# Annuary Calendar

## Introduction

Some time ago I invented a solar calendar in which the months are approximately lunar.

In this calendar a year has 12 months alternating between 29 and 30 days. To these is added an intercalary month of 30 days once every 32 ordinary months before a month of 29 days. The calendar as such has an 8 year cycle of 2922 days, giving an average year of 365.25 day (same as Julian Calendar). The month runs about 1 1/2 days short of a lunar month each 8 year cycle (i.e. 1/2 day short per intercalary month). Because every 33rd month is intercalary, I call it the IC33 calendar.

The year can be made more accurate by shortening one intercalary month every 128 years to 29 days (Mean Tropical Year) [IC33-128] or 3 intercalary months every 400 years [IC33-400] (Gregorian year).

## Tracking the Drift of the Moonphase

Around August 1998 discovered a simple way of tracking the slow drift of the lunar month against this calendar month, which works for any variety of year. For each month I define a lunar index that changes infrequently. It can take any value from 1.0 to 29.5 in whole or half numbers. If it's a whole number, the new moon is reckoned to be on that day of the month, else you round down for 29 day months and up for 30 day months.

The lunar index changes exactly halfway between two intercalary months (to effect the 17th month after) and immediately before and after a 29 day intercalary month. The change is an increase of 0.5, except in the case were the lunar index is already 29.5. Then it changes to 1.0 and the first month with 1.0 (which has 29 days) has no new moon day, because the previous month has one at the end. So the lunar index cycles through 58 values before returning to its original value and one month misses a new moon day in each such cycle.

## The Annuary Calendar Itself

I chose to use a Gregorian-like IC33 calendar [1C33-400] and start the era 2800 years and two days earlier than the Gregorian AD/CE, so to fit in with the Gregorian calendar and that the lunar index for years 0 and 1 is 1.0 . The intercalary months are shortened to 29 days in years ending in 99 and years ending in 00, but not divisible by 400. I call this particular calendar The Annuary Calendar after the name of its first month.

## The Months

The months are named as follows with intercalary months in brackets:

```Annuary,   Bebry,    Carch,    Daipril,  (Eapril),
Fay,       Gyne,     Huly,     Igust,    (Jawgust),
Keptember, Luctober, Myvember, Nicember, (Ocember).
```

### The Month Start Dates

Except between the end of a 29 day intercalary month and a dropped leap-day, all months start on the following Gregorian dates:

```Annuary Calendar Month Start dates
(position corresponding to name as shown above)

Remainder 0:  (e.g. 4800 begins 30 Dec 1999)

30 Dec   28 Jan   27 Feb   27 Mar
26 Apr   25 May   24 Jun   23 Jul
22 Aug   20 Sep   20 Oct   18 Nov   18 Dec

Remainder 1:  (e.g. 4801 begins 17 Jan 2001)

17 Jan   15 Feb   17 Mar   15 Apr
15 May   13 Jun   13 Jul   11 Aug
10 Sep   09 Oct   08 Nov   07 Dec

Remainder 2:  (e.g. 4802 begins 6 Jan 2002)

06 Jan   04 Feb   06 Mar   04 Apr
04 May   02 Jun   02 Jul   31 Jul
30 Aug   28 Sep   28 Oct   26 Nov

Remainder 3:  (e.g. 4803 begins 26 Dec 2002).

26 Dec   24 Jan   23 Feb   24 Mar
23 Apr   22 May   21 Jun   20 Jul   19 Aug
18 Sep   17 Oct   16 Nov   15 Dec

Remainder 4:  (e.g. 4804 begins 14 Jan 2004)

14 Jan   12 Feb   13 Mar   11 Apr
11 May   09 Jun   09 Jul   07 Aug
06 Sep   05 Oct   04 Nov   03 Dec

Remainder 5:  (e.g. 4805 begins 2 Jan 2005)

02 Jan   31 Jan   02 Mar   31 Mar
30 Apr   29 May   28 Jun   27 Jul
26 Aug   24 Sep   24 Oct   22 Nov

Remainder 6:  (e.g. 4806 begins 22 Dec 2005)

22 Dec   20 Jan   19 Feb   20 Mar  19 Apr
19 May   17 Jun   17 Jul   15 Aug
14 Sep   13 Oct   12 Nov   11 Dec

Remainder 7:  (e.g. 4807 begins 10 Jan 2007)

10 Jan   08 Feb   10 Mar   08 Apr
08 May   06 Jun   06 Jul   04 Aug
03 Sep   02 Oct   01 Nov   30 Nov
```

## The New Moon Days of Months

The lunar index for Annuary 4805 (2 Jan 2005) to Igust 4807 (2 Sept 2007) inclusive is 10.0 so all those months have a new moon day on the 10th. After that for the next 33 months, the lunar index is 10.5 so the new moon day is the 10th day of the 29 day months and the 11th day of the 30 day months.

