Mujitsu and Tairaku's Shakuhachi BBQ

I've been searching the web and recently stumbled upon something....

http://communication.ucsd.edu/shaku/Sha … /0205.html

it's a response from Monty Levinson about the bore of the Shakuhachi..... here it is...



I came across a printed version of these graphs several years ago
(pre-Internet) and have been told that they represent a composite of
many shakuhachi whose parameters have been averaged for each length
of flute. At that time, I used them along with a database of
numerous bore profiles I personally measured when developing a
process for mathematically scaling shakuhachi of different sizes.
Needing to find a constant that defined the ratio of cross-sectional
bore diameter to pitch (c.p.s), I used this data to analyze three
critical points along the length of the resonating air column. In
this process I made a 2.3' (Key of B-flat) based on a very
well-playing 1.8' (Key of D). The result was quite remarkable. The
2.3' not only played in tune with excellent resonance, but exhibited
many of the timbral characteristics of the instrument from which it
was scaled. All of which is to say that these graphs may have some
practical value and be worth fussing with.


What are these "three critical points along the length of the resonating air column"

where are their locations?   are they a constant?    any info is appreciated....   

I know all about the 1/4, 1/2 and 3/4 points etc.... but i've never heard of this before...

thanks a million....


jacques