Tunborough wrote:We need the thickness at each tone hole, including those in the foot joint, and at the embouchure hole.
I'd like the outside diameter at the foot, although it doesn't make a whole lot of difference.
Take wall thicknesses everywhere as 4mm for the purposes of this experiment. The foot diameter is for flange effect?
Is -153 mm the position of the centre of the embouchure hole?
Yep
How can the diameter of the first foot tonehole be bigger than the bore diameter at that point?
When I look in there, I can see the walls sloping inwards. So, yes the side branch is bigger than the pipe!
On the compressed flute, is the open end of the headjoint still 19 mm, leaving a sudden step at the junction with the first body section?
Correct. Doesn't seem like a good idea. On the Uncompressed flute, I've lined up the slope of the body to meet the bore of the head at 19mm.
This sudden reduction of bore at the start of the cone is very common, as you'll see from the bore graph further up. Indeed, it's very rare to see a flute that doesn't have it. So the question I'm hoping we can answer is whether it was intended by the maker, or is an artifact of aging, including tenon compression.
So far, with a bunch of assumptions about other parameters, I've got A4 in tune on the compressed flute; D4 is 63 cents flat, F#4, C#5 and C#6 are about 40 cents flat. "Uncompressing" that tenon makes everything flatter, by 20 cents at A4 and 10 cents at D4. Where's the tuning slide? If I shorten the headjoint by 6 mm, A4 is in tune and D4 is 53 cents flat; F#4 is still 40 cents flat. (All this is relative to E.T. What temperament would you like me to use?
The tuning slide is 22mm open at A=440Hz, so there's plenty of room for sharpening! Indeed, with the slide fully closed, xxo ooo plays Bb which seems a bit much.
So, no other wild effects from "decompressing"? But while it nudges the low D slightly in the right direction, it doesn't explain the flat-footed-ness.
Stick with ET as we have found no clear evidence of other temperaments. The errors the flutes show far exceed the (mostly) small deviations temperaments would make.
So it sounds like your system is looking promising? The figures you quote are about right. (F# isn't quite that flat but I notice the hole is well undercut. Can we handle undercutting in the system? Measuring it accurately might be tricky.)
We might want to add more bore points to capture the real bore profile more accurately. Then I'll ask for more tuning information.
OK. Are you entering into new territory here, or have you already done some conical flute measurements?