Mark Lindley has suggested that the origin of mollified meantone in France may well have been the misinterpretation Mersenne’s instructions for setting regular 1/4 comma meantone. Because of the vagueness as to whether the terms “forte” and “foible” (strong and weak) apply to the note (strong = sharp and weak = flat) or the interval (strong = wide and weak = narrow), it is possible to read his instructions in such a way that the descending fifths F – Bb and Bb – Eb are tempered too wide by 1/4 comma rather than too narrow. This confusion was repeated in the same manner in the instructions of Jean Denis, and finally officially codified in Chaumont’s 1695 recipe where these intervals/notes are labeled “foible ou forte” (take your pick!). As true as this appears to be, the practical result does little to mollify the problems of regular 1/4 comma meantone. The wide fifth is still rather wide for tolerable use. D# is gained at the expense of Eb, the major thirds B – D# and Eb – G becoming equally-poor (they are Pythagorean “thirds”); F# – Bb is reduced slightly in it harshness (compare it to the bad meantone “thirds” C# – F and G# – C), though at the cost of a markedly impure Bb – D (almost as bad as in Equal Temperament); and finally, the bad “thirds” C# – F and G# – C are not improved at all. Thus it would appear that the gains hardly outweigh the loses. Nonetheless, it does seem to have opened the door for experimentation in this direction, setting the stage for the slightly more sophisticated solutions of Rameau and D’Alembert.
Disclaimer: the attribution of comma fractions to the tempered fifths is done by an automatic table look-up function. If the exact value is not in the table, the system grabs the nearest lower value. Naturally, my table does not have all possible fractions of both commas for both narrow and wide fifths. Therefore, with all modified meantone temperaments, for those fifths which “close the circle”, i.e. fill in the gap left by the departure from pure meantone logic, the amount of tempering has been somewhat arbitrarily chosen, exactly as one does when tuning an instrument, although in this case, working with decimal values for the proportion of the fifth. Therefore, the final size may not represent any fraction of any given comma, and there is no guarantee that the amount of tempering indicated as a comma fraction in the graphic is precise. The value indicated in cents, however, is derived from the proportion, and is therefore completely trustworthy.