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PostPosted: Sun Oct 04, 2020 2:38 am 
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Hello! My understanding is that nowadays flute designs are normally based on great old simple system models (Rudall, Pratten) and then makers introduce their own design improvements such they can obtain better performances (correct 440Hz tuning, hard D, stronger sound,…).

My question regards flutes in different keys. How is normally the size/design scaling done? I believe Rudall Rose made Bb and Eflat flutes, but what is normally the correct procedure to scale them? For instance, starting from a standard D flute:

-I understand the length of the flute can just be scaled geometrically applying the wavelength ratio of the two low notes on each flute, including tone holes.
-Bore can also be scaled, and I believe would work, but I do not think this is done this way cause maybe the effect on tone would be quite dramatic. What is then normally the procedure for selecting a given bore?

Just for the record, I am looking into making an Eflat flute from a D flute drawings/design.

Thanks!


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PostPosted: Sun Oct 04, 2020 5:40 am 
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Joined: Sun Dec 12, 2004 4:12 pm
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Location: Malua Bay, on the NSW Nature Coast
Woah. Hasn't anyone warned you about meddling with the Space-Time continuum?

I think it's possible to scale over short distances, in fact, I think I have done it. D up to Eb for example. D down to Bb might be a bigger ask.

D to Eb is a semitone, which (in equal temperament) is 2^(1/12) = 1.05946. Because we are going up in pitch (and therefore things should get closer together), you would divide the D measurements by this factor to get you into the Eb ball park. Recognise that, because of second order effects, some subsequent tweaking might prove necessary. For example, I would start my finger holes smaller than I expect to need, and work up. If that didn't satisfy, I might then move the holes a little and try again.

Tunborough might come in here and say, why not use Wind Instrument Designer to help. If he did, I would listen.


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PostPosted: Sun Oct 04, 2020 7:56 am 
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What got me started down the whole acoustic modelling rabbit-hole was trying to scale a D whistle down to Bb. I tried simple multiplication. I got a nice little whistle out of it, but only because I started out with the holes drilled way smaller than my predictions, intending to enlarge them; the whistle was in pretty good tune with these way smaller holes, so I left them that way.

Not everything is linear in frequency. The bore diameter, for example, varies with the inverse of frequency to the power of 5/6. See viewtopic.php?f=1&t=84789&start=45#p1045576. For hole position and diameter, you might get away with Terry's suggestion. Because D to Eb isn't a big step, you might get in the right neighbourhood if you divide the dimensions by 1.06.


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PostPosted: Sun Oct 04, 2020 8:09 am 
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Going from big to small doesn't scaling discard the possibility of making the two third finger hole positions acoustically better?

I think a big reason for me liking my F flute is that the tone seems better balanced than a D.


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PostPosted: Sun Oct 04, 2020 8:23 am 
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This makes me think of partial differential equations. Hold all things equal, and the perturb one to observe the effect.


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PostPosted: Mon Oct 05, 2020 5:27 am 
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Many thanks! Then if I summarize, to go from D to Eb:
-Length can be scaled with factor 1.0595.
-Bore can be scaled with the same factor or, using the expression from Tunborough (ratio of inverses of frequency to the power of 5/6), with factor 1.0493.

I'll try first just scaling everything with 1.0595 to see how it goes, but it kind of makes sense that the bore scaling factor is a bit smaller.


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