The Archetypes Calendar denotes days by means of three numbers, year-month-day, where the day number ranges from 1 through 30, the month number ranges from 1 through 13, and the year number is an integer (-2, -1, 0, 1, 2, 3, ...).

Each year has 12 or 13 months, and each month has 29 or 30 days. Most years have 12 months. A year with 13 months is called a long year.

All odd-numbered months have 30 days and all even-numbered months have 29 days, except that in some years the 10th month has 30 days; such a year is called a leap year (by analogy with leap years in the Gregorian or Julian Calendars). A long year may also be a leap year and vice-versa.

ARC years are grouped into consecutive periods of 1,803 years called ARC periods. The first year in an ARC period has position 1, the second has position 2, and so on up to position 1803. The linear numbering of years is related to the cycles of ARC periods, and to the Julian day number system (and thus to empirical time), as follows:

(a) The ARC years 443 through 2245 constitute an ARC period.

(b) The Julian day number of the first day of this ARC period is 897,474.

More generally, an ARC year numbered y occupies position ((y + 1360) mod Y) + 1 in some ARC period, where Y = 1803. For example, ((4300 + 1360) mod 1803) + 1 = 252, so the year 4300 ARC has position 252 in some ARC period.

The rules for when a year is a long year and when a year is a leap year are as follows, where L1 = 664 and L2 = 350:

(i)  A year with position p is a long year if and only if ((p*L1) + (Y-1)/2) mod Y < L1.

(ii)  A year with position p is a leap year if and only if ((p*L2) + (Y-1)/2) mod Y < L2.

More clearly, these rules are:

(i)  A year with position p is a long year if and only if (664*p + 901) mod 1803 < 664.

(ii)  A year with position p is a leap year if and only if (350*p + 901) mod 1803 < 350.

It is possible, but not certain, that rule (ii) might be augmented to specify which even-numbered month (not just the 6th) has an extra day.

For example, the the year 4300 ARC has position 252 (as shown above), so taking p = 252 we find that 664*252 + 901 = 168229, and 168229 mod 1803 = 550, which is less than 664, so ARC year 4300 is a long year. Also 350*252 + 901 = 89101, and 89101 mod 1803 = 754, which is not less than 350, so ARC year 4300 is not a leap year. Thus 4300 ARC has 13 months with alternating 30 and 29 days.

The names of the first seven months are the same as the classical Greek or Roman names of the deities associated with the seven celestial bodies known to the ancients. The names of the last five are those of deities which can plausibly be associated with the three planets discovered within the last three centuries, namely, Uranus, Neptune and Pluto. The following table gives the names of the months and the number of days in each month.

 Month number Month name Number of days Month number Month name Number of days 1 Apollo 30 7 Chronos 30 2 Diana 29 8 Prometheus 29 3 Hermes 30 9 Orpheus 30 4 Aphrodite 29 10 Sophia 29 or 30 5 Ares 30 11 Dionysus 30 6 Zeus 29 12 Demeter 29 In a long year: 13 Persephone 30

A month consists of three consecutive tweeks. The first two always have 10 days, while the third may have 9 or 10 days, for a total of 29 or 30 days in a month.

The days of the tweek are named after the Sun and the planets of the solar system. The order of days in the tweek (corresponding to the distance of the planets from the Sun) is as follows (reading from left to right, that is, Sun Day, Mercury Day, ..., Mars Day, Jupiter Day, ..., Pluto Day):

 Sun Day Mercury Day Venus Day Earth Day Mars Day Jupiter Day Saturn Day Uranus Day Neptune Day Pluto Day

Note that not all tweeks have a Pluto Day, because some final tweeks in a month have only nine days.

This completes the definition of the Archetypes Calendar.

A note on the origin of this calendar is the origin.

