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: `

-  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 