PVC flute temperament

Irish Flute
1

Hello All,

I am about to embark on making PVC flutes a la Doug Tipple’s design. I have one of his, and it’s really quite wonderful, considering it’s a bit of water pipe. I have a background in mathematics and physics, so I have some degree of comprehension of the acoustics involved. It’s great to have the flutomat calculator available online. My question is this. Flutomat allows you to specify the value in cents of the note you want. All well and good. But what sort of temperaments are the flutes used for Irish music typically in?

There’s a very useful page here explaining the calculations, mostly based on the acoustics by Benade and also Fletcher. The starting point here is a table of just intonation intervals.

https://pages.mtu.edu/~suits/fingers.html

But are these flutes tempered just? I don’t hear that. They are most certainly not equal tempered. What is the traditional sort of tempering used in simple system flutes? Sure, I can just measure Doug’s instrument, but I want a more comprehensive understanding of what is most commonly used.

I am aware this is a large size can of wriggling worms to open!

2

I’d say our traditional flutes are Bad-tempered, Andro. The music of the era calls for Well-tempered or Equal-tempered but 19th century flutes present no proof of either. The errors far exceed the relatively subtle tweakings of temperaments. Especially those flutes with the very flat feet or elongated body scaling or both.

Further the errors are understandable. Because of the limitations of our hand’s stretch, it’s hard to get F# up to F#, and c# up to c# without making c-nat (crossfingered) too sharp. That’s why Boehm spat the dummy and started again with his mechanised approach.

The test for me for whether a temperament was in place and being successfully implemented would be are the ratios in the second octave the same as the first. Nah, they’re all over the place.

Whether we should have a temperament is another question. Given we only play in 2 or 3 scales (G, D and occasionally A scales, in the various modes that employ those scales) it would seem to be attractive to come up with a temperament that favoured them. But you’d have to get all the concertina and box makers on side first. The pipers would of course point out that they follow a different God, the God of Drones, and the piano tuners would mutter about stretched scales. (Presumably MIDI pianos have somehow got around that? Or haven’t got to it? And aren’t likely to get to it?)

I’d aim for ET and see how far you get.

3

Be warned that Flutomat, and most of the math on Prof. Suits page, are aimed at fipple flutes, and only the first octave. Allowing for the headspace between the embouchure hole and the stopper is a whole other kettle of fish.

4

Andro

Measure Doug’s flute and plug those numbers into the Flutomat. Measure the pitch yourself and compare with the predictions.

if Prediction => Total Fail
____download “WIDesigner”
else
____crack open the champers
endif

5

Hi Tunborough, the flutomat I am looking at here:

http://www.iotic.com/flutomat/

seems to be for side blown flute, as it gives the position of the blow hole, and even the lip coverage percentage. I didn’t think it’s for fipple flutes. Am I missing the point? Also, Prof. Suits article seems to be for side blown flutes, as he only mentions at the end the necessary corrections for a fipple flute.

For the next octave, the Tipple Farjado wedge seems to work pretty well on my Tipple, so I will experiment with that. As for stoppers, I thought the usual starting point is the bore diameter away from the centre of the embouchure, to begin with?

I’m aware that this is an iterative process. As Prof. Suits says, if you are going to make one, plan on making at least two.

6

I wasn’t aware of that implementation of Flutomat. It certainly is for a transverse flute.

Please put it to the test as Terry suggests, and let us know the results. If they aren’t satisfactory, you can find WIDesigner at https://github.com/edwardkort/WWIDesigner/wiki. (The flute model is still a work in progress, but you may find it already gives useful results.)

7

I reckon you’ll find the wedge pretty well essential, as the plain cylinder will be very flat by the time you get to second octave B.

It’s hard to be definitive about the position of the stopper face, because it will interact with the size of the wedge! The stopper will have more effect in the third octave than either of the lower two.

I’m aware that this is an iterative process. As Prof. Suits says, if you are going to make one, plan on making at least two.

Heh heh, I like that. And of course, if the second one goes really well, you might want to make lots more!

I did a school exercise many years back where I got the kids to make simple piccolos out of electrical conduit. Pretty much drove the teachers demented!

