Nelson (and all):
Nelson, I just wanted to let you know how much I have enjoyed reading you
website. I even have some
printouts sitting next to (forgive me) the john.
I'm a physicist at NASA, and I just started learning to play. I also have been
trying to make some shakuhachi for fun. As a hobby I have been, on an off
over the last few months,
been developing the mathematics (re-developing probably) of the following
problem: given the desired
set of acoustic impedances for each note in a cylindrically symmetric
bore, and a measure of the "fit" of the actual
impedances to the desired ones, what is the optimal bore shape. In the
most complex cases (probably most cases) the
final optimization calculation would be performed
computationally rather than analytically.
Mathematically this is quite doable, but this begs the question of what
"the desired acoustic impeadances" are.
One way to simplify the specification is to specify the peaks (one
parameter) or the peak and widths (two parameters) of the primary
and desired overtones for each fingering. Many other could be devised.
I assume that the width of the lowest frequency peak would be correlated
with the frequency envelope
of the note, and the peaks and shape of the other peaks would determine the
timbre. Beyond tuning and other quantifiable features let
me state that - to head off the stampede to tell me this, that I *do*
understand the there are many subtile features of the quality of sound
that it might not be able to quantify. Nevertheless their "source" is
right there in the acoustic impeadances.
Does anyone have any thoughts about how they would specify the playing
characteristics of a great shachuhachi.
I'm a complete novice at this, other than having a formal training as a
physicist, but it might even be possible
for me to "translate" or postulate a translation of a more musical notion
of quality (in some cases, and with
a big maybe). There are a number of questions I would then be interested
in exploring such as:
1) Can specific bore shapes of great shakuhachi be roughly explained based
on the criteria
I'm trying to track down?
2) How many shapes can produce the same "sounds" and how close are these
shapes in
"shape space"?
3) How would you optimize a particular perturbation to the bore (somewhat
mathematically equivalent to
a single step in the whole optimization, but may be of use to shakuhachi
makers)?
4) If Monty Levenson can make shakuhachi bores to an exact specification
from and existing bores, what would
a "synthetically" designed bore sound like?
etc. etc.
My apologies for the blasphemous nature of this enquiry, but any thoughts
would be appreciated.
Marko Millonas
At 12:39 PM 9/15/2003 -0600, you wrote:
>To All,
>
>There is a new page of various bits of flute information.
>
>http://www.navaching.com/shaku/bits.html
>
>Nelson
>
>List subscription information is at:
> http://communication.ucsd.edu/shaku/listsub.html
List subscription information is at:
http://communication.ucsd.edu/shaku/listsub.html
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