Re: Date and time on Cindu: yearly update

OK, so here's what I have as the character of the calendar, with the
clarifications from our discussion here.

* A year consists of 16 months.  The first day of the first month is
in the nominal northward equinox (i.e. the vernal equinox in the
northern hemisphere, the autumn equinox in the southern hemisphere).

* Each month consists of four seven-day weeks plus a blank day called
Cinjurak, which falls between week days 14 and 15 of the month. That
makes a total of 29 days per month and 464 days per (common) year.

* Three out of every 19 years is a leap year containing an extra day.
The extra day, which is also blank, falls in the vicinity of one of
the solstices or equinoxes, progressing forward one season every leap
year.

* If the leap day is near an equinox, it is inserted before the first
day of that month (month 1 or 9).  This means that in 3 out of every
76 years the first day of a calendar year is not day 1 of month 1, but
a leap day preceding it.

* If the leap day is near a solstice, it is inserted after Cinjurak of
that month (month 5 or 13).

* The leap cycle is based around years 700, 706, and 713 being leap,
with the leap day falling in the Spring in 700.

If you agree with all of that, then the rest falls out of the math:

* To determine if a year is leap and, if so, the season of the leap
day, take the remainder of the New Count after dividing by 76 ( = 4 ×
19, the number of seasons times the number of years in a leap cycle).
If you get 3, 29, or 54, it's a leap year whose leap day falls in the
Autumn; if 10, 35, or 60, then Winter; Spring if 16, 41, or 67; and
Summer if 22, 48, or 73. Any other number means it's not a leap year.

So, quick test of the arithmetic:

700 ÷ 76 is 9 with a remainder of 16, so it's a Spring leap day.
706 ÷ 76 is 9 with a remainder of 22, so it's a Summer leap day.
713 ÷ 76 is 9 with a remainder of 29, so it's an Autumn leap day.

etc.

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