Hi Blöchl,
Speaking as a harpsichordist myself, with a background in maths and theoretical physics, and consequently a lifelong student of tuning and temperaments, what you say is a little unusual in that a majority of scholars and musicians believe the Well Tempered Clavier was written to establish quite the opposite - that compositions can be made in all the keys and when an appropriate temperament is chosen - not equal temperament, that idea re WTC has been discarded long ago - pieces can be played effectively and well tuned, without offence to the ear, and furthermore the well tempered circulating temperaments of the 18C do indeed show different affekt and colour due to the maths of the tuning and relative tempering amounts of fifths and thirds and how they are distributed.
The title page says:
Das Wohltemperirte Clavier oder Præludia, und Fugen durch alle Tone und
Semitonia, so wohl tertiam majorem oder Ut Re Mi anlangend, als auch
tertiam minorem oder Re Mi Fa betreffend. Zum Nutzen und Gebrauch der
Lehrbegierigen Musicalischen Jugend, als auch derer in diesem studio
schon habil seyenden besonderem Zeitvertreib auffgesetzet und
verfertiget von Johann Sebastian Bach. p. t: Hochfürstlich
Anhalt-Cöthenischen Capel-Meistern und Directore derer Camer Musiquen.
Anno 1722.
The well-tempered Clavier, or Preludes and Fugues through all the tones
and semitones, both as regards the tertiam majorem or Ut Re Mi [i.e.,
major] and tertiam minorem or Re Mi Fa [i.e., minor]. For the profit and
use of the studious musical young, and also for the special diversion
of those who are already skilful in this study, composed and made by
Johann Sebastian Bach, for the time being Capellmeister and Director of
the Chamber-music of the Prince of Anhalt-Cothen. In the year 1722.
While it does not state the intention to show all keys are playable, it most certainly does not indicate any intention to show how horrid G sharp major would sound. In fact, the very title 'Well Tempered' indicates it is a demonstration of what well tempering can do - allow all keys, major and minor, which meantone systems cannot. As to what tuning system JSB was advocating, it is hard to say, but my money lies with the Lehmann solution, a very nice well tempering, whether Bach intended that exact recipe or not.
I have never seen reference on the internet to WTC being intended as a demonstration of how bad certain keys sound. Every historical tuning treatise was an effort to increase and improve the number of usable keys over time. So I beg to respectfully differ with your claim.
I do note also that when this topic came up I immediately thought your context, then unstated, must have been 18C practice, predating ET.
This is probably off topic by now, and we should move to a tuning list!
By the way, have a look at the Digital Bach Archive and see how Bach writes the key signatures in the WTC. It's interesting. Also note that almost all the pieces have the right hand predominantly in the soprano clef, not treble. There is only one modern edition that dares to do this, as far as I know!
When I get time I intend to make my own scholarly edition of the WTC with the proper original clefs, using lilypond (to come back on topic!)
Andrew