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I used a 3D Printer to make a kid's Recorder. It plays surprisingly well. However, it's not tuned to match the common recorder used in schools. Using a phone-app tuner, the base mouth-piece section of the print blows a (very high) A, while a Yamaha school recorder blows an A♭.

One of the nice things about 3D printers is you can scale your models. I'd like to scale this model so it will be tuned closer to what we see widely for sale.

The question is in two parts:

1. Is this a reasonable thing to do (will scaling the whole model result in something playable, where things like finger holes are still in the right places)? Alternatively, would I do better to add some length to the tube, and if so should it be before or after the fingering holes?




2. What ratio (in percent) should I scale the part up to tune down from the A to the A♭?

Have a look at the picture at https://www.moeck.com/en/service/faq/the-recorder-family.html. The instruments are indeed (roughly, at least) scaled proportionally in all three dimensions. I would do that, especially since you're talking about a small change of scale rather than printing an alto or tenor recorder from plans for a soprano.

I would try to measure the frequency of your recorder playing an A. Then I would divide that by 440 and use the result as the scaling factor to increase all three dimensions of the model to be printed.

Alternatively, you could try doing the same with just the head joint, measuring the frequency both of the one you printed and of the Yamaha to calculate the scaling factor.

I would try to be fairly precise with this measurement, since the last thing you want is an instrument that can only get close to 440 Hz.

After reading the page you linked to in the question, I have a couple of additional thoughts:

The pitch of the head joint by itself may not be so important. Two well-made recorders that both play in concert pitch could conceivably have a different pitch coming from the head joint because of differences in design. The length of the head joint might be slightly longer in one than the other, even though the assembled instruments have the same length. I would assemble the final instrument and do my best to tune it before deciding that the solution is to change the scale of the model.

You should scale the length and the hole spacing should be scaled along with the length. You might want to have the hole sizes scale up also. You should probably not scale it up in all three dimensions, only the length. And you should make sure that the finger holes don’t lose their circular shape when scaled.

I think you want to make it 6% longer (1.0564 times its original length).

You certainly need to make the complete instrument before you try to scale it, as another answer said. Unless the design is an accurate copy of the Yamaha recorder, the pitch of the head joint on its own could be anything. In particular, it will depend on the design of the joint between the head and the rest of the instrument.

To scale an instrument "properly" is a very complicated task. For example to make an instrument that plays accurately in tune, the position of the finger holes depends on their diameter, and professional instrument makers tweak such things by applying single coats of varnish to change the shape of the hole, not by changing the shape to the precision of a 3D printer!

Note that in the pictures of the printed recorder, the finger holes are not all the same size. That is not an accident - they need to be different sizes to make the instrument play in tune. But whether you can print the different sizes accurately enough is another question.

So there is little point worrying about such details, and you might as well scale everything by the same amount. To lower the pitch by one semitone, increase the size by a factor of 1.059. The finger holes should be repositioned in the same proportion.

If you want to be slightly more ambitious, you could apply the same scaling rule that is used to make organ pipes have the same timbre over a wide range of pitches. To achieve that, the high pitched pipes have to be relatively fatter than the low pitched ones. A typical scale factor would increase the diameter (both internal and external) by 1.044 per semitone, compared with 1.059 for the length.

This sounds like a fun project, but you are never going to produce a professional-quality instrument this way, so don't set your standards unrealistically high!

If you wanted to scale the design by a larger amount, for example to make an alto or tenor recorder instead of a soprano, then simple scaling is not feasible. If nothing else, you will need to move the finger holes so the player can reach them, and adjust the intonation by changing their diameter as mentioned earlier. There is no real alterative to either practical trial and error, or very sophisticated computer modelling - and the modelling usually only gives a starting point for trial and error, in any case!

You can certainly scale it. But build the whole thing before you decide it's wrong. It doesn't matter what note the first section alone plays - you never WILL play the first section alone. Judge it when all three sections are assembled. I suspect the problem will go away.

(However, I note one comment on the Thingiverse site:

"I printed this. It looks, sounds, and plays beautifully. However, it's tuned to a few tick above C#. Any geniuses out there know of a decent way to either tune the design, or else tune the printed instrument via modification? Even with all the joints just barely hanging onto each other, it's still just a tick or two above C."

User error or poor design?)