## Correlation with the Common Era Calendar

In order to relate the Archetypes Calendar to the Gregorian (or Common Era) Calendar it is sufficient to associate a date in the Archetypes Calendar with a Julian day number. By the definition of the calendar the date 443-1-1 ARC denotes the day with Julian day number 897,474 (which is -2255-02-05 CE). This establishes a one-to-one correspondence between ARC dates and Julian day numbers and so between ARC dates and CE dates. 1-1-1 ARC denotes the day with Julian day number 736,030 (which is -2697-01-30 CE). Here are some examples of date sequences:

```    CE Calendar    ---------- Archetypes Calendar ---------    Julian day number
2010-03-07     4708-01-22  Mercury Day, Apollo 22, 4708        2,455,263
2010-03-08     4708-01-23    Venus Day, Apollo 23, 4708        2,455,264
2010-03-09     4708-01-24    Earth Day, Apollo 24, 4708        2,455,265
2010-03-10     4708-01-25     Mars Day, Apollo 25, 4708        2,455,266
2010-03-11     4708-01-26  Jupiter Day, Apollo 26, 4708        2,455,267
2010-03-12     4708-01-27   Saturn Day, Apollo 27, 4708        2,455,268
2010-03-13     4708-01-28   Uranus Day, Apollo 28, 4708        2,455,269
2010-03-14     4708-01-29  Neptune Day, Apollo 29, 4708        2,455,270
2010-03-15     4708-01-30    Pluto Day, Apollo 30, 4708        2,455,271
2010-03-16     4708-02-01      Sun Day, Diana 1, 4708          2,455,272
2010-03-17     4708-02-02  Mercury Day, Diana 2, 4708          2,455,273
2010-03-18     4708-02-03    Venus Day, Diana 3, 4708          2,455,274
```

```    CE Calendar    ---------- Archetypes Calendar ---------    Julian day number
2011-01-28     4708-12-24     Earth Day, Demeter 24, 4708      2,455,590
2011-01-29     4708-12-25      Mars Day, Demeter 25, 4708      2,455,591
2011-01-30     4708-12-26   Jupiter Day, Demeter 26, 4708      2,455,592
2011-01-31     4708-12-27    Saturn Day, Demeter 27, 4708      2,455,593
2011-02-01     4708-12-28    Uranus Day, Demeter 28, 4708      2,455,594
2011-02-02     4708-12-29   Neptune Day, Demeter 29, 4708      2,455,595
2011-02-03     4709-01-01       Sun Day, Apollo 1, 4709        2,455,596
2011-02-04     4709-01-02   Mercury Day, Apollo 2, 4709        2,455,597
2011-02-05     4709-01-03     Venus Day, Apollo 3, 4709        2,455,598
2011-02-06     4709-01-04     Earth Day, Apollo 4, 4709        2,455,599
2011-02-07     4709-01-05      Mars Day, Apollo 5, 4709        2,455,600
2011-02-08     4709-01-06   Jupiter Day, Apollo 6, 4709        2,455,601
```

```    CE Calendar    ---------- Archetypes Calendar ---------    Julian day number
2012-12-16     4710-12-03     Venus Day, Demeter 3, 4710       2,456,278
2012-12-17     4710-12-04     Earth Day, Demeter 4, 4710       2,456,279
2012-12-18     4710-12-05      Mars Day, Demeter 5, 4710       2,456,280
2012-12-19     4710-12-06   Jupiter Day, Demeter 6, 4710       2,456,281
2012-12-20     4710-12-07    Saturn Day, Demeter 7, 4710       2,456,282
2012-12-21     4710-12-08    Uranus Day, Demeter 8, 4710       2,456,283
2012-12-22     4710-12-09   Neptune Day, Demeter 9, 4710       2,456,284
2012-12-23     4710-12-10     Pluto Day, Demeter 10, 4710      2,456,285
2012-12-24     4710-12-11       Sun Day, Demeter 11, 4710      2,456,286
2012-12-25     4710-12-12   Mercury Day, Demeter 12, 4710      2,456,287
2012-12-26     4710-12-13     Venus Day, Demeter 13, 4710      2,456,288
2012-12-27     4710-12-14     Earth Day, Demeter 14, 4710      2,456,289
```

