Similarly, the for the Vallotti temperament
Also this is clearly an attempt to equalise the character of the different keys. Let us now look at a mean tone temperament. Mean tone temperament is actually an indication for a class of temperaments.
The next chart shows the mean tone temperament by Pietro Aaron from 1523.
This looks a bit like the traverso. Only g♯ is strangely low and b♭ very high, but this seems to be the case also e.g. in pure intervals etc. I general there are very large deviations here.
The mean tone temperament of John Holden of 1770 is found in the next chart.
Again a"no go".
In "Le temperament musical" from Dominique Devie , It is shown that the Rameau temperament of 1726 on bes for a particular flute is pretty precisely right. With thanks to Mr.Pernin who pointed this reference out to me. It seems to me that this is correct.
This is a slightly different from . However comparing this with the eight originals and also with what I know about many more originals we see a striking resemblance.
-d slightly high, this is not like the originals where usually d1 is a bit low. However, d1 may be just low in our usage at 415. In the first half eighteenth century the optimum joint may have been more between 398 and 408! With a fixed foot this would explain the difference.
-e♭ slightly high
-e just a bit low, not significant
-f clearly high
-f♯ sharp clearly low
-g a bit high
-g♯ almost equal temperament, this is something to discuss, because the relatively high g♯ found on many copies may not be desirable (it is not necessary) and due to copying of warp or other artefacts of time
-a practically equal temperament (choice as reference)
-b low which can easily be done, but should we(?), on the eight originals it varies
-c slightly high
-c♯ slightly low
This to me is rather representative for original flute tuning. However let me stress again as an old schoolmaster that I have no real information about the meaning of the clearly present differences between the eight originals and the Rameau tuning shown above.
However the presence of many of the peculiarities of the tuning of the traverso is clear. The Rameau tuning is chosen for keyboard. We often think that the peculiarities of the traverso are forced upon us by the construction of the instrument. The peculiarities of the traverso most likely were there before 1726. So, did Rameau choose his tuning to suite the ensemble playing with the flute? Or did the traverso makers choose the peculiarities and could they more or less at will have chosen others?
These questions need a lot more consideration than I am able to give them in this short space.
note: the foregoing does not imply that I am in any way advocating the Rameau tuning for normal usage. The normal practice of using a more equilibrated tuning on the keyboard and using the possibility of the player of the traverso to adapt to this, as is common practice, is of course quite sensible. However, in the meantime there is some reliable evidence that in practice this works beautifully as well!
Jane Bowers, Mozart and the flute, Early music, Feb. 1992
J.J.H.R Ribock, Bemerkungen ueber die floete, 1782, facsimile,Frits Knuf, Buren, Gelderland, 1980
Adam Carse, Musical wind instruments, Da Capo Press, New York,1965
Owen H.J. Jorgensen, Tuning, Michigan University press, 1991, ANSI 239.48-1984
Margaret Neuhaus, The complete baroque flute fingering book, Flute studio, 1986 (originally, now
Otto Steinkopf, Zur Akustik der Blasinstrumente, Ed. Moeck,nr 5029
G.J v.d. Heijde, Effects applicable to tuning et. FOMRHI Comm. No 503
 Dominique Devie, Le temperament musical, Societee de musicologie de Languedoc, Beziers, 1990
remark: Knuf no longer exists. They have been taken over by some German company. As soon as I know the details I will give them here.