Dave,
> you
> wouldn't like to post the expressions used to generate the graphs would you?
L=Length=(Speed of Sound/2*Hz of note)-(Bore^4/(8^4))
Aspect Ratio=(0.125 L)/((Speed of Sound/2*Hz of note)-L)^(1/4)
These equations are ad hoc in that they fit the data points, but I don't
have a good understanding of them. They're fourth power which seems very odd
to me.
> I guess that for a tapered bore you're taking the average aspect ratio?
Yes. It's hard to talk about an aspect ratio with shakuhachi because the
bores are so irregular, but the equations give a method. I'll include
another method in another page I'm building.
> the Hopkins/Benade booklet/papers. Flame me if I'm wrong but these seem to
> take into account bore variations but only in that they affect the tonehole
> air column length due to wall thickness not the
> variation in bore volume.
I've never been able to wrestle them down in anything except straight tube
circumstances.
> Is it possible to derive expressions for tone hole placement based on bore
> volume(as a func. of length) and solve these ( numerically i guess)?
It's probably possible but I don't have a clue.
Nelson
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