**
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