8

I am going to make lots if I can master the tuning matters. I found a source of high quality ‘furniture grade’ Schedule 40 PVC pipe that can supply colours other than white. Get ready for orange, red, yellow, and blue flutes! If nothing else, they will look happy.

9

Good! I’ll know to look out for you when I see brightly coloured flutes being tooted on at folk festivals!

Now don’t just limit yourself to the idea of the Fajardo wedge (although as I’ve mentioned, you’re unlikely to find a plain cylinder very rewarding). A downside of the wedge is that it produces a D-shaped bore around the embouchure hole where the air-column still has some rotary activity.

Consider the possibilities offered by casting a plug in the head over a Boehm-shaped former, or softening the head end of the tubing (suitable chemical plus heat?), and drawing it out over a similar Boehm-shaped former. The former could just be wood, suitably greased so it doesn’t become a permanent inconvenience!

Note I’ve only talked about tapering the head end. You could taper the body alternatively, but it’s a lot more work.

10

Hi Terry,

Curiously, I have been considering exactly the same thing about the headjoint for my design, having had a good look inside the Tipple headjoint with the wedge - just another bit of smaller diameter pipe shaved down to a wedge, with the inner curve still left in it.

Is the Boehm parabolic design ideal an actual parabolic curve, or just a conical approximation?

11

I guess this answers my own question:

http://www.mcgee-flutes.com/Carte-on-Boehm’s-patent.htm

Nothing like a parabola.

So my question shifts to, would there be a good acoustical tuning reason to use a parabola, given that nowadays there are many ways to make such a headjoint or insert, 3D printing for example.

12

No, but let me make a really careful distinction. Although Carte appears to be quoting Boehm, I think he is really misquoting him, and badly. Keep in mind Boehm is the technical person here, Carte is the flute-salesman.

Boehm wanted to make it clear to us that it wasn’t a linear taper. He used the expression “approached the parabola”. If you plot it on an exaggerated scale (e.g. make width ten times length), you can see easily what he meant. That part of the bore is a bulging cone, if you will.

But Carte went all sciency-wyiency (apologies, Doctor) over it and tried to evoke images of search lights and other focused beams. I’m not at all convinced I would have liked Carte.

And I imagine that Boehm settled on his bulging cone shape for good reasons. He wasn’t a man to go half-measures. I’m sure I would have enjoyed Boehm.

So my question shifts to, would there be a good acoustical tuning reason to use a parabola, given that nowadays there are many ways to make such a headjoint or insert, 3D printing for example.

Hang on, can I “call a friend”?

Earth calling Tunborough, Earth calling Tunborough, come in please, Tunborough…

This would seem a very interesting study for WIDesigner, with not many data points needed. The effects of plain cylinder, tapered cylinder, cylinder with Boehm taper, then fiddle later. Thoughts?

[FX: faint sounds of Tardis landing, fade up to threatening, episode ends…]

13

Sorry, I realize this might seem unreasonably pedantic to some, but I think it is a litte unfair to claim that Boehm’s head bore profile is nothing like a parabola. In my mind, the key point about its’ parabolicness is that the rate of change in bore diameter is not constant. In other words, there is a curve (even if only slight) to the bore’s profile. To argue that this bore is not parabolic because it does not have a diameter of zero at the stopper is especially unfair when we simultaneously describe Irish flutes as having a conical bore. After all, a cone tapers from a circular base to a point. The body bore of our flutes does not terminate in a point, i.e., the bore diameter does not reach zero anywhere. So, we call our flute bodies conical because their bore profile resembles the shape of some part of a longer cone that terminates outside of the bounds of our flute. Similarly, Boehm’s head bore is parabolic in the sense that it resembles the shape of part of some much longer parabola that terminates far beyond the stopper.

So, perhaps his point in describing it as parabolic was to distinguish it from a straight taper.

14

I agree, Paddler, which is why I drew that careful distinction above. Boehm, I believe, was not inaccurate, in describing a section of a parabola. But Carte went much further, trying to use pseudo-scientific jargon to flog his 1851 pattern flute. E.G:

“The parabola-head-joint seems to effect that for propagating sound, which the parabolic reflector does for propagating light. The vibrations are concentrated in, and propelled from the one, as the rays of light are concentrated in, and transmitted from the other, both with superior velocity and power.”

