slightly “flatter” than the lower octave …I believe Guido Gonzato mentions this too. The difference is fairly insignificant, the layman wouldn’t notice it and this can be compensated by blowing a little harder (notes can be made sharper or flatter depending how hard we blow). In fact, I believe, the whole set-up of a whistle is essentially a compromise, with each maker (and player for that matter) putting his own stamp on it which is, I think, a good thing as it makes the whistle quite a personal instrument for expressing a piece of music… It may be possible to over analyse the the whole thing if we’re not careful …what do you think?
Hope that helps?
John (from www.redheadwhistles.com)
Good comments, John. Thank you.