# ONE DAY BEFORE Full Moon Day and Lunar Week

## Introduction

Making use of the fact that a mean Gregorian Month is about one day longer than a lunar month, I came up with the a way of defining an approximate fullmoonday for almost every month, so that the fullmoonday for any month is usually ONE DAY BEFORE last months's.

I have modified the original calendar to make the fulloonday wander less from the actual full moon and to put the other days of the month into a lunar week.

## Rules for the ONE DAY BEFORE Fullmoondays

Each month of the Gregorian calendar is usually given one fullmoonday, which occurs on or close to a full moon.

They are defined by the following rules:

1. The fullmoonday(s) of each month is ONE DAY BEFORE the fullmoonday(s) of the previous month, except for February and March.
2. Any month that has a fullmoonday on the 1st or 2nd also has one 29 days later, provided the month is long enough.
3. February has a fullmoonday TWO DAYS BEFORE the last fullmoonday of January, if it's in range, else it has no fullmoonday.
4. March has its fullmoonday(s) ONE DAY BEFORE the fullmoonday(s) of January, except in an even-numbered non-leap year or the year before a year divisible by 16. Then it the SAME DAY AS the fullmoonday of January.
5. 23 November 1999 is a fullmoonday.
```Fullmoondays 1999-2001

1999      2000    2001
Jan   2,31      21      10
Feb   -         19       8
Mar   2,31      20       9
Apr   1,30      19       8
May   29        18       7
Jun   28        17       6
Jul   27        16       5
Aug   26        15       4
Sep   25        14       3
Oct   24        13       2,31
Nov   23        12       1,30
Dec   22        11       29

NB: 1999 is before 2000 which is divisible by 16.
```

A March fullmoonday occurs either 11 days before or 18 days after, except in an even non-leap year or the year before a year divisible by 16, then it's either 10 days before or 19 days after.

```March Fullmoondays 1985-2016
Year  FMD    Year  FMD
1985   6      2001   9
1986  25      2002  28
1987  14      2003  17
1988   3      2004   6
1989  21      2005  24
1990  11      2006  14
1991  29      2007   3
1992  18      2008  21
1993   7      2009  10
1994  26      2010  29
1995  15      2011  18
1996   4      2012   7
1997  22      2013  25
1998  12      2014  15
1999  2,31    2015   5
2000  20      2016  23
```

Each 16-year cycle delays the fullmoonday 3 days or advances it 26 days, except when there is a dropped leap day. Then is 4 days delay 25 day advance.

## The ONE DAY BEFORE Lunar Week

A lunar week can be defined by counting the days of the month, except any fullmoondays in a 7-day cycle so that the day after any fullmoonday is day 1. If February has no fullmoonday, its first day is day 1.

The 7-day cycle of the lunar week is interrupted by the fullmoonday and at the end of certain months the same day of the lunar week will be repeated on the first day of the next month. This may also happen to the fullmoonday. The two days can then be distinguished by their month. Each day of the lunar week progresses according to rules 1 to 4 as the fullmoonday does.

For the year 2001 they are as follows (note the near-regular progression of the month in the lunar week through the year):

```      JANUARY                    FEBRUARY

FM d1 d2 d3 d4 d5 d6 d7    FM d1 d2 d3 d4 d5 d6 d7
1  2        1  2  3  4  5  6  7
3  4  5  6  7  8  9     8  9 10 11 12 13 14 15
10 11 12 13 14 15 16 17       16 17 18 19 20 21 22
18 19 20 21 22 23 24       23 24 25 26 27 28
25 26 27 28 29 30 31

MARCH                       APRIL

FM d1 d2 d3 d4 d5 d6 d7    FM d1 d2 d3 d4 d5 d6 d7
1        1  2  3  4  5  6  7
2  3  4  5  6  7  8     8  9 10 11 12 13 14 15
9  10 11 12 13 14 15 16       16 17 18 19 20 21 22
17 18 19 20 21 22 23       23 24 25 26 27 28 29
24 25 26 27 28 29 30       30
31

MAY                        JUNE

FM d1 d2 d3 d4 d5 d6 d7    FM d1 d2 d3 d4 d5 d6 d7
1  2  3  4  5  6              1  2  3  4  5
7  8  9 10 11 12 13 14     6  7  8  9 10 11 12 13
15 16 17 18 19 20 21       14 15 16 17 18 19 20
22 23 24 25 26 27 28       21 22 23 24 25 26 27
29 30 31                   28 29 30

JULY                        AUGUST

FM d1 d2 d3 d4 d5 d6 d7    FM d1 d2 d3 d4 d5 d6 d7
1  2  3  4                    1  2  3
5  6  7  8  9 10 11 12     4  5  6  7  8  9 10 11
13 14 15 16 17 18 19       12 13 14 15 16 17 18
20 21 22 23 24 25 26       19 20 21 22 23 24 25
27 28 29 30 31             26 27 28 29 30 31

SEPTEMBER                  OCTOBER

FM d1 d2 d3 d4 d5 d6 d7     FM d1 d2 d3 d4 d5 d6 d7
1  2                           1
3  4  5  6  7  8  9 10      2  3  4  5  6  7  8  9
11 12 13 14 15 16 17        10 11 12 13 14 15 16
18 19 20 21 22 23 24        17 18 19 20 21 22 23
25 26 27 28 29 30           24 25 26 27 28 29 30
31

NOVEMBER                    DECEMBER

FM d1 d2 d3 d4 d5 d6 d7     FM d1 d2 d3 d4 d5 d6 d7
1  2  3  4  5  6  7  8         1  2  3  4  5  6  7
9 10 11 12 13 14 15         8  9 10 11 12 13 14
16 17 18 19 20 21 22        15 16 17 18 19 20 21
23 24 25 26 27 28 29        22 23 24 25 26 27 28
30                          29 30 31
```
If the lunar week were adopted as the working week, the following suggestion could be used: Day 1, day 7 and the fullmoonday would be holidays. If day 2, day 3 or day 4 is repeated, the first day 2 would be a holiday. If day 5 or day 6 is repeated, the last day 6 would be a holiday. With an average of about 49.5 lunar weeks in a year, this would provide about 247.5 working days per year. If this were not enough, one could drop the additional holiday arising from the repeated day to get about 254 working days. This is still less than the 260.8875 working days in a Gregorian 7-day week.

The day of the lunar week is repeated after any month of 31 days, except January and after February in any even numbered year or year before a year divisible by 16. This fact along with a given fullmoonday is sufficient to specify the lunar week.

## Long Term Accuracy

Over 16 years, the fullmoonday migrates back though 5 26/29 months, except when the Gregorian calendar drops a leapday, then it is 5 25/29 months. Over 400 years, this is 147 9/29 months. Over 11,600 years, it's 4272 months.

This effectively intercalates 4272 lunar months adding them to the 139200 solar months, giving 143472 lunar months. This gives a mean lunar month of 29*146097/143472 = 29.530591.. days.

This is more accurate than the Hebrew calendar, but not as accurate as the Gregorian Easter rule. The difference is less than 2 hours per millennium.

The 11600-year cycle of 4272 intercalary months is equivalent to sixteen 725-year cycles of 267 intercalary months, which is used by the old version of ONE DAY BEFORE. The ONE DAY before cycle is also the same as the lunar cycle used by my Anuuary Calendar, which is a solar calendar with near lunar months and a simple rule for tracking the slow drift of moonphase relative to the month.