Dear Ed., I have never assumed that. What we know is that since his very early keyboard works Bach composed for a perfectly circular temperament (thus excluding both meantone and French modified variants), and also that the way he used accidentals and thirds in the WTC appears carefully crafted for the features of a significantly unequal temperament. At this point, there are indeed variants, Werckmeister III, Vallotti, whatever, and they are susceptible of infinite subtle variations, but we are always within the same “type” of Wohltemperierte thing: the major thirds curves are always similar.
PS: Paraphrasing Ed’s sentence, “in my professional musical life (and also as a professional tuner”), spanning six decades with significant time devoted to theoretical and practical work on historical temperaments, I have also tuned in many ways. Back to our discussion on the appropriate tuning for some works of Bach, we could keep discussing details on end: AFAIK no scholar has ever assumed that Bach tuned always in the same way. We just try to deduce information from the historical evidence. This places very clear boundaries on which temperament variations are or are not historical, and are or are not nice sounding for the repertoire.
I have yet another observation. The idea that one can use different temperaments at different times is blatantly modern. Just to give an example: for centuries in the Middle Ages they tuned Pythagorean: pure fifths, no variations at all! Then throughout most of the 16th and 17th centuries they all tuned meantone: most of them 1/4-comma (in spite of largely academic discussions about comma-fraction), most of them G#-Eb wolf: again no variations! The idea that it was good to have a choice between different temperaments largely arises with Werckmeister and his successful broadcasting of the German circular temperaments. And even so, it is a distinct possibility that quite a few German musicians selected a single temperament by Werckmeister and tuned to it for decades: no source known to me allows to think otherwise.
In the particular case of J.S. Bach, the mathematical analysis performed by Barnes (and re-scrutinised by at least two other modern researchers) about the distribution of major thirds in the different tonalities in WTC vol. I and II, yields a surprising result (for details see my U.T. book): twenty years having elapsed between vol. I and vol. II, Bach’s frequency of use of the different 12 major thirds is remarkably similar. This strongly suggests (although it does not prove) that he was using the same temperament.
Jägermeister is not a joke, but Ketil Haugsand’s long-proposed temperament. I doubt it has any more affiliation with German alcohol manufacture than the baroque composer Heinichen.
If I wrote at some point that CPE Bach was identical to Equal, I stand corrected!
In at least two published works of mine, the U.T: book and my rebuttal to Lehman’s review, I list four “Almost-Equal” temperaments, thus clearly NOT Equal: one by Neidhardt (surely the one you mention), CPE Bach, a 19th c. Italian proposal by a De Lorenzi and my own version of the Almost-Equal. The full detail is explained on p. 150 of my U.T: book, complete with a chart.
My newest article about this (2021-22) was published in November. It is the first piece in the current issue of the “Bach” journal (Riemenschneider). Pick up a free copy of it here: Bradley Lehman's Home Page
There is a lot of theory and history in there. Among other things, it shows why critics of the 2005 paper missed the point of the argument, and it shows why Vallotti has some rough spots in the Goldberg Variations.
Members may be interested to know that all the articles in the Riemenschneider Bach Journal are available on JSTOR if you have access. Many large state libraries can provide free access to JSTOR. With the exception that JSTOR applies an IP window of various time periods to journals and the RBJ is only avilable up to 2021 at the moment, but the other articles by @bpl are available.