Dear Walter and Calendar People

I've been thinking about a calendar where every month has 30 days and every day belongs to one of these months and hence a solar calendar has leap months once every 6 or 5 years.

I thought a good cycle for this calendar would be 372 years of 65 leap years, which is equal to 647 Balinese 210-day cycles and about 4601 lunations. The mean year is about 365.241936 days.

The leap year rule could define year Y to be a leap year if and only if the remainder from dividing

65*Y + 186 by 372 is less than 65.

I found that any 23-year period has 4 leap years and hence 8400 days = 40 Balinese 210-day cycles, except for 7 start years in each 372-year cycle (about 1.88%).

The cycle has complexity 5, so a rule defining the leap years in terms of the structure of the sequence of leap years would be complicated.

Karl

Sunday Epsilon February 2019