Interesting. How well does the tuning correspond to predictions? Nederveen's thesis is dated... older than you, I'd guess. There are newer models for toneholes and flute excitation.

I am using the revised edition which was updated in 1998 (the original was 1969). There are newer methods, like FEM and transfer matrix, but this seemed like a well-documented approach that would run fast enough for me to embed it in a statistical optimization algorithm to judge the merits of arbitrary hole arrangements. With this approach, I can "judge" about 200,000 virtual flute models per minute. However, if you are able to recommend some other research for download or purchase I would be interested in investigating. For Nederveen, his first-order approximation wasn't enough, and I had to be sure to add his corrections for closed holes and end-flange which some authors seem to omit when they cover his work. Once I included corrections for those, it came into tune quite nice it seems. There are still things I would like to be able to characterize mathematically, for example, the effects of undercutting tone holes.

Very kool!

WIDesigner, https://github.com/edwardkort/WWIDesigner/wiki, uses transfer matrix models of the bore, toneholes, and excitation mechanism to perform rapid impedance calculations. Algorithm sources are listed here: https://github.com/edwardkort/WWIDesign ... bliography. The tonehole model in particular comes from the work of Antoine Lefebvre. He used FEM models to analyze air flow in toneholes and distilled the results to a transfer matrix model.

For your purposes, optimizing tonehole size and position, I'd suggest that a heavy-duty global optimizer is overkill. For that task, WIDesigner gets good results with Michael Powell's local optimizer BOBYQA, Bounded Optimization BY Quadratic Approximation. A global optimizer doesn't earn its keep until you start optimizing bore profiles as well.

I looked into 3D printing my Folk Flute model this winter, using the commonly available plastics. I shelved this project when I found out that these aren't archival and that one should go to some of the more difficult plastics such as the Nylons or ABS that require better machines. My 3D printer (JGAurora A5S) which I set up but have yet to even test. I researched it while recovering from knee replacement surgery this winter. Then I had to jump right in to a pile of accumulated flute orders followed by the Coronavirus and getting us all in good shape to handle that (this included finishing a long bathroom remodel project) and I am finally going to catch up with my last year's leftover orders and this winter's queue and have a fairly open summer. I am scheduling all new orders for the fall, except for my popular folk flutes which I spend about 1 week per month on.

I will be using this printer to help prototype an alto flute with an unusual bore.

Am curious what printer you used, as well as the filament. Also, how long did it take? These would be good things to know.

As far as the acoustical parameters, there is much that can be done. Contact me privately if you want to discuss these. I am glad someone is pursuing this approach!

Casey

This is great stuff, thanks! This will keep me busy researching for a bit. You are probably right regarding the optimizer being overkill, but I figure it leaves me room to grow if I unlock the bore diameters and tonehole heights etc from being fixed constants (and it currently runs for less than a minute each redesign/rebuild).

The printer I used is the Anycubic Predator. I bought this specifically for printing the flute, and it is my first 3D printer (on sale at the time too). I chose this one because it is a "delta" printer. These are different in that they operate without moving the bottom print bed, and they have a larger vertical print dimension. This was so that I could print the flute parts vertically without them falling over due to bed motion. Also, the bore is a more perfect circle printed in this orientation, avoiding a "staircase" effect that would occur if printed laterally.

The filament used is PLA 1.75mm diameter filament. The one in the photo is a metallic silver color. This has no metal content, but there are composite filaments (like 50% wood, or 30% copper metal, etc). Composites may require hardened nozzles and reduce accuracy. For now, I am sticking with PLA because it is easy to print accurately, it has a density similar to blackwood (ABS filament is closer to boxwood) and PLA does not omit noxious fumes when printing (ABS does FYI).

I spent about 6 months designing the flute in my free time (software engineer by trade), but as far as printing goes, each of the three flute-parts take less than 7 hours to print, so around 20 hours printing time for an entire flute. I usually print one or two parts in a day, checking on them every hour or so to make sure it didn't fail and start spewing plastic spaghetti.

Absolutely these density figures are pretty correct (of course). However, speaking as an instrument maker and woodworker, while high density is desirable, I think there is more to it than that. I cannot submit much science about it, but Blackwood has different performance to PLA for sure. However, I would like to hear.

