
Let me first give the Haka information from
the Langwill index [1]

-what were temperaments used at the time
-what do we call the lowest note
-where do we put the cork
-establish the pitch of a/1.
The Haka flute in the Ehrenfeld
collection is a good case to study.
The music played on it is difficult to establish it
seems because the traverso was not much mentioned at the time. It may be
reasonable to think that recorder music was also played on it. There are air de
cours that are allegedly (Kate Clark, Nancy Hadden) played on the traverso.
However, if we take the recorder music as a starting point and that was in
fashion, then flutes in f, c and d would be logical.
The cork in my opinion should always be put
at the position where the octave and the second octave of the lowest note are
exact.
If we do this for the Haka and were to call
the lowest note a d it would be about 370 Hz. If on the other hand we were to
call the lowest note a c it would be 415 Hz = 370*2**1/6 for b it would be 440.
This is a nice coincidence because it means that the Haka is usable with our
present standards!
We may wonder why Haka made the flute
conical. The following reasoning may be interesting in this connection. I do not
think that wanting many different new properties for the flute at the same time
is logical. Therefore we may wonder what the main new aspect is. I think that
the e flat in the second octave with the help of the key and seventh hole is a
logical choice. This seventh hole is very small. So if we drill this hole in
about the same spot in a flute that was wider at that spot the hole would have
to be even smaller. But then the hole would not function any more. Therefore the
single reason for making the flute conical may have been to have a narrower bore
at the spot of the e flat hole!!!
Moreover, about two centuries later Boehm
discovered that he did not need conicity if he could place the finger holes
where he wanted with a size he wanted, more or less of course. This
points in the same direction. In between there have been very conical flutes
with quite large seventh hole nevertheless!
[1] The New Langwill Index. Tony Bingham London, ISBN 0-946113-04-1