The Lunar indices and new moon days for years 4789 to 4820 (1989-01-02 to 2021-01-01 AD) inclusive are:

```Annuary Range   Gregorian Range           Index 29dm 30dm
4789A to 4791I  1989-01-02 to 1991-09-02   7.0    7    7
4791K to 4794D  1991-09-03 to 1994-05-03   7.5    7    8
4794F to 4796N  1994-05-04 to 1997-01-01   8.0    8    8
4797A to 4799I  1997-01-02 to 1999-09-02   8.5    8    9
4799K to 4802D  1999-09-03 to 2002-05-03   9.0    9    9
4802F to 4804N  2002-05-04 to 2005-01-01   9.5    9   10
4805A to 4807I  2005-01-02 to 2007-09-02  10.0   10   10
4807K to 4810D  2007-09-03 to 2010-05-03  10.5   10   11
4810F to 4812N  2010-05-04 to 2013-01-01  11.0   11   11
4813A to 4815I  2013-01-02 to 2015-09-02  11.5   11   12
4815K to 4818D  2015-09-03 to 2018-05-03  12.0   12   12
4818F to 4820N  2018-05-04 to 2021-01-01  12.5   12   13
```
The dark moon (astronomical new moon) will usually occur on the new moon day or the previous day. For example, the eclipse of 11 August 1999 occurred on 8 Igust 4799 (day before new moon day) and the eclipse of 29 March 2006 occurred on 10 Daipril 4806 (a new moon day). Most months in my Yerm calendar begin on the new moon day, but when the lunar index is higher, more (but still a minority) will begin the next day.

I've also defined a lunar index for the full moon, which progresses in the same way as the lunar index for the new moon and is either 14 greater or 15 less than the new moon lunar index.

## The Solar Days of Months

Because a year may have either 12 or 13 months, a given month may move around up to a month relative to the seasons. To enable a more accurate scheduling relative to the seasons, each non-intercalary month has a solarday.

The month after an intercalary month has its first day as a solar day, then each month has its solar day one day later. Because there are 32 rather than 30 months between each successive pair of intercalary months, there are two occasions when this progression of the solar day is halted. These are the nineth month after the intercalary month (solar day halts at 8) and the twenty fifth month after the intercalary month (solar day halts at 23).

Over the 8-year cycle the solar day of each month is:

```
Month      Year of 8-year Cycle
0  1  2  3  4  5  6  7

Annuary    20  1 12 23  5 16 27  8
Bebry      21  2 13 24  6 17 28  9
Carch      22  3 14 25  7 18 29 10
Daipril    23  4 15 26  8 19 30 11
Eapril                       XX
Fay        23  5 16 27  8 20  1 12
Gyne       24  6 17 28  9 21  2 13
Huly       25  7 18 29 10 22  3 14
Igust      26  8 19 30 11 23  4 15
Jawgust             XX
Keptember  27  8 20  1 12 23  5 16
Luctober   28  9 21  2 13 24  6 17
Myvember   29 10 22  3 14 25  7 18
Nicember   30 11 23  4 15 26  8 19
Ocember    XX
```
NB: The intercalary months (marked `XX`) have no solar day.

The solar days are not only useful for tracking the seasons, but also for reckoning the insertion intercalary months (after a solar day on the 30th). Also the halfway point when the lunar index is changes is when the solar day changes from 15 to 16.

## Long Term Accuracy

The new and full moon days repeat once every 11600 years, giving a mean period of 29.530591 days. The 11600 years is the absolute cycle of this ONE DAY BEFORE calendar, the 725-years cycle is relative to the Gregorian calendar.

## The Seven Day Week

The 33 month cycle of this calendar has one day more than a whole number of weeks, except when the intercalary month is shortened, then it has a whole number of weeks. So 1 Annuary 4805 was Sunday 2 January 2006 and 33 months later 1 Keptember 4807 will be Monday 3 September 2007.