Anyone's an expert in overtone flutes?

Hi there.
I hope some of you can help me. I know some people who could make an
overtone flute for me (I mean the one with no finger holes). But before I
can tell them what to do, I have to make a few calculations. And this is
what I'm not sure about.
I've been playing this instrument for nearly a year. I always thought that
closing the opposite end of the flute shifts the overtones down by 1/2 of
the fundamental frequency (for example, with the open end there is 200Hz,
400Hz, 600, 800, 1000, etc. so I thought that with the closed end there
should have been 100, 300, 500 700, 900, etc.). That would mean that a
regular part of the overtone series could be achieved by playing the
closed-end and the open-end overtones alternately. But when I compared these
with a software-generated overtone series, I discovered that the closed-end
overtones were a bit higher than they should actually be. I've seen more
overtone flutes and all of them had this problem. On some of them it was a
pitch-shift of about 10 cents, but on others it was 30 cents or even more.
Now I'm a bit confused. Is it really impossible to make such a flute which
makes a regular part of the overtone series if playing the closed-end and
the open-end overtones alternately? And if not, what can be done for at
least minimizing the error?
Thanks to anyone's suggestions.
Petr

--- In tuning@yahoogroups.com, Petr Paøízek <p.parizek@t...> wrote:
> I've been playing this instrument for nearly a year. I always thought tha=
t
> closing the opposite end of the flute shifts the overtones down by 1/2 of=

> the fundamental frequency (for example, with the open end there is 200Hz,=

> 400Hz, 600, 800, 1000, etc. so I thought that with the closed end there
> should have been 100, 300, 500 700, 900, etc.). That would mean that a
> regular part of the overtone series could be achieved by playing the
> closed-end and the open-end overtones alternately.

Ingenious! I never thought of that!

> Is it really impossible to make such a flute which
> makes a regular part of the overtone series if playing the closed-end and=

> the open-end overtones alternately? And if not, what can be done for at
> least minimizing the error?

I read in Bart Hopkin's book (lost now) that open-end pipes have an "effect=
ive length"
longer than the pipe itself. There's a simple equation related to the pipe=
's diameter;
that might explain the varying amounts of detuning. Anyone have this book?=

Suggestion: stop the flute with a shorter stopped tube so that the stopped =
length
matches the open effective length. Getting it to seal could be a problem t=
hough...

Jacob

I use an overtone flute for 'divide by pi', on gigs, etc.

One plays alternate overtones by stopping the end or not, and
changing the breath pressure. It's quite cool and effective, and has
a nice air of ritualistic primitivism about it.

The model I bought is plastic, and made in Sweden. They are very
reasonably priced. Here's the link:

http://www.soundwell.com/multiflute-e.htm

Cheers,
Aaron.