– when taken as C# - ought to be in harmony as a fifth with the G# where one stopped before. The final fifths will be a little too wide, like the thirds. But the harshness will be tolerable if the tuning across the octaves is done properly, and besides, these fifths are so situated that they are rarely used." Among the notable points of this description: 1: there is a possible misprint or similar thoughtless mistake, or else an instruction to cover some of the ground twice, in that the third-stage stopping point, D flat, would have been tuned already as C# before the G#, and so the expected stopping point of the third stage might more naturally be E flat/D#, to be checked against the G#. So D flat (re bemol) might have been a misprint etc. for E flat (mi bemol). 2: There might have been no need for the user to actually widen any of the fifths, if only the ones between CGDAE had been narrowed: things should have worked out if all the others had just been left pure. This highlights also that the instructions are not quite specific on what to do about the fifths E->B and B->F#: to narrow them like the earlier ones? (which would necessitate some widening further along the chain), or to leave them pure? (in which case all the rest could be pure too). And then, how to distribute the amounts of any widening of the remaining fifths? 3: According to the degree of any widening used, some of the thirds would actually be made worse than necessary. This point seems possibly to have escaped the originators and users of the method described here, as of other methods involving widening fifths. Perhaps it is possible to be too precise about this kind of thing. Maybe the intent of an 18th-century description, such as the one referenced and discussed above, was that complete precision was not sought at all, rather to give a guideline for completion in practice, according to the taste and ear of the individual musician. The two scales, both referred to as temperament ordinaire by Huygens and by Rousseau/Encyclopedie, have in common the degree of tempering applied to the fifths CGDAE. The difference between them is that the 'wolf' error arising in the chain of fifths is either left whole in only one of those remaining fifths