PETIN M.I.
PETIN - METON calendar
Contents - http://Petin1Mikhail.narod.ru/index.htm
The rules of the PETIN-METON Calendar
The PETIN-METON Calendar contains two basic calendars: a lunar-solar calendar (19-year Meton cycles, see the Table 3 of the Enclosure 1 - http://Petin12Mikhail.narod.ru/index.htm ) and a solar calendar (the annual continuous numbering of days from the Southern solstice date - December, 21, see the Table 1 of the Enclosure 1 - http://Petin10Mikhail.narod.ru/index.htm ).
1. The rules of the lunar-solar calendar
(1) The basic year of Meton cycle (19 years) has 12 lunar months with odd
numbered months with 30 days and even numbered month with 29 days and
a total of 354 days.
(2) Years whose number has a remainder of 3, 4, 7, 11, 12, 15, 19 have
a 13th month of 30 days added to the basic year giving a total of 384 days.
(3) Years whose number has a remainder of 1, 5, 9, 13 have an extra day
added to the 12th month of the basic year giving a total of 355 days.
(4) An exception to rule (3) are variants M1-M4, 1, 2, 3 (see also:
http://Petin48Mikhail.narod.ru/index.htm ,
http://Petin51Mikhail.narod.ru/index.htm ):
- variant M1–M4: Duration of Month 12 is equal to 30 days in 1, 5, 9, 13-th years
of each Meton cycle, but:
- - 29 days - in 57n + 20-th year of each 361-year M2 cycle
in each 741-year M3 cycle of each 1463-year M4 cycle
(where: n - integers from 0 up to 5,
M1 - M4 cycles - Petin cycles);
- variant 1: Duration of Month 12 is equal to 30 days in 1, 5, 9, 13-th years of each Meton cycle, but:
- 29 days - in 57n + 20-th year of each 304-year Hipparh cycle,
(where: n - integers from 0 up to 4);
See also the formula: 52{24[5(L+s+L) +L] +L}=380 380 lunar years
and Table-calendars: http://CalendarPetin-Meton.narod.ru/table-calendars.htm
- variant 2: Duration of Month 12 is equal to 30 days 1, 5, 9, 13-th years of each Meton cycle, but:
- 29 days - in 57n+20 years of each 304-year Hipparh cycle in each 855-year cycle B
(where: n - integers from 0 up to 4);
- 29 days - in 16 250-th year of each 32 490-year cycle C (B, C - Petin cycles).
- variant 3: Duration of Month 12 is equal to 30 days 1, 5, 9, 13-th years of each Meton cycle, but:
- 29 days - in 1-st year of each 57-year cycle A in each 418-year cycle D;
- 30 days - in 400-th year of each 418-year cycle D,
- 30 days - in 837-th year of each 855-year cycle B,
- 29 days - in 16 250-th year of each 32 490-year cycle C (A, B, C, D - Petin cycles).
(5) The Date 01, Month 1, Year 1, Meton cycle 1 begins on December 21, 4694 BCE
Gregorian proleptic calendar (= December 21, -4693 Astronomical Gregorian calendar
with 00:00 UT on 00,00 InD (Independent days) -
http://Petin65Mikhail.narod.ru/index.htm .
(6) The 1st, 8th, 16th and 23rd day of each month is the first day of
a lunar week and is called Monday. Subsequent days of the lunar week are
Tuesday, Wednesday etc. and the 8th day when it exists is a second day off -
Lunaday.
Each 30-day month has 4 weeks:
Date of month
Monday 1 8 16 23
Tuesday 2 9 17 24
Wednesday 3 10 18 25
Thursday 4 11 19 26
Friday 5 12 20 27
Saturday 6 13 21 28
Sunday 7 14 22 29
Lunaday - 15 - 30
Each 29-day month has 4 weeks:
Date of month
Monday 1 8 16 23
Tuesday 2 9 17 24
Wednesday 3 10 18 25
Thursday 4 11 19 26
Friday 5 12 20 27
Saturday 6 13 21 28
Sunday 7 14 22 29
Lunaday - 15 - -
(7) An exception to rule (2) is that year 19 of every 6479th year cycle counting from the beginning
of the calendar (i.e. 19th year of every 341st Meton cycle) has no 13th month of 30 days giving a total
of 354 days instead of 384 days.
It allow to compensate the drift of calendar Meton lunar cycles concerning a calendar solar
cycles in the new Global Calendar.
(8) Lunar year according to the rule (4) is named a LeapM, if the number of days of given lunar
year is equal to 354 instead of 355 days. All other lunar years are named the Simple.
(9) The variants of creation of the PETIN-METON Calendar (for mean
Lunation = 29,53058885 days) is the following:
1) the accuracy is within limits of -1,2040 to +1,6107, if sequence of Meton
cycles is the following:
52{24[5(L+s+L)+L]+L}= 380 380 years,
where:
L = Meton simple = 19 lunar years = 235 lunations = 6940 days,
s = Meton leap = 19 lunar years = 235 lunations = 6939 days.
The misalignment range is 2.81 days.
2) the accuracy is within limits of -1,3616 to +1,4566, if sequence of Meton
cycles is the following:
260{2[6(L+s+L)+L]+L+2[6(L+s+L)+L]}= 380 380 years.
The misalignment range is 2.82 days.
(10) For the short term PETIN-METON Calendar variants of creation calendar
(for mean Lunation = 29,5305885 days) is the following:
1) the accuracy is within limits of -1,1058 to +1,6107, if sequence of Meton
cycles is the following:
24[5(L+s+L)+L] +L = 5 x 1463 = 7315 years,
The misalignment range is 2.72 days.
2) the accuracy is within limits of -1,2634 to +1,4566, if sequence of Meton
cycles is the following:
5{2[6(L+s+L)+L]+L+2[6(L+s+L)+L]}= 5 x 1463 = 7315 years.
The misalignment range is 2.72 days.
2. The rules of the solar calendar
The natural solar cycle (365,242195 days) is submitted in the given calendar by an solar calendar (tropical) as integers (1 … 365 or 366 days).
The duration of simple solar year is equal to 365 days, but (in accordance with a standard Gregorian (Clavius) way of correction) years:
а) multiple of 4, are equal to 365+1 = 366 days;
б) multiple of 100, are equal to 365 days;
в) multiple of 400, are equal to 365+1 = 366 days;
г) multiple of 3200, are equal to 365 days;
д) multiple of 134 400, are equal to 365+1 = 366 days.
The Leap Day (date 366) of a leap-year is established in a new calendar consistently between dates 70 and 71 of a solar calendar (see Table 1 - http://Petin10Mikhail.narod.ru/index.htm and Months 2 - 3 - http://Petin30Mikhail.narod.ru/index.htm ). Thus it is not required to change the date and structure of lunar months.
Table 1 - http://Petin10Mikhail.narod.ru/index.htm - illustrates the transition from a solar calendar
(continuous numbering of dates) to a solar Gregorian calendar. The continuous numbering of dates in the
solar calendar concerning the date of the Southern solstice provides connection of the given Global Calendar
with any former or existing calendars.
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Contents - http://Petin1Mikhail.narod.ru/index.htm