Most flutes would want a movable cork, to allow for adjustment of tuning in the relevant octaves. I'd be surprised if the algorithm you have used for hole size and placement gets both octaves bang on right off the bat. How is the octave tuning working out?

The PLA intrigued me due to its source (made from corn), density similar to blackwood, and relative ease of use. However, it flows with time and so for an instrument that I would send to a client it would be inappropriate.

My original plan was to rough these out on the printer, then do a finish reaming or sanding of the bore after hand cutting the embouchure. Printing them horizontally may actually be a good thing as the staircase effect simulates wood grain to some extent. A further thought is that a perfectly circular bore isn't desirable from an acoustical point of view. Wooden flute bores deform to a very slight ovality with time and I think this boosts their performance. Even some of the modern flute makers in metal slightly deform their metal tubes for similar effect.

Casey

Yeah, I am sure there is more to it than density (like microstructure) but quantifying that is a challenge to be sure. I think I will add a movable "cork" in an upcoming version, as I could see that being useful. My octave tuning seems pretty good for now, the second octave seems about 10c sharper than the first.

Do you have a source for the info about PLA flowing with time? My understanding was that PLA actually holds up better than ABS does, at least below the glass transition temperature. As far as sanding and finishing, PLA is quite brittle so that might be a limiting factor. Another issue with printing to consider is that large "overhangs" are not allowed. Imagine trying to print a box with a lid. Printing the bottom and the walls will not be a problem, but once you get to the top or "lid" it won't work if you are just printing in thin air (the plastic will just fall into the box). This issue would arise with printing a tube horizontally, unless support structures were also printed inside the bore that could be removed later. At first, I started down the path of trying to print an existing flute model and discovered it would be better to design a flute especially for additive manufacturing where the design can work around geometrical limitations.

I am considering PETG filament, which has a little higher density (1.27g/cm3) but less brittle than PLA and has a higher glass transition at 80C (ABS is still higher at 105C).

I will try to find time to make some recordings this week as sound samples since a few seem interested

This is very Interesting.

Though I do prefer a black one. Im very curious to try. But since its COVID season, I cant risk it though.

Maybe after the pandemic.

Can you also print an 8 whole flute?

_________________
Quote by Zig Ziglar: “Success occurs when opportunity meets preparation”

Certainly are, Starlight. (I'm tempted to call you Captain Starlight, as we had two, not just one, bushrangers here in Australia back in the 19th century with that name. http://bushrangersau.blogspot.com/2011/ ... light.html )

Now, I should be grumpy with you. I've been beavering away for 55 years now, making Irish flutes the hard way - assiduously seeking out and measuring old flutes from all around the world, doing my best to interpret what I found, updating them to modern tuning and performance standards, excavating new examples of them from solid dead trees by the time-honoured methods, and then introducing new constructional techniques within that traditional framework. And then you decide to dump it all and take a short cut! The absolute nerve of some people!

But no, not grumpy at all. Excited that we might be moving on from Phase II - "the old flute revival" - to Phase III - "new flute design and realisation". This has to be what the future looks like. Long awaited. Go for it!

I'd be interested to see the tuning you've achieved so far. It tells us about the tuning (obviously!) but also the performance of the flute, as the performance is so dependent upon the support of the partials. You might find one of the systems at: http://www.mcgee-flutes.com/RTTA.htm helpful in determining where it's at. Or include a slow scale among your sound recordings and we'll all gleefully tell you where you're going wrong! (Only joking!)

Great to have an answer up your sleeve to the question of the future: "Grandad, what did you do during the Covid 19 lockdowns?" "Oh, nothing much, young fella. Just redesigned the Irish Flute..."

Interested too to appreciate the benefits and challenges of printing as a process. Density, stability, precision, finish, longevity - oh, Brave New World! We just did the best we could with the old dead trees!

I guess at some point we have to bring those pesky humans back into the equation, and have one or more well-qualified fluters in your area do A-B comparisons between their favourite flute and your new instrument. We have to be aware that they will possibly struggle to maintain objectivity, just as we-who-cannot-be-there may struggle to interpret their responses.

We look forward to the challenges ahead, and commend you on the journey so far! Keep us in touch!

Wood??!!

Yeah.. can you print a wood alone?

What sorcery is this?

_________________
Quote by Zig Ziglar: “Success occurs when opportunity meets preparation”