30-day month calendar with leap months

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30-day month calendar with leap months

k.palmen@btinternet.com
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
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Re: 30-day month calendar with leap months

Walter J Ziobro

Dear Karl et al

An interesting cycle Such a cycle of 135870 days would also have 3882 35 day periods (which the Indonesians call Wetonans) and two such Cycles of 271740 days would have 9705 28 day periods

Walter Ziobro




On Sunday, March 3, 2019 K PALMEN <[hidden email]> wrote:

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