Mersenne semitone

In the Wikipedia article on Mersenne, we learn that he suggested a
value of (2/(3-sqrt(2))^(1/4) for the semitone; this can also be written
((6+2sqrt(2))/7)^(1/4) and is about 100.44 cents, which seems to be
flirting with equal temperament, suggesting a fifth of size
((24+8sqrt(2))/7)^(1/4), which is about 1/14-comma. Can someone tell
me how he proposed to use this semitone to produce a tuning of twelve
notes?