The dates in the Common Era Calendar of new year's day in the Archetypes Calendar for ARC years 4699 through 4755 are shown below:

 ```ARC year Begins on CE Long? Leap? 4699 2001-01-24 Yes 4700 2002-02-12 Yes 4701 2003-02-02 4702 2004-01-22 Yes 4703 2005-02-09 4704 2006-01-29 Yes 4705 2007-02-17 Yes 4706 2008-02-07 4707 2009-01-26 Yes 4708 2010-02-14 4709 2011-02-03 4710 2012-01-23 Yes Yes 4711 2013-02-11 4712 2014-01-31 Yes 4713 2015-02-19 4714 2016-02-08 4715 2017-01-27 Yes 4716 2018-02-15 Yes 4717 2019-02-05 ``` ```ARC year Begins on CE Long? Leap? 4718 2020-01-25 Yes 4719 2021-02-12 4720 2022-02-01 4721 2023-01-21 Yes Yes 4722 2024-02-10 4723 2025-01-29 Yes 4724 2026-02-17 4725 2027-02-06 4726 2028-01-26 Yes Yes 4727 2029-02-14 4728 2030-02-03 4729 2031-01-23 Yes 4730 2032-02-11 4731 2033-01-30 Yes Yes 4732 2034-02-19 4733 2035-02-08 4734 2036-01-28 Yes 4735 2037-02-15 4736 2038-02-04 Yes ``` ```ARC year Begins on CE Long? Leap? 4737 2039-01-25 Yes 4738 2040-02-13 4739 2041-02-01 4740 2042-01-21 Yes 4741 2043-02-09 Yes 4742 2044-01-30 Yes 4743 2045-02-17 4744 2046-02-06 4745 2047-01-26 Yes 4746 2048-02-14 4747 2049-02-02 Yes 4748 2050-01-23 Yes 4749 2051-02-11 4750 2052-01-31 Yes 4751 2053-02-18 4752 2054-02-07 Yes 4753 2055-01-28 Yes 4754 2056-02-16 4755 2057-02-04 ```

All new year's days in the Archetypes Calendar occur from January 21 to February 21. As is clear from the table above, the month and day numbers of the CE dates of new year's days in the Archetypes Calendar which are exactly 19 years apart are often the same, or if not then they differ by one day. This is an effect of the 19-year Metonic Cycle.

## The Archetypes Calendar

This is an accurate lunisolar calendar with mostly 10-day 'tweeks' (ten-day-weeks) which approximates the Chinese Calendar. It was invented by Peter Meyer in March-April 2010 and slightly revised by him in July 2011.

Each year has 12 or 13 months (13-month years are called 'long'), and each month has 29 or 30 days. All odd-numbered months have 30 days and all even-numbered months have 29 days, except that in some years ('leap years') the 10th month has 30 days. A long year may also be a leap year.

ARC years are grouped into consecutive periods of 1,803 years called ARC periods. The ARC years 443 through 2245 constitute an ARC period. The Julian day number of the first day of this ARC period is 897,474 (which establishes the correlation with the Common Era Calendar).

The rules for long and leap years are:
A year with position p (1,2,3,...) in an ARC period is a long year if and only if (664*p + 901) mod 1803 < 664.
A year with position p is a leap year if and only if (350*p + 901) mod 1803 < 350.

A month consists of three consecutive tweeks. The first two always have 10 days, while the third may have 9 or 10 days, for a total of 29 or 30 days in a month. A complete definition of this calendar, along with names of the months and the weeks, and various properties of the calendar, is at the Archetypes calendar.

This calendar has interesting connections to the Chinese Lunar Calendar . The range of new year's days of both calendars in the Common Era Calendar is the same (namely, January 20 through February 21). It is almost always true that a year in the Archetypes Calendar is a long year if and only if the corresponding Chinese year has 13 months.

The day and month numbers of dates in the two calendars for all 365,618 days over the range 4400-01-01 ARC (= 1702-01-28 CE) through 5400-12-29 ARC (= 2703-02-07 CE) were compared, and it was found that when intercalary months in the Chinese Calendar are ignored 50.78% of the days had the same day and month numbers in both calendars, for example, 79-28-09-24 CHL = 4709-09-24 ARC (= 2011-10-20 CE).

This is interesting because the Chinese Calendar is based on the determination of the exact times of dark moons and solar terms by means of complicated astronomical calculations, whereas the Archetypes Calendar is based on the fairly simple rules given above.