Let us start with defining what we mean by pitch.
This is the frequency we call a/1. The other notes then follow from the temperament chosen.
In the eighteenth century there was no rigorous standard. To say
that there was no standard at all would be wrong as well because nobody would
play a/1 at 350 Hz or at 495 Hz on a traverso. So there was a range a/1 might be
anywhere between 385 Hz and 485 Hz.
Because in orchestras different instruments play together they had to adapt much more then for instance at present, where a flute is pulled a little bit or a violin is tuned.
Traverso's are therefore found with widely varying pitches and different means to adapt to a certain extent to the optimal pitch they were aimed at. In Tromlitz  a nice description of the different middle pieces, cork screw and foot register can be found.
Basically the flute is lengthened or shortened by using
different length left hand pieces. These have a different bore and finger hole
arrangement. However, it is a bit comparable with changing a dress made for some
body else by only cutting of from the bottom. The waist will be at the wrong
place that way, and an optimal result means changing the whole dress.
Changing the whole dress here simply would mean another flute. Some in between
possibilities were used.
The cork was moved of course. The longer the middle piece the further the cork should go in. Also the foot joint was lengthened. For this purpose a small inset piece register was added to the foot joint, to be pulled out or pushed in as required by the chosen middle piece.
The revival of playing eighteenth century music on original
instruments or copies of such instruments therefore posed a problem.
On the one hand it was discovered that the early
eighteenth century music played so much nicer on lower instruments, as
they had used at the time. On the other hand it was found impossible to go back
to the situation where there were many different pitches.
At that time the practice of playing on new recorders at 440 Hz as well as on lower pitched instruments gave the idea to choose a new low pitch standard at 415 Hz. This is a half tone below the 440 Hz standard. The advantage was thought to be the fact that a harpsichord could be quickly changed from the high to the low pitch by shifting the keyboard over half a tone and than retuning a bit. At present we have a third standard, which is 392 Hz, so a whole tone under 440 Hz.
There are early French instruments at this pitch. We also know that Frederick the Great liked to play at this pitch from the signs of usage on a particular left hand piece of his flute.
Traverso's clearly were made to play best at a certain pitch. To
play slightly lower the left hand piece could be pulled out a little bit, say up
to two or three mm. However it was much better even for that amount to have a
different middle piece. This was quite common. I do not believe that these
different middle pieces were aimed at bridging large pitch gaps. Although up to
six different middle pieces were not uncommon most of them were useless. Only
two or thee middle pieces could be used by a normal player without offending the
The Beukers has three exchange pieces, optimal at 408 Hz and reasonable at 415 Hz. I have changed certain tuning characteristics to make the copies optimal at 415 Hz. But the 408 Hz still is better.
Middle pieces as far apart as half a tone cannot both work well in my opinion. So I will not make a traverso with a middle piece for 415 Hz and 440 Hz, or with a middle piece for 415 Hz and 392 Hz. I think that 408Hz and 415 or 392 Hz and 398 are reasonable, but even there I have chosen to recalculate the instrument completely from 398 to 392 to have it optimal.
More in general one might say that a standard at 392 Hz or 415 Hz is not completely strange because good originals exist at those pitches. However it is my impression that we would have better been served with standards at 400 and 408 because many instruments have the best middle piece at those pitches. I realise full well that, without corroborating evidence this is not a very scientific statement and maybe I will collect this at some point in the future.
The bible on the subject of pitch is the Ph. D. Thesis of Bruce Haynes .
 Bruce Haynes, Pitch standards in the Baroque and Classical periods. Available from UMI services http://www.umi.com ISBN 0-612-08519-08 J.G.Tromlitz, Ausfuehrlicher und gruendlicher Unterricht die Floete zu spielen, Facsimile Frits Knuf Buren 1973, 1985