OK, so let's assume that Gregorios's reform paralleled that of Gregory
down to the exact date of the switch.  *Here*, that was Friday, 1582
October 5  OS = October 15  NS.  *There*, that would have been 1586
Υπερβερεταίο 11/21.  Presumably they would have tried to get the
Easter tables lined up with the actual full moon after the following
spring equinox (1583/1587).  According to the Gregorian epact table,
1583 has an epact of 7.

That 7 represents the age of the moon on 1 January, which means that
the nominal new moon was a week earlier on Christmas 1582, which
corresponds to 2 Αυδυναίο 1587 *there*.  So the WHATL epact for the
year 1587 would be the age of the moon on Christmas Eve *here*, which
was 29 (wraps on the new moon at 30=0).

To verify, I applied the Alexandrian method manually.  Christmas Eve
in 1582 Gregorian was a Friday, so the first Κυριακό of the new WHATL
year would be the 3rd of Αυδυναίο, making the Dominican(*) Letter C.
Sure enough, using the Alexandrian computus on a WHATL calendar with
an Epact of 29 and Dominican Letter of C yields the same date for the
Paschal full moon (6 April = 12 Ξανθικό) and therefore Easter (10
April = 16 Ξανθικό).

So now that I can do it manually I just need to derive the correct
offsets to adjust for the general formula and then I can determine
Easter for any WHATL year programmatically (and do analyses, such as
find out exactly how often it coincides with Gregorian Easter).

(*) So what's "Dominican" in TAKE? :)

Mark J. Reed <[log in to unmask]>