Haka.

 

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

From this it is not clear when Haka made the flute. However there was a good connection between Paris and Amsterdam, so it is unlikely that Haka made this flute with a clear renaissance fingering the end of the century. It is not impossible but my guess would be that he tried it somewhere around 1680 or earlier. Establishing the pitch of a particular traverso often is the topic of a debate.  Basically four issues are involved. -first and foremost; what music would have been played on the instrument

-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!

to be continued

[1] The New Langwill Index. Tony Bingham London, ISBN 0-946113-04-1