Re: 103-year Cycle

Dear Calendar People

I thought of mentioning the 103-year cycle of 25 leap days again, because the number of days (37620) it has a large number of divisors, so is ideal for a variety of calendars where the number of days in a month or week does not vary, but the number of months or weeks in a year does vary.

37620 = (2^2) * (3^2) * 5 * 11 * 19 leading to the following calendars (amongst others):

103 years normally of 73 five-day weeks, but with five long years of 74 weeks. The intervals between the long years could be 21,20,21,20,21.

103 years normally of 61 six-day weeks, but with 13 short years of 60 weeks. The short years would occur once every 8 years except one that occurs after 7 years.

103 years consisting of 43 short years of 40 nine-day weeks and 60 long years of 41 weeks.

103 years consisting of 54 long years of 37 ten-day weeks and 49 short years of 36 ten-day weeks. There could be five periods of 21 or 19 years in which the two types of year alternate. Only one such period would have 19 years and the other four would have 21 years.

103 years normally of 33 eleven-day week, but with 21 long years of 34 weeks. The long years would  normally occur once every five years.

103 years normally of 20 eighteen-day months, but with 30 long years of 21 months.

103 years normally of 19 nineteen-day months, but with 23 long years of 20 months

103 years normally of 18 twenty-day months, but with 27 long years of 19 months.

103 years normally of 12 thirty-day months, but with 18 long years of 13 months.

103 years normally of 11 thirty-three-day months, but with 7 long years of 12 months.

103 years normally of 10 thirty-six-day months, but with 15 long years of 11 months.

The main drawback is the rather long mean year of about 365.242718 days. It would be interesting to run several of these calendar concurrently,

Also if a lunisolar calendar were to have a basic year of 354 days to which is occasionally added a leap month of 30 days, then the addition of 20 leap days every 103 year would make the calendar very accurate, provided the leap months occur at an accurate rate.

Karl

10(05(10

---

Scanned by iCritical.