Remains only to explain the periods of 15 and 18 years, in the first and second part of Ayil Meshulash.
Observe that between 5366 and 5501 were exactly 9 periods of 15 years, whereas 28 periods of 15 years are until 5786, the Tikkun of 420. The count to 288, 16*18, from 5501 to 5789, thus started exactly in sync, kind of like stimulated emission. This was in fact the Tikkun. It appears that Ramchal accomplished it, and the GR"A became aware of it. The two counts stay exactly in sync, every 90 years. The last time the Tikkun was felt was in 5771.
Surmising, two parallel counts exist since 5501, representing the heavenly powers of Moshiach ben David, and of Moshiach ben Yosef.