Patrick,

The problem with letting technicians go on without discussion is that:
1) They don't agree with each other 100% of the time on the facts.
2) They don't even always agree with themselves.

Joe,
"The "parabola" is a result of figuring cross sectional area."
I believe that you may have meant cross-sectional geometry.
It was referred to as paraboloidal and that is only an approximation by Boehm's acoustic changes to increase the sound projection of the instrument. This is an area where the technician does not necessarily need delve very deeply into unless one is reconstructing a particular HJ taper in exact measurements.

At any rate, I'd believe that the "straight linear taper" that you insist upon exists rarely in flutes even back to the Baroque body joint(s) tapers. Of four heads that I could immediately try, none of them had a straight taper as you suggest all of them decreased in taper at the cork end as I wrote. One head joint (Old 3SB head that I don't play) had a slightly loose cork (Shrunk from drying out and age) that was loose enough to remove. It fit equally snug returning it from the crown end as from the tenon end. Not that I would advocate inserting a cork assy. from the crown end. I only did this to prove to myself my point. Actually at no time did I ever recommend inserting a cork from the head end. and I could see how a manufacture interested in tight tolerances could make the metal disk very close to the bore diameter as you had suggested.

"You are not going to use cork to stretch metal in this manner...that's silly..."
Actually, I would say that it is very possible for a hard and dry cork to deform a standard wall silver tube. I would put nothing past people when that possibility exists. Gawd, ( I would not recommend trying this but you can easily temporarily deform the silver tube a bit with thumb and index on the tenon end. Fortunately, there is a certain amount of elasticity to the metal.

I would again state that since we are arguing on the same side of the fence, one should not put the cork assy. into the flute from the crown end.

The thread is now quite long and I had missed a few concepts.
I see now that the taper can be considered to be linear, to all practical effects. Also that playing with a +4mm cork misadjustment is very unusual and most probably sound degrading. And that is not necessary to adjust to tenths of millimetres, which in any case I cannot measure and most probably will not be able to appreciate by ear.
I will attempt it tomorrow, moving the cork with the crown and eventually with the help of a wood dowel (I will have to build one) if it does not move with a reasonable torque on the crown. And will inform on the results, of course.

Bilbo, you are correct, they don't always agree, so lets get back to Angelina Jolie's LIPS!!

"The "parabola" is a result of figuring cross sectional area." I believe that you may have meant cross-sectional geometry. It was referred to as paraboloidal and that is only an approximation by Boehm's acoustic changes to increase the sound projection of the instrument.

Most of the measured Boehm samples are straight linear taper. Only very few are considered "paraboloidal" and that is only because the straight taper begins in a different location.. Maybe you should re-read his book pgs 16-17...

Boehm experimented to find suitable proportions for a fundamental tone which was manifested in a bore to length ratio which he also identifies in his book..That has nothing to do with which taper is where. (He experimented for both head and body to make a decision)

The taper is required due to perturbation weight functions to make the third register possible and bring the registers in tune.

The reduction necessary that Boehm figured out is a 10% reduction of the bore to the stopper plate. Theoretically, what is beyond the stopper plate is moot, however in practicality, they are a continuation of the same taper. It's the difference in the starting point of the straight taper that leads one to infer a "parabolodial" shape. But the taper is straight and as a result of it's starting location, a steeper rate of taper with particular tuning and playing characteristic tendencies is the result.

This is an area where the technician does not necessarily need delve very deeply into unless one is reconstructing a particular HJ taper in exact measurements.

All the technician needs to know is that a cork starting out as cylindrical must fit into a conical bore with the mechanical ability to seal at the larger end of the taper in its proper, functional location....

At any rate, I'd believe that the "straight linear taper" that you insist upon exists rarely in flutes even back to the Baroque body joint(s) tapers.

Baroque body tapers have nothing to do with this discussion. you are talking about bore perturbations for a completely different purpose. That is irrelevant to this discussion.

Of four heads that I could immediately try, none of them had a straight taper as you suggest all of them decreased in taper at the cork end as I wrote.

Well let's see the measurments graphed out then...

One head joint (Old 3SB head that I don't play) had a slightly loose cork (Shrunk from drying out and age) that was loose enough to remove. It fit equally snug returning it from the crown end as from the tenon end.

So now I see...The 3sb's have a slow or smaller rate of taper. If you did your measurments you would realize that and if you worked on enough gemeinhardts you would know that. Comercially available RAW corks are not supplied large enough to fit snug in the tenon end. How could a leaking stopper cork be equally snug in two different diameters? C'mon bilbo...that's really stretching it...

I said: "You are not going to use cork to stretch metal in this manner...that's silly..." Bilbo replied: Actually, I would say that it is very possible for a hard and dry cork to deform a standard wall silver tube.

Maybe if you used a raw supplied cork and hammered it into place....maybe....We are talking of stretching the metal...not deforming. The cork can make the tube a bit more round if it wasn't in the first place...I will only give you that much...

Joe B

No, I have no intention of reopening the intense debate on tapers and the like.

Just that I would like to tell you that I finally readjusted the position of the cork (placed it dead center) in my Yamaha and the problem with Eb practically disappeared.

I do not notice any degradation on the tuning of the third octave, the F# is as difficult as always and a few notes are as sharp as they were before the change....

My teacher also noticed the change in tone quality. But she was quite startled when I told her that I had moved the cork 4mm

What!!! she said, the Yamaha!!!?

But everything is running smooth now.

Thank you all a lot for your opinions and help.