We’ve probably all played a Boehm flute at one time or other. I don’t think any of us feel that audience members were at significant risk of being taken down by the sonic boom emanating from it!

“Look out, he’s carrying a flute!”

Boehm’s mention of the hemispherical stopper face was also interesting, although I’ve never come across one. I did make one once, but wasn’t convinced I could tell the difference. Perhaps after we sort out every other issue the flute presents, we should revisit that one? What shall we do in 2020?

15

Sorry Terry, I think I somehow missed your post there. I was replying to Andro’s comments in the previous post (as were you). Anyhow, I agree. Carte’s description doesn’t make any sense to me.
He seems to have been confusing the effects of the parabolic head (to correct tuning issues) and the effects of a large cylindrical bore and larger, uniform, tone holes, which had numerous effects including making the flute louder. Carte seems to be suggesting that the parabolic head is what makes the flute so loud.

16

WIDesigner does not yet have an optimizer for setting the stopper position, but it does need one. Optimizing the bore profile of the headspace is probably not something needed for routine use, but it would be interesting to put one together just to see what happens.

17

I’ve done extensive experimentation with both Fajardo wedges (like Doug uses) and parabolic tapers in the head, and there is definitely no comparison. The parabolic taper is far superior, if you have a way to pull it off. The wedges are certainly better than nothing if you are trying to get better intonation out of a cylindrical flute.

18

Ah, thanks for that confirmation, Geoffrey. I’ve not done any extensive experiments there, I think maybe just one wedge inside one cylinder flute, and was quite put off. While the tuning was greatly improved, the performance seemed to drop way at about the same rate! Whereas I have made cylinder wooden flutes with a reamed Boehm-style bore in the head and got very satisfactory results. E.G:

So, maybe take that on board, Andro. Something certainly needs to be done to overcome the cylinder flute’s tuning, but the wedge is possibly not the best solution.

Now the other trick I’ve heard about but never tried is the Sanders Spike (from memory!). I understand it takes the form of a conical spike protruding from the face of the stopper and pointing down the bore. The cross-sectional area of the spike is designed to take up the same volume from the same places in the cylinder as the Boehm head taper would have reduced it. In practical terms, I imagine you’d make it part of the stopper arrangement. Because the air column is free to rotate about it, it might present less disruption compared to the Wedge (even though it might seem the opposite!). Can anyone report back on that?

19

That’s a fine looking flute!

The spike definitely sounds like a better idea, and I’d be curious to try it. I don’t love the idea of a spike in the headjoint for some reason, but conceptually it seems like it would cause less interference. Sounds like we had the identical experience, Terry: better tuning at the cost of a seriously choked off voice. They still played (after a fashion), but they were not free-blowing and they felt like they were fighting me. Some players loved them, but I never could.

20

Thank you. You’ll note I did a few changes to the traditional (if relatively uncommon) 19th century cylinder bore flutes. Particularly at the joints, which are really thin-walled and often cracked for that reason. Especially as I would have cork-buffered the slides at the bottom of head/top of the body. So it’s clearly possible to get around that issue without having to turn the whole thing into a baseball bat.

The spike definitely sounds like a better idea, and I’d be curious to try it. I don’t love the idea of a spike in the headjoint for some reason, but conceptually it seems like it would cause less interference.

I think cleaning the head after playing will be a bit trickier, but probably not impossible. If you have a plain cylinder flute lying around somewhere it would be easy to knock up a spiked stopper for it. I haven’t looked at the maths, but I imagine that wouldn’t be an impediment? Now am I right in thinking that to give us an effectively bulging (“parabolic”) bore, we’d need a thinned spike?

Sounds like we had the identical experience, Terry: better tuning at the cost of a seriously choked off voice. They still played (after a fashion), but they were not free-blowing and they felt like they were fighting me. Some players loved them, but I never could.

Yeah. I toyed with the idea of siting the wedge under the embouchure hole, so that the hole passes through the wedge. That would give one full revolution before the spiralling air column comes back around to the wedge. I wonder if that’s enough to allow it to straighten out?